Valid HTML 4.0! Valid CSS!
%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "5.284",
%%%     date            = "20 February 2024",
%%%     time            = "16:15:36 MST",
%%%     filename        = "elefunt.bib",
%%%     address         = "University of Utah
%%%                        Department of Mathematics, 110 LCB
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone       = "+1 801 581 5254",
%%%     FAX             = "+1 801 581 4148",
%%%     URL             = "http://waww.math.utah.edu/~beebe",
%%%     checksum        = "01453 80537 357544 3625705",
%%%     email           = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at computer.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "BibTeX; bibliography; convergence
%%%                        acceleration; elementary functions; sequence
%%%                        acceleration; special functions",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography of publications about
%%%                        the computation of the elementary functions
%%%                        (square root, exponential, logarithm,
%%%                        trigonometric, inverse trigonometric,
%%%                        hyperbolic, inverse hyperbolic, ...), and
%%%                        some selected special functions (Bessel,
%%%                        cumulative normal distribution, elliptic
%%%                        integral, exponential integral, Gamma,
%%%                        inverse normal distribution, log-Gamma, psi,
%%%                        ...), in computer programming languages.
%%%                        Additional references to articles, books, and
%%%                        conference proceedings provide more
%%%                        mathematical background.
%%%
%%%                        At version 5.274 (21 October 2023), about a
%%%                        dozen references have been added on
%%%                        polynomial evaluation: see the remarks, and
%%%                        references, in entry Todd:1955:MWN, and the
%%%                        keyword phrase ``number of multiplications to
%%%                        evaluate a polynomial'' in other entries.
%%%
%%%                        At version 5.284, the year coverage looked
%%%                        like this:
%%%
%%%                             1819 (   1)    1888 (   0)    1957 (  11)
%%%                             1820 (   0)    1889 (   0)    1958 (   9)
%%%                             1821 (   0)    1890 (   0)    1959 (  20)
%%%                             1822 (   0)    1891 (   0)    1960 (  17)
%%%                             1823 (   0)    1892 (   1)    1961 (  28)
%%%                             1824 (   0)    1893 (   0)    1962 (  23)
%%%                             1825 (   0)    1894 (   0)    1963 (  37)
%%%                             1826 (   0)    1895 (   0)    1964 (  48)
%%%                             1827 (   0)    1896 (   0)    1965 (  37)
%%%                             1828 (   0)    1897 (   1)    1966 (  27)
%%%                             1829 (   0)    1898 (   0)    1967 (  35)
%%%                             1830 (   0)    1899 (   0)    1968 (  35)
%%%                             1831 (   0)    1900 (   0)    1969 (  37)
%%%                             1832 (   0)    1901 (   0)    1970 (  40)
%%%                             1833 (   0)    1902 (   0)    1971 (  33)
%%%                             1834 (   0)    1903 (   0)    1972 (  34)
%%%                             1835 (   0)    1904 (   0)    1973 (  33)
%%%                             1836 (   0)    1905 (   0)    1974 (  27)
%%%                             1837 (   0)    1906 (   0)    1975 (  38)
%%%                             1838 (   0)    1907 (   0)    1976 (  39)
%%%                             1839 (   0)    1908 (   0)    1977 (  42)
%%%                             1840 (   0)    1909 (   0)    1978 (  36)
%%%                             1841 (   0)    1910 (   0)    1979 (  38)
%%%                             1842 (   0)    1911 (   0)    1980 (  33)
%%%                             1843 (   1)    1912 (   0)    1981 (  52)
%%%                             1844 (   0)    1913 (   0)    1982 (  50)
%%%                             1845 (   0)    1914 (   1)    1983 (  43)
%%%                             1846 (   0)    1915 (   0)    1984 (  51)
%%%                             1847 (   0)    1916 (   0)    1985 (  38)
%%%                             1848 (   0)    1917 (   0)    1986 (  38)
%%%                             1849 (   0)    1918 (   0)    1987 (  37)
%%%                             1850 (   0)    1919 (   1)    1988 (  57)
%%%                             1851 (   0)    1920 (   0)    1989 (  97)
%%%                             1852 (   0)    1921 (   2)    1990 (  51)
%%%                             1853 (   0)    1922 (   0)    1991 (  57)
%%%                             1854 (   0)    1923 (   0)    1992 (  46)
%%%                             1855 (   0)    1924 (   1)    1993 (  52)
%%%                             1856 (   0)    1925 (   1)    1994 (  60)
%%%                             1857 (   0)    1926 (   1)    1995 (  51)
%%%                             1858 (   0)    1927 (   0)    1996 (  43)
%%%                             1859 (   0)    1928 (   0)    1997 (  40)
%%%                             1860 (   0)    1929 (   0)    1998 (  39)
%%%                             1861 (   0)    1930 (   1)    1999 (  58)
%%%                             1862 (   0)    1931 (   1)    2000 (  42)
%%%                             1863 (   0)    1932 (   0)    2001 (  44)
%%%                             1864 (   0)    1933 (   0)    2002 (  33)
%%%                             1865 (   0)    1934 (   2)    2003 (  39)
%%%                             1866 (   0)    1935 (   1)    2004 (  45)
%%%                             1867 (   0)    1936 (   0)    2005 (  35)
%%%                             1868 (   0)    1937 (   3)    2006 (  27)
%%%                             1869 (   0)    1938 (   1)    2007 (  36)
%%%                             1870 (   0)    1939 (   0)    2008 (  34)
%%%                             1871 (   0)    1940 (   1)    2009 (  37)
%%%                             1872 (   0)    1941 (   2)    2010 (  32)
%%%                             1873 (   0)    1942 (   2)    2011 (  46)
%%%                             1874 (   0)    1943 (   3)    2012 (  30)
%%%                             1875 (   0)    1944 (   3)    2013 (  30)
%%%                             1876 (   0)    1945 (   3)    2014 (  41)
%%%                             1877 (   0)    1946 (   1)    2015 (  42)
%%%                             1878 (   0)    1947 (   0)    2016 (  45)
%%%                             1879 (   0)    1948 (   4)    2017 (  21)
%%%                             1880 (   0)    1949 (   6)    2018 (  30)
%%%                             1881 (   0)    1950 (   3)    2019 (  21)
%%%                             1882 (   0)    1951 (   7)    2020 (  26)
%%%                             1883 (   0)    1952 (   3)    2021 (  14)
%%%                             1884 (   0)    1953 (   7)    2022 (  12)
%%%                             1885 (   0)    1954 (  10)    2023 (   5)
%%%                             1886 (   0)    1955 (  14)    2024 (   5)
%%%                             1887 (   0)    1956 (   8)
%%%
%%%                             Article:       1850
%%%                             Book:           219
%%%                             InBook:           2
%%%                             InCollection:    56
%%%                             InProceedings:  222
%%%                             Manual:           2
%%%                             MastersThesis:    4
%%%                             Misc:            24
%%%                             Periodical:       1
%%%                             PhdThesis:       20
%%%                             Proceedings:     96
%%%                             TechReport:      87
%%%                             Unpublished:      3
%%%
%%%                             Total entries: 2586
%%%
%%%                        At version 4.00, this bibliography was
%%%                        significantly extended by merging in the 262
%%%                        entries from the bibliography given in entry
%%%                        Fullerton:1980:BEM.  That document was not
%%%                        available electronically on the Internet, and
%%%                        the original bib/refer bibliography data from
%%%                        which the report was derived may have been
%%%                        lost with the death of its author, so a
%%%                        printed copy of the report was scanned and
%%%                        converted to searchable text.  Its entries
%%%                        were then compared with the previous contents
%%%                        of this file, and the extensive collections
%%%                        in the TeX User Group and BibNet Project
%%%                        archives.  All of the publications that
%%%                        Fullerton covered are marked with a citedby
%%%                        keyword, and his notes are included in remark
%%%                        keyword values prefixed by his name.
%%%
%%%                        At version 5.00 of 1-Dec-2011, numerous
%%%                        references on hypergeometric functions and on
%%%                        convergence acceleration of sequences were
%%%                        added.  Particularly with special functions,
%%%                        many standard series expansions converge too
%%%                        slowly to be useful, but acceleration
%%%                        techniques can sometimes provide a dramatic
%%%                        improvement, making such sums numerically
%%%                        practical.  The new entries in that area all
%%%                        contain the phrase `convergence acceleration'
%%%                        in their keywords values.  See entry
%%%                        Willis:2012:AGH for a good recent survey of
%%%                        both areas.
%%%
%%%                        This bibliography has been collected from
%%%                        bibliographies in the author's personal
%%%                        files, from the OCLC WorldCat and
%%%                        Contents1st databases, from the American
%%%                        Mathematical Society MathSciNet database,
%%%                        from the ACM Computing Archive CD-ROM,
%%%                        and from the computer science bibliography
%%%                        collection on ftp.ira.uka.de in
%%%                        /pub/bibliography to which many people of
%%%                        have contributed.
%%%
%%%                        Numerous errors in the sources noted above
%%%                        have been corrected.  Spelling has been
%%%                        verified with the UNIX spell and GNU ispell
%%%                        programs using the exception dictionary
%%%                        stored in the companion file with extension
%%%                        .sok.
%%%
%%%                        BibTeX citation tags are uniformly chosen as
%%%                        name:year:abbrev, where name is the family
%%%                        name of the first author or editor, year is a
%%%                        4-digit number, and abbrev is a 3-letter
%%%                        condensation of important title
%%%                        words. Citation tags were automatically
%%%                        generated by software developed for the
%%%                        BibNet Project.
%%%
%%%                        This bibliography is sorted by year, and
%%%                        within each year, by author and title key,
%%%                        using ``bibsort -byyear''.  Cross-referenced
%%%                        proceedings entries appear at the end,
%%%                        because of a restriction in the current
%%%                        BibTeX.
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================
%%% A delimited macro \toenglish ... \endtoenglish is NECESSARY here.
%%% The more conventional undelimited form \toenglish{...} has braces
%%% that prevent BibTeX's downcasing operation, and the alternate form
%%% {\toenglish{...}} is considered a `special character' by BibTeX,
%%% and all of {...} gets downcased.  We avoid the name \english to
%%% prevent conflicts with language options in packages like Babel.
%%%
%%% To suppress output of English translations of non-English titles,
%%% use
%%%     "\def \toenglish #1\endtoenglish{\unskip}"
%%% instead.
%%%
%%% Alternative Cyrillic definitions are supplied in the event that
%%% cyracc.def is not loaded.
@Preamble{"\input bibnames.sty"
  # "\def \toenglish #1\endtoenglish{[{\em English:} #1\unskip]} "
  # "\ifx \undefined \booktitle    \def \booktitle      #1{{{\em #1}}}          \fi"
  # "\ifx \undefined \cyr          \let \cyr = \relax                           \fi"
  # "\ifx \undefined \cdprime      \def \cdprime          {''}                  \fi"
  # "\ifx \undefined \k            \let \k = \c                                 \fi"
  # "\ifx \undefined \mathrm       \def \mathrm         #1{{\rm #1}}            \fi"
  # "\ifx \undefined \operatorname \def \operatorname   #1{{\rm #1}}            \fi"
  # "\ifx \undefined \pkg          \def \pkg            #1{{{\tt #1}}}          \fi"
  # "\ifx \undefined \TM           \def \TM               {${}^{\sc TM}$}       \fi"
  # "\hyphenation{ Rich-ard }"
}

%%% ====================================================================
%%% Acknowledgement abbreviations:
@String{ack-nhfb = "Nelson H. F. Beebe,
                    University of Utah,
                    Department of Mathematics, 110 LCB,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    Tel: +1 801 581 5254,
                    FAX: +1 801 581 4148,
                    e-mail: \path|beebe@math.utah.edu|,
                            \path|beebe@acm.org|,
                            \path|beebe@computer.org| (Internet),
                    URL: \path|https://www.math.utah.edu/~beebe/|"}

@String{ack-mv =  "Matti Vuorinen,
                   Department of Mathematics and Statistics,
                   University of Turku,
                   Vesilinnantie 5,
                   20014 Turku, Finland,
                   e-mail: \path|vuorinen@utu.fi|,
                   URL: \path|http://users.utu.fi/vuorinen/|"}

@String{ack-nj =  "Norbert Juffa,
                  2445 Mission College Blvd.,
                  Santa Clara, CA 95054,
                  USA,
                  e-mail: \path|norbert@@iit.com|"}

@String{ack-rfb = "Ronald F. Boisvert,
                  Applied and Computational Mathematics Division,
                  National Institute of Standards and Technology,
                  Gaithersburg, MD 20899, USA,
                  Tel: +1 301 975 3812,
                  e-mail: \path=boisvert@cam.nist.gov="}

%%% ====================================================================
%%% Institution abbreviations:
@String{inst-ANL                = "Argonne National Laboratory"}
@String{inst-ANL:adr            = "9700 South Cass Avenue, Argonne, IL
                                  60439-4801, USA"}

@String{inst-ATT-BELL           = "AT\&T Bell Laboratories"}
@String{inst-ATT-BELL:adr       = "Murray Hill, NJ, USA"}

@String{inst-BERKELEY-CS        = "Department of Computer Science, University
                                  of California"}
@String{inst-BERKELEY-CS:adr    = "Berkeley, CA, USA"}

@String{inst-CECM               = "Centre for Experimental and Constructive
                                  Mathematics (CECM) at Simon Fraser
                                  University (SFU)"}
@String{inst-CECM:adr           = "Burnaby, BC V5A 1S6, Canada"}

@String{inst-CPAM-UCB           = "Center for Pure and Applied Mathematics,
                                  University of California, Berkeley"}
@String{inst-CPAM-UCB:adr       = "Berkeley, CA, USA"}

@String{inst-CSC                = "Center for Scientific Computing,
                                  Department of Mathematics, University of
                                  Utah"}
@String{inst-CSC:adr            = "Salt Lake City, UT 84112, USA"}

@String{inst-INST-ADV-STUDY     = "Institute for Advanced Study"}
@String{inst-INST-ADV-STUDY:adr = "Princeton, NJ, USA"}

@String{inst-IPTC               = "{Institut f{\"u}r Physikalische und
                                  Theoretische Chemie}"}
@String{inst-IPTC:adr           = "{Universit{\"a}t Regensburg, D-93040
                                  Regensburg}"}

@String{inst-LASL               = "Los Alamos Scientific Laboratory"}
@String{inst-LASL:adr           = "Los Alamos, NM, USA"}

@String{inst-LORIA-INRIA-LORRAINE = "LORIA/INRIA Lorraine"}

@String{inst-LORIA-INRIA-LORRAINE:adr = "B{\^a}timent A, Technop{\^o}le de
                                  Nancy-Brabois, 615 rue du jardin
                                  botanique, F-54602
                                  Villers-l{\`e}s-Nancy Cedex, France"}

@String{inst-MATH-NPS           = "Department of Mathematics, Naval Postgraduate
                                  School"}
@String{inst-MATH-NPS:adr       = "Monterey CA 93943, USA"}

@String{inst-PRINCETON          = "Princeton University"}
@String{inst-PRINCETON:adr      = "Princeton, NJ, USA"}

@String{inst-STAN-CS            = "Stanford University, Department of
                                  Computer Science"}
@String{inst-STAN-CS:adr        = "Stanford, CA, USA"}

%%% ====================================================================
%%% Journal abbreviations:
@String{j-ACM-COMM-COMP-ALGEBRA = "ACM Communications in Computer Algebra"}

@String{j-ACTA-INFO             = "Acta Informatica"}

@String{j-ACTA-MATH             = "Acta Mathematica"}

@String{j-ACTA-NUMERICA         = "Acta Numerica"}

@String{j-ADV-APPL-MATH         = "Advances in Applied Mathematics"}

@String{j-ADV-COMPUT-MATH       = "Advances in Computational Mathematics"}

@String{j-ADV-QUANTUM-CHEM      = "Advances in Quantum Chemistry"}

@String{j-AM-J-MATH             = "American Journal of Mathematics"}

@String{j-AMER-MATH-MONTHLY     = "American Mathematical Monthly"}

@String{j-AMER-STAT             = "The American Statistician"}

@String{j-ANAL-APPL             = "Analysis and Applications (Singapore)"}

@String{j-ANN-APPL-STAT         = "Annals of Applied Statistics"}

@String{j-ANN-INST-STAT-MATH-TOKYO = "Annals of the Institute of
                                  Statistical Mathematics"}

@String{j-ANN-MATH-ARTIF-INTELL = "Annals of Mathematics and Artificial
                                  Intelligence"}

@String{j-ANN-STAT              = "Annals of Statistics"}

@String{j-ANZIAM-J              = "The ANZIAM Journal"}

@String{j-APPL-COMPUT-HARMON-ANAL = "Applied and Computational Harmonic
                                  Analysis. Time-Frequency and
                                  Time-Scale Analysis, Wavelets,
                                  Numerical Algorithms, and
                                  Applications"}

@String{j-APPL-MATH-COMP        = "Applied Mathematics and Computation"}

@String{j-APPL-MATH-LETT        = "Applied Mathematics Letters"}

@String{j-APPL-MATH-SCI-RUSE    = "Applied Mathematical Sciences (Ruse)"}

@String{j-APPL-NUM-MATH         = "Applied Numerical Mathematics: Transactions
                                  of IMACS"}

@String{j-APPL-OPTICS           = "Applied Optics"}

@String{j-APPL-STAT             = "Applied Statistics"}

@String{j-ARCH-HIST-EXACT-SCI   = "Archive for History of Exact Sciences"}

@String{j-ARCH-RAT-MECH-ANAL    = "Archive for Rational Mechanics and Analysis"}

@String{j-ASTROPHYS-SPACE-SCI   = "Astrophysics and Space Science"}

@String{j-ATMOS-SCI-LETT        = "Atmospheric Science Letters"}

@String{j-AUST-J-STAT           = "Australian Journal of Statistics"}

@String{j-AUSTRALIAN-J-PHYS     = "Australian Journal of Physics"}

@String{j-AUTOMATICA            = "Automatica: the journal of IFAC, the
                                  International Federation of Automatic
                                  Control"}

@String{j-BELL-SYST-TECH-J      = "The Bell System Technical Journal"}

@String{j-BIOMETRIKA            = "Biometrika"}

@String{j-BIT                   = "BIT (Nordisk tidskrift for
                                  informationsbehandling)"}

@String{j-BIT-NUM-MATH          = "BIT Numerical Mathematics"}

@String{j-BRITISH-J-PHILOS-SCI  = "British Journal for the Philosophy of
                                  Science"}

@String{j-BULL-AMS              = "Bulletin of the American Mathematical
                                  Society"}

@String{j-C-R-ACAD-BULGARE-SCI  = "Comptes rendus de l'Acad{\'e}mie bulgare
                                  des sciences"}

@String{j-CACM                  = "Communications of the ACM"}

@String{j-CALCOLO               = "Calcolo"}

@String{j-CAN-J-MATH            = "Canadian Journal of Mathematics =
                                   Journal canadien de
                                   math{\'e}matiques"}

@String{j-CAN-MATH-BULL         = "Bulletin canadien de
                                  math\-{\'e}\-mat\-iques = Canadian
                                  Mathematical Bulletin"}

@String{j-CCCUJ                 = "C/C++ Users Journal"}

@String{j-CELEST-MECH-DYN-ASTR  = "Celestial Mechanics and Dynamical Astronomy"}

@String{j-CENTAURUS             = "Centaurus: An International Journal of the
                                  History of Science and its Cultural Aspects"}

@String{j-COLLEGE-MATH-J        = "College Mathematics Journal"}

@String{j-COMM-PURE-APPL-MATH   = "Communications on Pure and Applied
                                  Mathematics (New York)"}

@String{j-COMMUN-STAT-SIMUL-COMPUT = "Communications in Statistics: Simulation
                                  and Computation"}

@String{j-COMMUN-STAT-THEORY-METH = "Communications in Statistics: Theory and
                                  Methods"}

@String{j-COMP-ARCH-NEWS = "ACM SIGARCH Computer Architecture News"}

@String{j-COMP-J                = "The Computer Journal"}

@String{j-COMP-PHYS-COMM        = "Computer Physics Communications"}

@String{j-COMPUT-APPL-MATH      = "Journal of Computational and Applied
                                  Mathematics"}

@String{j-COMPUT-MATH-APPL      = "Computers and Mathematics with Applications"}

@String{j-COMPUT-MATH-MATH-PHYS = "Computational Mathematics and Mathematical
                                  Physics"}

@String{j-COMPUT-PHYS           = "Computers in Physics"}

@String{j-COMPUT-PHYS-REP       = "Computer Physics Reports"}

@String{j-COMPUT-SCI-ENG        = "Computing in Science and Engineering"}

@String{j-COMPUT-STAT-DATA-ANAL = "Computational Statistics \& Data Analysis"}

@String{j-COMPUTER              = "Computer"}

@String{j-COMPUTING             = "Computing: Archiv fur informatik und
                                  numerik"}

@String{j-COMPUTING-SUPPLEMENTUM = "Computing. Supplementum"}

@String{j-CONST-APPROX          = "Constructive Approximation"}

@String{j-CYBER                 = "Cybernetics"}

@String{j-DDJ                   = "Dr. Dobb's Journal of Software Tools"}

@String{j-DESIGNS-CODES-CRYPTOGR = "Designs, Codes, and Cryptography"}

@String{j-DOKL-AKAD-NAUK        = "Doklady Akademii nauk SSSR"}

@String{j-EDN                   = "EDN"}

@String{j-ELECT-LETTERS         = "Electronics Letters"}

@String{j-ELECT-NOTES-THEOR-COMP-SCI = "Electronic Notes in Theoretical
                                  Computer Science"}

@String{j-ELECTRON-COMMUN-JPN   = "Electronics and communications in Japan"}

@String{j-ELECTRON-TRANS-NUMER-ANAL = "Electronic Transactions on Numerical
                                Analysis (ETNA)"}

@String{j-ELECTRONIC-DESIGN     = "Electronic Design"}

@String{j-ELECTRONICS           = "Electronics"}

@String{j-ELECTRONIK            = "Elektronik"}

@String{j-ELEKTRONIKER          = "Elektroniker (Switzerland)"}

@String{j-ELEK-RECHENANLAGEN    = "Elektronische Rechenanlagen"}

@String{j-EMBED-SYS-PROG        = "Embedded Systems Programming"}

@String{j-ENTROPY               = "Entropy"}

@String{j-EXP-MATH              = "Experimental mathematics"}

@String{j-FIB-QUART             = "Fibonacci Quarterly"}

@String{j-FORM-METHODS-SYST-DES = "Formal Methods in System Design"}

@String{j-HEWLETT-PACKARD-J     = "Hew\-lett-Pack\-ard Journal: technical
                                  information from the laboratories of
                                  Hew\-lett-Pack\-ard Company"}

@String{j-HIST-MATH             = "Historia Mathematica"}

@String{j-HIST-SCI-2            = "Historia Scientiarum. Second Series.
                                  International Journal of the History
                                  of Science Society of Japan"}

@String{j-IBM-JRD               = "IBM Journal of Research and Development"}

@String{j-IBM-SYS-J             = "IBM Systems Journal"}

@String{j-IBM-TDB               = "IBM Technical Disclosure Bulletin"}

@String{j-IEE-PROC-COMPUT-DIGIT-TECH = "IEE Proceedings. Computers and Digital Techniques"}

@String{j-IEEE-CGA              = "IEEE Computer Graphics and Applications"}

@String{j-IEEE-COMMUN-LET       = "IEEE Communications Letters"}

@String{j-IEEE-J-SOLID-STATE-CIRCUITS = "IEEE Journal of Solid-State Circuits"}

@String{j-IEEE-MICRO            = "IEEE Micro"}

@String{j-IEEE-SIGNAL-PROCESS-LETT = "IEEE Signal Processing Letters"}

@String{j-IEEE-SPECTRUM         = "IEEE Spectrum"}

@String{j-IEEE-TRANS-CIRCUITS-SYST-2 = "IEEE Transactions on Circuits and
                                  Systems. 2, Analog and Digital Signal
                                  Processing"}

@String{j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS = "IEEE Transactions on
                                  Circuits and Systems II: Express Briefs"}

@String{j-IEEE-TRANS-COMM       = "IEEE Transactions on Communications"}

@String{j-IEEE-TRANS-COMPUT     = "IEEE Transactions on Computers"}

@String{j-IEEE-TRANS-ELEC-COMPUT = "IEEE Transactions on Electronic Computers"}

@String{j-IEEE-TRANS-EMERG-TOP-COMPUT = "IEEE Transactions on Emerging Topics in
                                  Computing"}

@String{j-IEEE-TRANS-INF-THEORY = "IEEE Transactions on Information Theory"}

@String{j-IEEE-TRANS-MICROWAVE-THEORY-TECH = "IEEE Transactions on Microwave
                                  Theory and Techniques"}

@String{j-IEEE-TRANS-PAR-DIST-SYS = "IEEE Transactions on Parallel and
                                    Distributed Systems"}

@String{j-IEEE-TRANS-SIG-PROC   = "IEEE Transactions on Signal Processing"}

@String{j-IEEE-TRANS-VLSI-SYST  = "IEEE Transactions on Very Large Scale
                                  Integration (VLSI) Systems"}

@String{j-IEEE-TRANS-VEH-TECHNOL = "IEEE Transactions on Vehicular Technology"}

@String{j-IEEE-TRANS-WIREL-COMMUN = "IEEE Transactions on Wireless
                                  Communications"}

@String{j-IJQC                  = "International Journal of Quantum Chemistry"}

@String{j-IJSAHPC               = "The International Journal of Supercomputer
                                  Applications and High Performance Computing"}

@String{j-IMA-J-NUMER-ANAL      = "IMA Journal of Numerical Analysis"}

@String{j-INFO-PROC-LETT        = "Information Processing Letters"}

@String{j-INT-J-COMPUT-INF-SCI  = "International Journal of Computer and
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%%% ====================================================================
%%% Bibliography entries, sorted by year and citation label:
@Article{Horner:1819:XNM,
  author =       "William George Horner",
  title =        "{XXI}. {A} new method of solving numerical equations
                 of all orders, by continuous approximation",
  journal =      j-PHILOS-TRANS-R-SOC-LOND,
  volume =       "109",
  pages =        "308--335",
  year =         "1819",
  CODEN =        "PTRSAV",
  DOI =          "https://doi.org/10.1098/rstl.1819.0023",
  ISSN =         "0370-2316 (print), 2053-9207 (electronic)",
  bibdate =      "Sat Oct 21 12:27:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://royalsocietypublishing.org/doi/pdf/10.1098/rstl.1819.0023",
  acknowledgement = ack-nhfb,
  fjournal =     "Philosophical Transactions of the Royal Society of
                 London",
  journal-URL =  "http://rsta.royalsocietypublishing.org/",
  keywords =     "Horner's nested form; number of multiplications to
                 evaluate a polynomial",
  read =         "1 July 1819",
  remark-1 =     "Communicated by Davies Gilbert, Esq. F.R.S.",
  remark-2 =     "On page 310 of this paper, Horner gives the steps of
                 the nested form as a chain of fused multiply-add
                 operations, and credits this idea to Joseph-Louis
                 Lagrange (1736--1813) in his 1813 book
                 \booktitl{\'e}{Theorie des fonctions analytiques}.",
  remark-3 =     "Knuth \cite[p. 486]{Knuth:1998:SA} gives this paper as
                 the reference for Horner's nested form, but also
                 reports that Isaac Newton used it in unpublished notes
                 150 years earlier, and that it was employed by the
                 Chinese in the 13th century CE.",
}

@Article{Lovelace:1843:SAE,
  author =       "Ada Augusta Lovelace",
  title =        "Sketch of the {Analytical Engine}",
  journal =      "Scientific Memoirs",
  volume =       "3",
  number =       "??",
  pages =        "666--731",
  month =        "????",
  year =         "1843",
  bibdate =      "Sun Aug 18 09:31:28 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprinted in \cite{Lovelace:1989:SAE}.",
  acknowledgement = ack-nhfb,
  keywords =     "Bernoulli numbers",
  remark =       "This paper contains what some view as possibly the
                 world's first computer program, a recipe for computing
                 Bernoulli numbers on Charles Babbage's Analytical
                 Engine, which was not successfully constructed until
                 more than a century after their deaths, in 1852 and
                 1871, respectively. It is not, however, the world's
                 first computational algorithm: that credit is given to
                 Euclid's procedure for fast computation of the greatest
                 common denominator, about 300 BCE, but possibly known a
                 few hundred years earlier.",
}

@Book{Greenhill:1892:AEF,
  author =       "Alfred George Greenhill",
  title =        "The Applications of Elliptic Functions",
  publisher =    pub-MACMILLAN,
  address =      pub-MACMILLAN:adr,
  pages =        "xi + 357",
  year =         "1892",
  bibdate =      "Wed Mar 15 08:21:33 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1847--1927",
  remark =       "Reprinted in \cite{Greenhill:1959:AEF}.",
}

@Article{Dawson:1897:NV,
  author =       "H. G. Dawson",
  title =        "On the Numerical Value of $\int_0^h e^{x^2} \, dx$",
  journal =      j-PROC-LONDON-MATH-SOC-1,
  volume =       "s1-29",
  number =       "1",
  pages =        "519--522",
  month =        nov,
  year =         "1897",
  CODEN =        "PLMTAL",
  DOI =          "https://doi.org/10.1112/plms/s1-29.1.519",
  ISSN =         "0024-6115 (print), 1460-244X (electronic)",
  ISSN-L =       "0024-6115",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  fjournal =     "Proceedings of the London Mathematical Society. First Series",
  journal-URL =  "http://plms.oxfordjournals.org/content/by/year",
  remark =       "This paper is the origin of Dawson's integral and the
                 function dawson(x).",
}

@Book{Kennelly:1914:TCH,
  author =       "Arthur E. (Arthur Edwin) Kennelly",
  title =        "Tables of Complex Hyperbolic and Circular Functions",
  publisher =    pub-HARVARD,
  address =      pub-HARVARD:adr,
  pages =        "iii + 212",
  year =         "1914",
  LCCN =         "QA342 .K45",
  bibdate =      "Sat Apr 1 14:49:41 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1861--1939",
  subject =      "Exponential functions",
}

@Book{Pairman:1919:TDT,
  author =       "Eleanor Pairman",
  title =        "Tables of the Digamma and Trigamma Functions",
  volume =       "I",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "9 + 11",
  year =         "1919",
  LCCN =         "QA47 .T7 no.1",
  bibdate =      "Sat Mar 25 16:17:54 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Tracts for computers",
  acknowledgement = ack-nhfb,
  remark =       "Edited by Karl Pearson. According to
                 \cite{Davis:1935:EPF}, the author coined the phrase
                 `polygamma function' in this booklet. English
                 dictionaries usually do not include the word
                 `polygamma'.",
  subject =      "Gamma functions",
}

@Book{Kennelly:1921:TCH,
  author =       "Arthur Edwin Kennelly",
  title =        "Tables of Complex Hyperbolic and Circular Functions",
  publisher =    pub-HARVARD,
  address =      pub-HARVARD:adr,
  pages =        "iii + 240",
  year =         "1921",
  LCCN =         "QA342 .K45 1921",
  bibdate =      "Sat Apr 1 14:49:41 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1861--",
  subject =      "Functions, Exponential",
}

@Article{King:1921:SNF,
  author =       "Louis Vessot King",
  title =        "On Some New Formulae for the Numerical Calculation of
                 the Mutual Induction of Coaxial Circles",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS,
  volume =       "100",
  number =       "702",
  pages =        "60--66",
  day =          "4",
  month =        oct,
  year =         "1921",
  DOI =          "https://doi.org/10.1098/rspa.1921.0070",
  ISSN =         "0950-1207 (print), 2053-9150 (electronic)",
  bibdate =      "Wed Feb 03 09:07:10 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  note =         "This is the first known publication of the AGM method,
                 discovered by the author in 1913, for computing
                 Jacobian elliptic functions. See also
                 \cite{King:1924:DNC,King:2007:DNC}.",
  URL =          "http://www.jstor.org/stable/93861",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society of London. Series A,
                 Containing Papers of a Mathematical and Physical
                 Character",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
}

@Book{King:1924:DNC,
  author =       "Louis Vessot King",
  title =        "On the Direct Numerical Calculation of Elliptic
                 Functions and Integrals",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "viii + 42",
  year =         "1924",
  LCCN =         "QA343",
  bibdate =      "Wed Feb 03 08:53:04 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  remark =       "The AGM method for Jacobian elliptic functions was
                 discovered by this book's author at McGill University
                 in 1913, first published in \cite{King:1921:SNF}, and
                 then in this monograph (reprinted in
                 \cite{King:2007:DNC}).",
}

@Article{Ritt:1925:EFT,
  author =       "J. F. Ritt",
  title =        "Elementary functions and their inverses",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "27",
  number =       "1",
  pages =        "68--90",
  year =         "1925",
  CODEN =        "TAMTAM",
  DOI =          "https://doi.org/10.1090/S0002-9947-1925-1501299-9",
  ISSN =         "0002-9947 (print), 1088-6850 (electronic)",
  ISSN-L =       "0002-9947",
  MRclass =      "30A05 (33B10)",
  MRnumber =     "MR1501299",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/journals/tran/1925-027-01/S0002-9947-1925-1501299-9/",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/tran/",
}

@Article{Dederick:1926:QDDc,
  author =       "L. S. Dederick",
  title =        "Questions and Discussions: Discussions: a Modified
                 Method for Cube Roots and Fifth Roots",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "33",
  number =       "9",
  pages =        "469--472",
  month =        nov,
  year =         "1926",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:38:12 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2299613",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Mahler:1930:NUG,
  author =       "K. Mahler",
  title =        "{{\"U}ber die Nullstellen der unvollstaendigen
                 Gammafunktionen}. ({German}) [{On} the zeros of the
                 incomplete gamma-functions]",
  journal =      j-REND-CIRC-MAT,
  volume =       "54",
  number =       "??",
  pages =        "1--41",
  month =        "????",
  year =         "1930",
  CODEN =        "RCMMAR",
  ISSN =         "0009-725X (print), 1973-4409 (electronic)",
  ISSN-L =       "0009-725X",
  bibdate =      "Sat Feb 18 14:57:12 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://carma.newcastle.edu.au/mahler/collected.html;
                 https://carma.newcastle.edu.au/mahler/docs/002.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Rendiconti del Circolo matematico di Palermo",
  language =     "German",
  remark =       "Based on doctoral dissertation, Frankfurt, Germany
                 (1927).",
}

@Book{Hobson:1931:TSE,
  author =       "Ernest William Hobson",
  title =        "The Theory of Spherical and Ellipsoidal Harmonics",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xi + 500",
  year =         "1931",
  LCCN =         "QA406 .H7",
  bibdate =      "Sat Apr 1 14:40:56 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1856--1933",
  subject =      "Spherical harmonics; Lam\'e's functions",
}

@Article{Kalbfell:1934:QDN,
  author =       "D. C. Kalbfell",
  title =        "Questions, Discussions and Notes: On a Method for
                 Calculating Square Roots",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "41",
  number =       "8",
  pages =        "504--506",
  month =        oct,
  year =         "1934",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:37:31 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2300417",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Book{McLachlan:1934:BFE,
  author =       "N. W. (Norman William) McLachlan",
  title =        "{Bessel} Functions for Engineers",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "xi + 1 + 192",
  year =         "1934",
  LCCN =         "QA408 .M3",
  bibdate =      "Sat Apr 1 14:44:36 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "The Oxford engineering science series",
  acknowledgement = ack-nhfb,
  author-dates = "1888--",
  subject =      "Bessel functions",
}

@Article{Davis:1935:EPF,
  author =       "H. T. Davis",
  title =        "An extension to polygamma functions of a theorem of
                 {Gauss}",
  journal =      j-BULL-AMS,
  volume =       "41",
  number =       "4",
  pages =        "243--248",
  month =        apr,
  year =         "1935",
  CODEN =        "BAMOAD",
  DOI =          "https://doi.org/10.1090/s0002-9904-1935-06055-0",
  ISSN =         "0002-9904 (print), 1936-881X (electronic)",
  ISSN-L =       "0002-9904",
  bibdate =      "Sat Mar 25 16:16:08 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/bull/all_issues.html",
  remark =       "A footnote on the first page says ``The name polygamma
                 is suggested by the paper, \booktitle{Tables of the
                 Digamma and Trigamma Functions}, by Eleanor Pairman,
                 Tracts for Computers, No. 1, 1919''
                 \cite{Pairman:1919:TDT}.",
}

@Article{Airey:1937:CFA,
  author =       "J. R. Airey",
  title =        "The ``converging factor'' in asymptotic series and the
                 calculation of {Bessel}, {Laguerre} and other
                 functions",
  journal =      j-PHILOS-MAG,
  volume =       "24",
  number =       "162",
  pages =        "521--552",
  month =        "????",
  year =         "1937",
  CODEN =        "PHMAA4",
  DOI =          "https://doi.org/10.1080/14786443708565133",
  ISSN =         "0031-8086",
  ISSN-L =       "0031-8086",
  bibdate =      "Thu Dec 01 14:26:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Philosophical Magazine",
  journal-URL =  "http://www.tandfonline.com/loi/tphm19",
}

@Article{Escott:1937:QDN,
  author =       "E. B. Escott",
  title =        "Questions, Discussions, and Notes: Rapid Method for
                 Extracting a Square Root",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "44",
  number =       "10",
  pages =        "644--646",
  month =        dec,
  year =         "1937",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:38:44 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2301484",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Ostrowski:1937:KAN,
  author =       "A. M. Ostrowski",
  title =        "{{\"U}ber die Konvergenz und die
                 Abr{\"u}ndungsfestigkeit des Newtonschen Verfahren}.
                 ({German}) [{On} the convergence and rounding strength
                 of {Newton}'s method]",
  journal =      "Rec. Math.",
  volume =       "2",
  number =       "??",
  pages =        "1073--1098",
  month =        "????",
  year =         "1937",
  bibdate =      "Mon Oct 23 14:58:35 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Ostrowski:1938:NMA,
  author =       "A. M. Ostrowski",
  title =        "On {Newton}'s method of approximation",
  journal =      "British Association for the Advancement of Science",
  volume =       "??",
  number =       "??",
  pages =        "392--??",
  month =        "????",
  year =         "1938",
  acknowledgement = ack-nhfb,
  bibdate =      "Mon Oct 23 14:57:22 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
}

@Book{Emde:1940:TEF,
  author =       "Fritz Emde",
  title =        "{Tafeln Elementarer Funktionen} ({German}) [Tables of
                 Elementary Functions]",
  publisher =    "B. T. Teubner",
  address =      "Leipzig, Germany and Berlin, Germany",
  pages =        "xii + 181",
  year =         "1940",
  LCCN =         "QA47 .E5",
  bibdate =      "Fri Jun 11 12:34:09 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://lccn.loc.gov/45006177",
  acknowledgement = ack-nhfb,
  author-dates = "1873--1951",
  language =     "German",
}

@Article{Stoner:1941:FEF,
  author =       "Paul Matthew Stoner",
  title =        "Fitting the Exponential Function and the {Gompertz}
                 Function by the Method of Least Squares",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "36",
  number =       "216",
  pages =        "515--518",
  month =        dec,
  year =         "1941",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:24 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314095;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
  URL =          "http://www.jstor.org/stable/2278959",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Book{Stratton:1941:ECS,
  author =       "Julius Adams Stratton and Philip M. (Philip McCord)
                 Morse and Lan Jen Chu and Reina Albagli Hutner",
  title =        "Elliptic cylinder and spheroidal wave functions,
                 including tables of separation constants and
                 coefficients",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xii + 127",
  year =         "1941",
  LCCN =         "QC174.2 .S78",
  bibdate =      "Sat Apr 1 14:32:29 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1901--1994",
  remark =       "A publication of the Technology Press, Massachusetts
                 Institute of Technology.",
  subject =      "Wave mechanics; Mathematics; Tables",
}

@PhdThesis{Dopper:1942:AOV,
  author =       "Herman Pieter Dopper",
  title =        "Asymptotische Ontwikkelingen van de Onvolledige
                 Gammafuncties. ({Dutch}) [{Asymptotic} developments of
                 the Incomplete Gamma Functions]",
  type =         "{Ph.D.} thesis",
  school =       "Rijksuniversiteit Groningen",
  address =      "Groningen, The Netherlands",
  pages =        "????",
  year =         "1942",
  bibdate =      "Sat Feb 18 14:32:59 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Dutch",
  remark =       "Cited in \cite{Paris:2016:UAE}.",
}

@Article{Lancaster:1942:MME,
  author =       "Otis E. Lancaster",
  title =        "Machine Method for the Extraction of Cube Root",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "37",
  number =       "217",
  pages =        "112--115",
  month =        mar,
  year =         "1942",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:24 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314096;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
  URL =          "http://www.jstor.org/stable/2279437",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Archibald:1943:TTF,
  author =       "Raymond Clare Archibald",
  title =        "Tables of Trigonometric Functions in Non-Sexagesimal
                 Arguments",
  journal =      j-MATH-TABLES-AIDS-COMPUT,
  volume =       "1",
  number =       "2",
  pages =        "33--44",
  month =        apr,
  year =         "1943",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-43-99136-7",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Original journal has only `R. C. A.' as author:
                 possibly R. C. Archibald. AMS metadata now shows the
                 full name.",
}

@Book{Tolke:1943:PFE,
  author =       "Friedrich T{\"o}lke",
  title =        "{Praktische Funktionenlehre. 1. Elementare und
                 elementare transzendente Funktionen, Unterstufe}.
                 ({German}) [{Practical} functional theory. 1.
                 {Elementary} and elementary transcendental functions,
                 lower stage]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 261",
  year =         "1943",
  bibdate =      "Mon Feb 13 19:15:35 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Turing:1943:MCZ,
  author =       "A. M. Turing",
  title =        "A method for the calculation of the zeta-function",
  journal =      j-PROC-LONDON-MATH-SOC-2,
  volume =       "48",
  pages =        "180--197",
  year =         "1943",
  ISSN =         "0024-6115 (print), 1460-244X (electronic)",
  ISSN-L =       "0024-6115",
  MRclass =      "10.0X",
  MRnumber =     "MR0009612 (5,173a)",
  MRreviewer =   "C. L. Siegel",
  bibdate =      "Sat Nov 19 13:23:32 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://turing.ecs.soton.ac.uk/browse.php/B/17",
  ZMnumber =     "0061.08304",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the London Mathematical Society. Second
                 Series",
  received =     "7 March 1939",
  remark =       "According to \cite[page 260]{Newman:1955:AMT},
                 publication was delayed four years by war-time
                 difficulties.",
}

@Article{Bateman:1944:GTB,
  author =       "Harry Bateman and Raymond Clare Archibald",
  title =        "A Guide to Tables of {Bessel} Functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "1",
  number =       "7",
  pages =        "205--308",
  month =        jul,
  year =         "1944",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1944-0011175-4",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  MRnumber =     "6,132b",
  MRreviewer =   "G. Szeg{\H{o}}",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Lehmer:1944:NCB,
  author =       "Derrick Henry Lehmer",
  title =        "Note on the Computation of the {Bessel} Function {$
                 I_n(X) $}",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "1",
  number =       "5",
  pages =        "133--135",
  month =        apr,
  year =         "1944",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-44-99053-8",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Original journal has only `D. H. L.' as author:
                 probably D. H. Lehmer. AMS metadata now shows the full
                 name.",
}

@Book{Lewis:1944:SCH,
  author =       "Charles J. Lewis",
  title =        "A survey of the confluent hypergeometric function",
  publisher =    "????",
  address =      "Washington, DC, USA",
  pages =        "155",
  year =         "1944",
  LCCN =         "QA351 .L53",
  bibdate =      "Sat Oct 30 21:06:31 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Hypergeometric functions",
}

@Article{Abramowitz:1945:ZCB,
  author =       "Milton Abramowitz",
  title =        "Zeros of certain {Bessel} functions of fractional
                 order",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "1",
  number =       "9",
  pages =        "353--354",
  month =        jan,
  year =         "1945",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1945-0011176-7",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  MRclass =      "65.0X",
  MRnumber =     "6,132c",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Briggs:1945:TAL,
  author =       "Lyman J. Briggs and Arnold N. Lowan",
  title =        "Tables of Associated {Legendre} Functions",
  publisher =    pub-U-COLUMBIA,
  address =      pub-U-COLUMBIA:adr,
  pages =        "xlvi + 303 + 3",
  year =         "1945",
  LCCN =         "QA406 .U5 1945",
  bibdate =      "Sat Apr 1 14:47:02 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Prepared by the Mathematical Tables Project and
                 conducted under the sponsorship of the National bureau
                 of Standards. Present volume begun under the auspices
                 of the Work Projects Administration for the City of New
                 York and completed with the support of the Office of
                 Scientific Research and Development. Lyman J. Briggs,
                 Director, National Bureau of Standards and official
                 sponsor. Arnold N. Lowan, Project Director,
                 Mathematical Tables Project. Reproduced by a photo
                 offset process.",
  subject =      "Legendre's functions",
}

@Book{Emde:1945:TEF,
  author =       "Fritz Emde",
  title =        "{Tafeln Elementarer Funktionen} ({German}) [Tables of
                 Elementary Functions]",
  publisher =    "Edwards Bros.",
  address =      "Ann Arbor, MI, USA",
  pages =        "xii + 181",
  year =         "1945",
  LCCN =         "????",
  bibdate =      "Fri Jun 11 12:34:09 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Original edition published in 1940.",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Anonymous:1946:MZC,
  author =       "Anonymous",
  title =        "More Zeros of Certain {Bessel} Functions of Fractional
                 Order",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "2",
  number =       "15",
  pages =        "118--119",
  month =        jul,
  year =         "1946",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1946-0016689-0",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Anonymous:1948:TBF,
  author =       "Anonymous",
  title =        "Tables of the {Bessel} Functions {$ Y_0 (x) $}, {$ Y_1
                 (x) $}, {$ K_0 (x) $}, {$ K_1 (x) $}, $ 0 \leq x \leq 1
                 $",
  volume =       "1",
  publisher =    pub-US-GPO,
  address =      pub-US-GPO:adr,
  pages =        "ix + 60",
  year =         "1948",
  LCCN =         "QA3 .U5 no. 1",
  bibdate =      "Sat Nov 04 16:47:30 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       ser-APPL-MATH-SER-NBS,
  acknowledgement = ack-nhfb,
}

@Book{Emde:1948:TEF,
  author =       "Fritz Emde",
  title =        "{Tafeln Elementarer Funktionen} ({German}) [Tables of
                 Elementary Functions]",
  publisher =    pub-TEUBNER,
  address =      pub-TEUBNER:adr,
  edition =      "Second",
  pages =        "xii + 181",
  year =         "1948",
  LCCN =         "QA55 .E5 1948",
  MRclass =      "65.0X",
  MRnumber =     "11,263k",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@TechReport{Tukey:1948:NSR,
  author =       "John W. Tukey",
  title =        "A note on the square-root iteration",
  type =         "SRG Memorandum report",
  number =       "10",
  institution =  inst-PRINCETON,
  address =      inst-PRINCETON:adr,
  pages =        "18",
  year =         "1948",
  bibdate =      "Tue May 15 08:00:09 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Wise:1948:IBF,
  author =       "M. E. Wise",
  title =        "The Incomplete Beta Function and the Incomplete Gamma
                 Function: An Acknowledgment",
  journal =      j-J-R-STAT-SOC-SER-B-METHODOL,
  volume =       "10",
  number =       "2",
  pages =        "264--264",
  month =        "????",
  year =         "1948",
  CODEN =        "JSTBAJ",
  DOI =          "https://doi.org/10.2307/2983781",
  ISSN =         "0035-9246",
  ISSN-L =       "0035-9246",
  bibdate =      "Fri Jan 23 11:53:21 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i349688;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-b.bib",
  URL =          "http://www.jstor.org/stable/2983781",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society. Series B
                 (Methodological)",
  journal-URL =  "http://www.jstor.org/journals/00359246.html",
}

@Article{Hartree:1949:NIP,
  author =       "D. R. Hartree",
  title =        "Notes on iterative processes",
  journal =      j-PROC-CAMBRIDGE-PHIL-SOC,
  volume =       "45",
  number =       "2",
  pages =        "230--236",
  month =        apr,
  year =         "1949",
  CODEN =        "PCPSA4",
  DOI =          "https://doi.org/10.1017/s0305004100024762",
  ISSN =         "0008-1981",
  ISSN-L =       "0008-1981",
  MRclass =      "65.0X",
  MRnumber =     "29268",
  MRreviewer =   "E. Bodewig",
  bibdate =      "Thu Aug 3 09:15:52 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Correction: in equation (29) at the bottom of page
                 233, replace the denominator term $ 2 y_0 $ by $ 2 y_1
                 $, matching the denominator in equation (32) on page
                 234.",
  URL =          "https://ui.adsabs.harvard.edu/abs/1949PCPS...45..230H",
  ZMnumber =     "0033.19003",
  acknowledgement = ack-nhfb,
  author-dates = "Douglas Rayner Hartree (27 March 1897--12 February
                 1958)",
  fjournal =     "Proceedings of the Cambridge Philosophical Society",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=PSP",
  keywords =     "$1/p$-th root; iterative process; reciprocal square
                 root; square root",
  ZBmath =       "3051117",
}

@Article{Lowan:1949:CLN,
  author =       "Arnold N. Lowan",
  title =        "The {Computation Laboratory of the National Bureau of
                 Standards}",
  journal =      j-SCRIPTA-MATH,
  volume =       "15",
  number =       "??",
  pages =        "33--63",
  month =        "????",
  year =         "1949",
  ISSN =         "0036-9713",
  bibdate =      "Thu Oct 26 11:15:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
  ZMnumber =     "0034.07002",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica: A Quarterly Journal Devoted to
                 the Philosophy, History, and Expository Treatment of
                 Mathematics",
  ZBmath =       "3052129",
}

@Book{Magnus:1949:FTS,
  author =       "Wilhelm Magnus and Fritz Oberhettinger",
  title =        "Formulas and theorems for the special functions of
                 mathematical physics",
  publisher =    "Chelsea Pub. Co.",
  address =      "New York, NY, USA",
  pages =        "172",
  year =         "1949",
  LCCN =         "QA41 M19e",
  bibdate =      "Sat Oct 30 18:44:51 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Translated from the German by John Wermer.",
  acknowledgement = ack-nhfb,
}

@Article{Mitchell:1949:TFA,
  author =       "K. Mitchell",
  title =        "Tables of the function $ \int_0^z - \log |1 - y| / y
                 \, d y $ with an account of some properties of this and
                 related functions",
  journal =      j-PHILOS-MAG,
  volume =       "40",
  number =       "302",
  pages =        "351--368",
  year =         "1949",
  CODEN =        "PHMAA4",
  DOI =          "https://doi.org/10.1080/14786444908561256",
  ISSN =         "0031-8086",
  bibdate =      "Sat Jun 17 17:47:16 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.tandfonline.com/doi/abs/10.1080/14786444908561256",
  acknowledgement = ack-nhfb,
  fjournal =     "Philosophical Magazine",
  journal-URL =  "http://www.tandfonline.com/loi/tphm19",
  received =     "9 April 1948",
}

@InProceedings{Polya:1949:RCP,
  author =       "G. P{\'o}lya",
  editor =       "J. Neyman",
  booktitle =    "Proceedings of the First Berkeley Symposium on
                 Mathematical Statistics and Probability",
  title =        "Remarks on computing the probability integral in one
                 and two dimensions",
  publisher =    pub-U-CALIFORNIA-PRESS,
  address =      pub-U-CALIFORNIA-PRESS:adr,
  pages =        "63--78",
  year =         "1949",
  bibdate =      "Sat Dec 16 17:23:49 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Book{USNBSCL:1949:TCH,
  author =       "{United States National Bureau of Standards
                 Computation Laboratory }",
  title =        "Tables of the confluent hypergeometric function {$ F(n
                 / 2, 1 / 2, x) $ and related functions}",
  volume =       "3",
  publisher =    pub-US-GPO,
  address =      pub-US-GPO:adr,
  pages =        "xxii + 73",
  year =         "1949",
  LCCN =         "QA3 .U5 no. 3",
  bibdate =      "Sat Oct 30 21:06:31 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Applied mathematics series",
  URL =          "http://openlibrary.org/works/OL1218358W/Tables_of_the_confluent_hypergeometric_function_F%28n_2_1_2_x%29_and_related_functions",
  acknowledgement = ack-nhfb,
  subject =      "Hypergeometric functions; Mathematics; Tables",
}

@Article{Norlund:1950:HF,
  author =       "Niels Erik N{\o}rlund",
  title =        "Hypergeometric functions",
  journal =      "Mat. Tidsskr. B.",
  volume =       "1950",
  number =       "??",
  pages =        "18--21",
  year =         "1950",
  MRclass =      "33.0X",
  MRnumber =     "MR0045259 (13,554e)",
  MRreviewer =   "S. C. van Veen",
  bibdate =      "Thu Dec 01 12:41:44 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "0067.29402",
  acknowledgement = ack-nhfb,
  language =     "Danish",
}

@Book{Tolke:1950:PFE,
  author =       "Friedrich T{\"o}lke",
  title =        "{Praktische Funktionenlehre. 1. Elementare und
                 elementare transzendente Funktionen}. ({German})
                 [{Practical} functional theory. 1. {Elementary} and
                 elementary transcendental functions]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xi + 440",
  year =         "1950",
  bibdate =      "Mon Feb 13 19:12:35 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Tricomi:1950:AEU,
  author =       "F. G. Tricomi",
  title =        "{Asymptotische Eigenschaften der unvollst{\"a}ndigen
                 Gammafunktion}. ({German}) [{Asymptotic} properties of
                 the incomplete gamma function]",
  journal =      j-MATH-Z,
  volume =       "53",
  number =       "2",
  pages =        "136--148",
  month =        apr,
  year =         "1950",
  CODEN =        "MAZEAX",
  DOI =          "https://doi.org/10.1007/BF01162409",
  ISSN =         "0025-5874 (print), 1432-1823 (electronic)",
  ISSN-L =       "0025-5874",
  bibdate =      "Sat Feb 18 14:47:24 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/BF01162409",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Zeitschrift",
  journal-URL =  "http://link.springer.com/journal/209",
  language =     "German",
}

@Article{Cadwell:1951:BNI,
  author =       "J. H. Cadwell",
  title =        "The Bivariate Normal Integral",
  journal =      j-BIOMETRIKA,
  volume =       "38",
  number =       "3/4",
  pages =        "475--479",
  month =        dec,
  year =         "1951",
  CODEN =        "BIOKAX",
  DOI =          "https://doi.org/10.2307/2332596",
  ISSN =         "0006-3444 (print), 1464-3510 (electronic)",
  ISSN-L =       "0006-3444",
  MRclass =      "60.0X",
  MRnumber =     "0045960 (13,662h)",
  MRreviewer =   "G. E. Noether",
  bibdate =      "Sat Jun 21 14:32:38 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00063444.html;
                 http://www.jstor.org/stable/i315418;
                 https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2332596",
  acknowledgement = ack-nhfb,
  fjournal =     "Biometrika",
  journal-URL =  "http://biomet.oxfordjournals.org/content/by/year;
                 http://www.jstor.org/journals/00063444.html",
}

@Article{Fogel:1951:FTE,
  author =       "{\`E}. K. Fogel'",
  title =        "A finite theory of elementary functions. {I}.
                 {Logarithmic} and exponential functions. ({Russian})",
  journal =      "Latvijas PSR Zin\=at{\c{n}}u Akad. V\=estis",
  volume =       "5",
  number =       "46",
  pages =        "801--813",
  year =         "1951",
  MRclass =      "33.0X",
  MRnumber =     "15,218b",
  MRreviewer =   "H. N. Shapiro",
  bibdate =      "Sat Apr 25 13:05:19 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@InProceedings{Gellman:1951:CCH,
  author =       "Harvey Gellman",
  booktitle =    "Proceedings of a Computation Seminar [{IBM Department
                 of Education, Endicot, NY, from December 5 to 9,
                 1949}]",
  title =        "The Calculation of Complex Hypergeometric Functions
                 with the {IBM Type 602-A} Calculating Punch",
  publisher =    "IBM",
  address =      "New York, NY, USA",
  pages =        "161--168",
  year =         "1951",
  bibdate =      "Mon Jun 18 06:09:24 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "A Computation Seminar, sponsored by the International
                 Business Machines Corporation, was held in the IBM
                 Department of Education, Endicot, NY, from December 5
                 to 9, 1949. Attending the Seminar were one hundred and
                 seven research engineers and scientists who are
                 experienced both in applying mathematical methods to
                 the solution of physical problems and in the associated
                 punched card methods of computation.",
}

@Article{Rutishauser:1951:BAK,
  author =       "Heinz Rutishauser",
  title =        "{Bemerkungen zur Arbeit von K. Emden ``Eine L{\"o}sung
                 f{\"u}r $ \int e^{b(x + a \cos x)} \, d x $}''.
                 ({German}) [{Remarks} on the work by {K. Emden, ``A
                 solution for $ \int e^{b (x + a \ cos x)} \, d x
                 $''}]",
  journal =      j-Z-ANGE-MATH-PHYS,
  volume =       "2",
  number =       "4",
  pages =        "292--293",
  month =        jul,
  year =         "1951",
  CODEN =        "ZAMPDB",
  DOI =          "https://doi.org/10.1007/bf02579691",
  ISSN =         "0044-2275 (print), 1420-9039 (electronic)",
  ISSN-L =       "0044-2275",
  MRclass =      "26.1X",
  MRnumber =     "44598",
  MRreviewer =   "F. J. Murray",
  bibdate =      "Mon Aug 24 21:56:15 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Heinz Rutishauser (30 January 1918--10 November
                 1970)",
  fjournal =     "Zeitschrift f{\"u}r Angewandte Mathematik und Physik.
                 ZAMP. Journal of Applied Mathematics and Physics.
                 Journal de Math\'{e}matiques et de Physique
                 Appliqu\'{e}es",
  journal-URL =  "http://link.springer.com/journal/33",
  language =     "German",
}

@Article{Salzer:1951:FCE,
  author =       "H. E. Salzer",
  title =        "Formulas for Calculating the Error Function of a
                 Complex Variable",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "5",
  number =       "34",
  pages =        "67--70",
  month =        apr,
  year =         "1951",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1951-0048150-3",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Salzer:1951:RTT,
  author =       "H. E. Salzer",
  title =        "Radix Table for Trigonometric Functions and their
                 Inverses to High Accuracy",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "5",
  number =       "33",
  pages =        "9--11",
  month =        jan,
  year =         "1951",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-51-99447-1",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Wilkes:1951:PPE,
  author =       "Maurice V. Wilkes and David J. Wheeler and Stanley
                 Gill",
  title =        "The Preparation of Programs for an Electronic Digital
                 Computer",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "167",
  year =         "1951",
  LCCN =         "QA76.5 .W55 1951",
  bibdate =      "Mon Feb 10 09:42:47 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also second edition \cite{Wilkes:1957:PPE}, and
                 reprint \cite{Wilkes:1982:PPE}.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Part I \\
                 Chapter 1. The Design of Programs for Electronic
                 Computing Machines / 1 \\
                 1-1 Introduction / 1 \\
                 1-2 Types of automatic computing machines / 2 \\
                 1-3 Description of the EDSAC / 3 \\
                 1-4 The EDSAC order code / 5 \\
                 1-5 Notes on the order code / 6 \\
                 1-6 The use of conditional orders / 7 \\
                 1-7 Modification of orders by the program / 8 \\
                 1-8 Multiaddress codes / 11 \\
                 1-9 Binary--decimal conversion / 12 \\
                 1-10 Checking facilities / 14 \\
                 Chapter 2. Input of Orders / 15 \\
                 2-1 Initial orders / 15 \\
                 2-2 Pseudo-orders / 17 \\
                 2-3 Examples / 17 \\
                 2-4 Control combinations / 17 \\
                 2-5 Starting the program / 18 \\
                 2-6 Use of code letters / 19 \\
                 2-7 Constants / 20 \\
                 2-8 Notation / 20 \\
                 Chapter 3. Subroutines and Parameters / 22 \\
                 3-1 Open subroutines / 22 \\
                 3-2 closed subroutines / 22 \\
                 3-3 preset parameters / 23 \\
                 3-4 program parameters / 23 \\
                 Chapter 4. Library Subroutines and their Use in
                 Constructing Programs / 25 \\
                 4-1 Library catalog / 25 \\
                 4-2 Input and output subroutines / 25 \\
                 4-3 Division subroutines / 27 \\
                 4-4 Trigonometrical and other functions / 27 \\
                 4-5 Quadrature / 27 \\
                 4-6 Assembly subroutines / 27 \\
                 4-7 Integration of differential equations / 32 \\
                 4-8 Processes, Interpretive subroutines / 34 \\
                 Chapter 5. Pitfalls / 38 \\
                 5-1 Proofreading of programs, points to be checked / 38
                 \\
                 5-2 Location of mistakes in a program / 39 \\
                 5-3 Counting operations / 41 \\
                 Chapter 6. Use of the EDSAC \& Its Associated Equipment
                 / 42 \\
                 6-1 Tape Punching \& editing facilities / 42 \\
                 6-2 Storage of library subroutines / 43 \\
                 6-3 EDSAC organization / 43 \\
                 6-4 EDSAC controls / 43 \\
                 Chapter 7. Examples / 45 \\
                 7-1 Example 1. Calculation of $\exp(-\sin x)$ / 45 \\
                 7-2 Example 2. Calculation of $\pi$ by evaluation of
                 definite integral / 48 \\
                 7-3 Alternative method for Example 2 / 52 \\
                 7-4 Example 2, with extra print orders for checking /
                 53 \\
                 7-5 Application of checking subroutine C11 to Example 2
                 / 54 \\
                 7-6 Example of integration of an ordinary differential
                 equation / 46 \\
                 7-7 Evaluation of a definite integral / 61 \\
                 7-8 Program to facilitate the solution of algebraic
                 equation / 66 \\
                 Part II. Specifications of Library Subroutines / 72 \\
                 A. Subroutines to carry out floating point arithmetic /
                 73 \\
                 B. Subroutines to carry out arithmetical operations on
                 complex numbers / 78 \\
                 C. Checking subroutines / 79 \\
                 D. Division subroutines / 82 \\
                 E. Exponential subroutines / 83 \\
                 F. General routines relating to functions / 84 \\
                 G. Subroutines for integration of ordinary differential
                 equations / 86 \\
                 J. Subroutines for calculating special functions
                 [Legendre polynomials] / 88 \\
                 K. Subroutines for the summation of power series / 88
                 \\
                 L. Subroutines for evaluating logarithms / 91 \\
                 M. Miscellaneous subroutines / 91 \\
                 P. Print subroutines / 92 \\
                 Q. Quadrature subroutines / 95 \\
                 R. Input subroutines / 96 \\
                 S. Subroutines for evaluation of fractional powers / 98
                 \\
                 T. Subroutines for calculating trigonometrical
                 functions / 99 \\
                 U. Subroutines for counting operations / 101 \\
                 V1. Multiplication of vector by symmetric matrix / 102
                 \\
                 V2. Addition and subtraction of $n$ dimensional vectors
                 / 103 \\
                 Part III. Programs of Selected Library Subroutines /
                 104 \\
                 Appendix A. Keyboard perforator code, etc. / 158 \\
                 Appendix B. The initial orders / 159 \\
                 Appendix C. Control combinations / 161 \\
                 Appendix D. Interpretive subroutines: example of
                 packing of orders / 162 \\
                 Appendix E. Methods of counting in a simple cycle / 164
                 \\
                 Index",
}

@InBook{Goncarov:1952:EFC,
  author =       "V. L. Gon{\v{c}}arov",
  booktitle =    "Encyclopaedia of elementary mathematics. {Book III}.
                 {Functions} and limits (the foundations of analysis)",
  title =        "Elementary functions of a complex variable",
  publisher =    "Gosudarstv. Izdat. Tehn-Teoret. Lit.",
  address =      "Moscow-Leningrad, USSR",
  pages =        "491--552",
  year =         "1952",
  MRclass =      "30.0X",
  MRnumber =     "14,1073c",
  MRreviewer =   "R. P. Boas, Jr.",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Goncarov:1952:EFR,
  author =       "V. L. Gon{\v{c}}arov",
  booktitle =    "Encyclopaedia of elementary mathematics. {Book III}.
                 {Functions} and limits (the foundations of analysis)",
  title =        "Elementary functions of a real variable. Limits of
                 sequences and functions. {The} general concept of a
                 function",
  publisher =    "Gosudarstv. Izdat. Tehn-Teoret. Lit.",
  address =      "Moscow-Leningrad, USSR",
  pages =        "9--296",
  year =         "1952",
  MRclass =      "27.2X",
  MRnumber =     "14,1070d",
  MRreviewer =   "R. P. Boas, Jr.",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kuipers:1952:PSE,
  author =       "L. Kuipers",
  title =        "Properties of some elementary functions",
  journal =      "Nederl. Akad. Wetensch. Proc. Ser. A. = Indagationes
                 Math.",
  volume =       "55",
  number =       "14",
  pages =        "388--393",
  year =         "1952",
  MRclass =      "27.0X",
  MRnumber =     "14,360e",
  MRreviewer =   "E. Frank",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Book{Bowman:1953:IEF,
  author =       "Frank Bowman",
  title =        "Introduction to Elliptic Functions with Applications",
  publisher =    "English Universities Press",
  address =      "London, UK",
  pages =        "115",
  year =         "1953",
  LCCN =         "QA343 .B76 1953",
  bibdate =      "Wed Mar 15 06:50:49 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  subject =      "Elliptic functions; Elliptische functies",
}

@InProceedings{Lovelace:1953:AET,
  author =       "Ada Augusta Lovelace",
  title =        "{Appendix 1}: {Extracts} From {{\booktitle{Taylor's
                 Scientific Memoirs}}, Vol. III}",
  crossref =     "Bowden:1953:FTT",
  pages =        "341--408",
  year =         "1953",
  bibdate =      "Fri Jun 08 08:33:30 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprint of \cite{Lovelace:1843:SAE}. Pages 400--408
                 describe the computation of the Bernoulli numbers.",
  acknowledgement = ack-nhfb,
}

@Article{Salzer:1953:RTO,
  author =       "Herbert E. Salzer",
  title =        "Radix Table for Obtaining Hyperbolic and Inverse
                 Hyperbolic Functions to Many Places",
  journal =      j-J-MATH-PHYS-MIT,
  volume =       "32",
  number =       "1--4",
  pages =        "197--202",
  month =        apr,
  year =         "1953",
  CODEN =        "JMPHA9",
  DOI =          "https://doi.org/10.1002/sapm1953321197",
  ISSN =         "0097-1421",
  ISSN-L =       "0097-1421",
  bibdate =      "Sat Aug 19 13:35:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib",
  URL =          "https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1953321197",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Math. Phys. (MIT)",
  fjournal =     "Journal of Mathematics and Physics (MIT)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590",
  onlinedate =   "April 1953",
}

@Article{Scherberg:1953:ACP,
  author =       "Max G. Scherberg and John F. Riordan",
  title =        "Analogue Calculation of Polynomial and Trigonometric
                 Expansions (in {Other Aids to Computation})",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "7",
  number =       "41",
  pages =        "61--65",
  month =        jan,
  year =         "1953",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-53-99373-9",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Stiefel:1953:ITF,
  author =       "E. Stiefel",
  title =        "{Zur Interpolation von tabellierten Funktionen durch
                 Exponentialsummen und zur Berechnung von Eigenwerten
                 aus den Schwarzschen Konstanten}. ({German}) [{On}
                 interpolation of tabulated functions by exponential
                 sums and on the calculation of eigenvalues from the
                 {Schwarz}'s constants]",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "33",
  pages =        "260--262",
  year =         "1953",
  CODEN =        "ZAMMAX",
  DOI =          "https://doi.org/10.1002/zamm.19530330806",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  MRclass =      "65.0X",
  MRnumber =     "59061",
  MRreviewer =   "D. C. Gilles",
  bibdate =      "Wed Sep 2 16:23:13 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)",
  fjournal =     "Zeitschrift f{\"{u}}r Angewandte Mathematik und
                 Mechanik. Ingenieurwissenschaftliche
                 Forschungsarbeiten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
  language =     "German",
}

@Article{Turing:1953:SCR,
  author =       "A. M. Turing",
  title =        "Some calculations of the {Riemann} zeta-function",
  journal =      j-PROC-LONDON-MATH-SOC-3,
  volume =       "3",
  number =       "3",
  pages =        "99--117",
  year =         "1953",
  CODEN =        "PLMTAL",
  ISSN =         "0024-6115 (print), 1460-244X (electronic)",
  ISSN-L =       "0024-6115",
  MRclass =      "65.0X",
  MRnumber =     "MR0055785 (14,1126e)",
  MRreviewer =   "D. H. Lehmer",
  bibdate =      "Sat Nov 19 13:23:32 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See corrections and improvements
                 \cite{Lehman:1970:DZR}, and \cite{Trudgian:2011:ITM}.
                 The latter comments: ``Turing's Method has become the
                 standard technique used in modern verification of the
                 Riemann hypothesis.'' See also
                 \cite{Lehmer:1956:RRZ}.",
  URL =          "http://turing.ecs.soton.ac.uk/browse.php/B/21",
  ZMnumber =     "0050.08101",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the London Mathematical Society. Third
                 Series",
}

@Article{Aaboe:1954:AKI,
  author =       "Asger Aaboe",
  title =        "{Al-K{\=a}sh{\v{\i}}}'s iteration method for the
                 determination of $ \sin 1^\circ $",
  journal =      j-SCRIPTA-MATH,
  volume =       "20",
  number =       "??",
  pages =        "24--29",
  month =        "????",
  year =         "1954",
  ISSN =         "0036-9713",
  ISSN-L =       "0036-9713",
  MRclass =      "01.0X",
  MRnumber =     "62046",
  bibdate =      "Thu Oct 26 11:15:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
  ZMnumber =     "0055.00104",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica: A Quarterly Journal Devoted to
                 the Philosophy, History, and Expository Treatment of
                 Mathematics",
  ZBmath =       "3086736",
}

@Article{Atta:1954:CGH,
  author =       "Susie E. Atta and Ward C. Sangren",
  title =        "Calculation of Generalized Hypergeometric Series",
  journal =      j-J-ACM,
  volume =       "1",
  number =       "4",
  pages =        "170--172",
  month =        oct,
  year =         "1954",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/320783.320785",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Tue Nov 08 21:50:00 1994",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "https://dl.acm.org/loi/jacm",
}

@Article{Cahill:1954:PCH,
  author =       "W. F. Cahill",
  title =        "Programs for Computing the Hypergeometric Series (in
                 Automatic Computing Machinery; Discussions)",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "8",
  number =       "45",
  pages =        "36--37",
  month =        jan,
  year =         "1954",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-54-99344-8",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Clenshaw:1954:PAE,
  author =       "C. W. Clenshaw",
  title =        "Polynomial approximations to elementary functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "8",
  number =       "47",
  pages =        "143--147",
  month =        jul,
  year =         "1954",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1954-0063487-2",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  MRclass =      "41.1X",
  MRnumber =     "16,128f",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@TechReport{Franklin:1954:CARa,
  author =       "J. Franklin and B. Friedman",
  title =        "A convergent asymptotic representation for integrals",
  institution =  "Division of Electromagnetic Research, Institute of
                 Mathematical Sciences, New York University",
  address =      "New York, NY, USA",
  pages =        "i + 17",
  year =         "1954",
  MRclass =      "40.0X",
  MRnumber =     "0068019",
  MRreviewer =   "J. G. van der Corput",
  bibdate =      "Tue Feb 06 15:03:36 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Res. Rep. No. BR-9",
  acknowledgement = ack-nhfb,
  remark =       "See applications in
                 \cite{Temme:2015:AMI,Navas-Palencia:2018:HPC}.",
}

@Article{LaFara:1954:MCI,
  author =       "Robert L. LaFara",
  title =        "A Method for Calculating Inverse Trigonometric
                 Functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "8",
  number =       "47",
  pages =        "132--139",
  month =        jul,
  year =         "1954",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1954-0063150-8",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@InCollection{Ostrowski:1954:TPA,
  author =       "A. M. Ostrowski",
  title =        "On two problems in abstract algebra connected with
                 {Horner}'s rule",
  crossref =     "Birkhoff:1954:SMM",
  pages =        "40--48",
  year =         "1954",
  bibdate =      "Fri Oct 20 10:13:10 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "number of multiplications to evaluate a polynomial",
  remark =       "TO DO: Find copy of this book section.",
}

@Article{Shenton:1954:INI,
  author =       "L. R. Shenton",
  title =        "Inequalities for the Normal Integral Including a New
                 Continued Fraction",
  journal =      j-BIOMETRIKA,
  volume =       "41",
  number =       "1/2",
  pages =        "177--189",
  month =        jun,
  year =         "1954",
  CODEN =        "BIOKAX",
  DOI =          "https://doi.org/10.2307/2333015",
  ISSN =         "0006-3444 (print), 1464-3510 (electronic)",
  ISSN-L =       "0006-3444",
  MRclass =      "62.0X",
  MRnumber =     "0061785 (15,884e)",
  MRreviewer =   "E. Lukacs",
  bibdate =      "Sat Jun 21 14:32:43 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00063444.html;
                 http://www.jstor.org/stable/i315422;
                 https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2333015",
  acknowledgement = ack-nhfb,
  fjournal =     "Biometrika",
  journal-URL =  "http://biomet.oxfordjournals.org/content/by/year;
                 http://www.jstor.org/journals/00063444.html",
}

@InProceedings{Todd:1954:MWN,
  author =       "John Todd",
  editor =       "????",
  booktitle =    "Transactions of {2nd Symposium on Applied Mathematics,
                 29 April 1954, University of Chicago}",
  title =        "Motivation for working on numerical analysis",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "????",
  year =         "1954",
  bibdate =      "Fri Oct 20 13:28:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "Sponsored by the American Mathematical Society and the
                 Office of Ordnance Research",
}

@Article{Booth:1955:NAP,
  author =       "A. D. Booth",
  title =        "A note on approximating polynomials for trigonometric
                 functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "9",
  number =       "49",
  pages =        "21--23",
  month =        jan,
  year =         "1955",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1955-0069579-7",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  MRclass =      "65.0X",
  MRnumber =     "69579",
  MRreviewer =   "L. Fox",
  bibdate =      "Tue Nov 14 17:19:58 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}

@TechReport{Carlson:1955:RAF,
  author =       "Bengt Carlson and Max Goldstein",
  title =        "Rational Approximations of Functions",
  type =         "Report",
  number =       "LA-1943",
  institution =  inst-LASL,
  address =      inst-LASL:adr,
  pages =        "iv + 46",
  month =        aug,
  year =         "1955",
  DOI =          "https://doi.org/10.2172/4374577",
  bibdate =      "Sat Dec 27 09:41:36 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.osti.gov/scitech/biblio/4374577-0deJO9/;
                 http://www.osti.gov/scitech/servlets/purl/4374577",
  acknowledgement = ack-nhfb,
  keywords =     "$-\ln(x)/(1 - x)$; $\art(x) / x$; $\cos(x)$;
                 $\exp(-x)$; $\sin(x) / x$; $\tan(x) / x$; $x \cot(x)$;
                 $x**(1/2)$; $x**(1/3)$; $x**(1/4)$; $x**(1/5)$;
                 $x**(1/6)$; $x**(1/7)$; continued fractions; rational
                 approximations",
  remark =       "Cited in \cite[page 71]{Abramowitz:1964:HMF}.",
}

@Article{Clenshaw:1955:NSC,
  author =       "C. W. Clenshaw",
  title =        "A Note on the Summation of {Chebyshev} Series",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "9",
  number =       "51",
  pages =        "118--120",
  month =        jul,
  year =         "1955",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1955-0071856-0",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  MRclass =      "65.0X",
  MRnumber =     "0071856",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  author-dates = "Charles William Clenshaw (15 March 1926--23 September
                 2004)",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Chebyshev series; Clenshaw algorithm; Clenshaw
                 summation; Horner polynomial evaluation",
  remark =       "Hidden inside \cite{Brenner:1955:TNS}, but important
                 in its own right for commentary on the recursive
                 algorithm for summation of Chebyshev series, and a
                 brief analysis of its accuracy.",
}

@Article{Froberg:1955:NTC,
  author =       "Carl-Erik Fr{\"o}berg",
  title =        "Numerical Treatment of {Coulomb} Wave Functions",
  journal =      j-REV-MOD-PHYS,
  volume =       "27",
  number =       "4",
  pages =        "399--411",
  month =        oct,
  year =         "1955",
  CODEN =        "RMPHAT",
  DOI =          "https://doi.org/10.1103/RevModPhys.27.399",
  ISSN =         "0034-6861 (print), 1538-4527 (electronic), 1539-0756",
  ISSN-L =       "0034-6861",
  bibdate =      "Tue May 22 16:36:44 MDT 2012",
  bibsource =    "http://rmp.aps.org/toc/RMP/v27/i4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/revmodphys1950.bib",
  URL =          "http://link.aps.org/doi/10.1103/RevModPhys.27.399;
                 http://rmp.aps.org/abstract/RMP/v27/i4/p399_1",
  acknowledgement = ack-nhfb,
  fjournal =     "Reviews of Modern Physics",
  journal-URL =  "http://rmp.aps.org/browse",
}

@Book{Hastings:1955:ADC,
  author =       "Cecil {Hastings, Jr.}",
  title =        "Approximations for Digital Computers",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "viii + 201",
  year =         "1955",
  ISBN =         "0-691-07914-5",
  ISBN-13 =      "978-0-691-07914-1",
  LCCN =         "QA76 .H37",
  bibdate =      "Mon Oct 01 15:59:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Assisted by Jeanne T. Hayward and James P. Wong, Jr.",
  series =       "The Rand series",
  acknowledgement = ack-nhfb,
  remark-1 =     "Reprinted 1957, 1959, 1962, 1966, and 1970. I have
                 fourth printing (1962).",
  remark-2 =     "Hastings gives a polynomial approximation for
                 computing random numbers from a normal distribution.",
  subject =      "Electronic digital computers; Numerical analysis",
  tableofcontents = "Preface / v \\
                 Part I \\
                 1: Concerning Best Fit / 3 \\
                 2: Linear Weights / 19 \\
                 3: An Iterative Procedure / 27 \\
                 4: Solution of Equations / 35 \\
                 5: Chebyshev Polynomials / 47 \\
                 6: Concerning Weights / 65 \\
                 7: Function With a Peak / 75 \\
                 8: Rates of Convergence / 83 \\
                 9: Choice of Form / 95 \\
                 10: A Scoring-Camera Problem / 115 \\
                 Part II \\
                 1: $\log_{10} x$ / 125 \\
                 5: $\phi(x) = (1 - e^{-x}) / x$ / 129 \\
                 8: $\arctan x$ / 132 \\
                 14: $\sin (\pi/2) x$ / 138 \\
                 17: $10^x$ / 141 \\
                 21: $W(x) = e^{-x} / (1 + e^{-x})^2$ / 145 \\
                 24: $P_k(x) = 1.72 + 42 x^2$ or $0.136 / x^2$ / 148 \\
                 27: $E'(x) = (1 / \sqrt{2 \pi}) e^{-(1/2)x^2}$ / 151
                 \\
                 30: ``Total Klein-Nishina Cross Section'' Function /
                 154 \\
                 31: $\Gamma(1 + x)$ / 155 \\
                 35: $\arcsin x$ / 159 \\
                 40: $\log_2 x$ / 164 \\
                 43: $\Phi(x) = (2 / \sqrt{\pi}) \int_0^x e^{-t^2} \,
                 dt$ / 167 \\
                 46: $K(k) = \int_0^{\pi/2} (1 / \sqrt{1 - k^2 \sin^2
                 \phi}) \, d\phi$ / 170 \\
                 49: $E(k) = \int_0^{\pi/2} (\sqrt{1 - k^2 \sin^2 \phi})
                 \, d\phi$ / 173 \\
                 52: $\ln(1 + x)$ / 176 \\
                 57: $e^{-x}$ / 181 \\
                 61: $\Phi(x) = (2 / \sqrt{\pi}) \int_0^x e^{-t^2} \,
                 dt$ / 185 \\
                 64: $-{\rm Ei}(-x) = \int_x^\infty (e^{-t} / t) \, dt$
                 / 188 \\
                 67: $q = (1 / \sqrt{2 \pi}) \int_{x(q)}^\infty
                 e^{-(1/2)t^2} \, dt$ / 191 \\
                 69: $W(z) = \int_0^\infty (e^(-u z) / (K_1^2(u) + \pi^2
                 I_1^2(u))) (1/u) \, du$ / 193 \\
                 71: $P(x) = \int_x^\infty (\sin(t - x) / t) \, dt$ /
                 195 \\
                 74: $Q(x) = \int_x^\infty (\cos(t - x) / t) \, dt$ /
                 195 \\
                 References for Part II / 201",
}

@Book{Hobson:1955:TSE,
  author =       "Ernest William Hobson",
  title =        "The Theory of Spherical and Ellipsoidal Harmonics",
  publisher =    "Chelsea Pub. Co.",
  address =      "New York, NY, USA",
  pages =        "500",
  year =         "1955",
  LCCN =         "QA406 .H7 1955",
  bibdate =      "Sat Apr 1 14:40:56 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1856--1933",
  subject =      "Spherical harmonics; Lam{\'e}'s functions",
}

@Book{McLachlan:1955:BFE,
  author =       "N. W. (Norman William) McLachlan",
  title =        "{Bessel} Functions for Engineers",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  edition =      "Second",
  pages =        "xii + 239",
  year =         "1955",
  LCCN =         "QA408 .M3 1955",
  bibdate =      "Sat Apr 1 14:44:36 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "The Oxford engineering science series",
  acknowledgement = ack-nhfb,
  author-dates = "1888--",
  subject =      "Bessel functions",
}

@Article{Motzkin:1955:EP,
  author =       "T. S. Motzkin",
  title =        "Evaluation of polynomials",
  journal =      j-BULL-AMS,
  volume =       "61",
  number =       "2",
  pages =        "163--163",
  month =        mar,
  year =         "1955",
  CODEN =        "BAMOAD",
  ISSN =         "0002-9904 (print), 1936-881X (electronic)",
  ISSN-L =       "0002-9904",
  bibdate =      "Fri Oct 20 09:06:44 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin of the American Mathematical Society",
  issue =        "635",
  journal-URL =  "http://www.ams.org/journals/bull/all_issues.html",
  keywords =     "number of multiplications to evaluate a polynomial",
  received =     "12 November 1954",
  remark =       "One-paragraph abstract only, with reference-less
                 mention of Ostrowski.",
}

@Article{Motzkin:1955:ERF,
  author =       "T. S. Motzkin",
  title =        "Evaluation of rational functions",
  journal =      j-BULL-AMS,
  volume =       "61",
  number =       "2",
  pages =        "163--163",
  month =        mar,
  year =         "1955",
  CODEN =        "BAMOAD",
  ISSN =         "0002-9904 (print), 1936-881X (electronic)",
  ISSN-L =       "0002-9904",
  bibdate =      "Fri Oct 20 09:06:44 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin of the American Mathematical Society",
  issue =        "635",
  journal-URL =  "http://www.ams.org/journals/bull/all_issues.html",
  keywords =     "number of multiplications to evaluate a polynomial",
  received =     "12 November 1954",
  remark =       "One-paragraph abstract only, with reference to Ostrowski.",
}

@Article{Norlund:1955:HF,
  author =       "Niels Erik N{\o}rlund",
  title =        "Hypergeometric functions",
  journal =      j-ACTA-MATH,
  volume =       "94",
  number =       "??",
  pages =        "289--349",
  month =        "????",
  year =         "1955",
  CODEN =        "ACMAA8",
  DOI =          "https://doi.org/10.1007/BF02392494",
  ISSN =         "0001-5962 (print), 1871-2509 (electronic)",
  ISSN-L =       "0001-5962",
  MRclass =      "33.0X",
  MRnumber =     "MR0074585 (17,610d)",
  MRreviewer =   "A. Erd{\'e}lyi",
  bibdate =      "Thu Dec 01 10:09:47 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Acta Mathematica",
  journal-URL =  "http://link.springer.com/journal/11511",
}

@Article{Preston:1955:ACS,
  author =       "F. S. Preston",
  title =        "An Analog Computer for the Solution of Tangents",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-4",
  number =       "3",
  pages =        "101--106",
  month =        "????",
  year =         "1955",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/IRETELC.1955.507908",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 15:10:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407908",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Robinson:1955:EAC,
  author =       "A. S. Robinson",
  title =        "An Electronic Analog Computing Technique for the
                 Solution of Trigonometric Problems",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-4",
  number =       "3",
  pages =        "95--101",
  month =        "????",
  year =         "1955",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/IRETELC.1955.5407907",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jun 30 15:10:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407907",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Salzer:1955:CZE,
  author =       "Herbert E. Salzer",
  title =        "Complex zeros of the error function",
  journal =      j-J-FRANKLIN-INST,
  volume =       "260",
  number =       "3",
  pages =        "209--211",
  month =        sep,
  year =         "1955",
  CODEN =        "JFINAB",
  DOI =          "https://doi.org/10.1016/0016-0032(55)90732-8",
  ISSN =         "0016-0032 (print), 1879-2693 (electronic)",
  ISSN-L =       "0016-0032",
  MRclass =      "65.1X",
  MRnumber =     "71880",
  MRreviewer =   "L. Fox",
  bibdate =      "Tue Nov 14 17:19:58 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Franklin Institute",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00160032",
  reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}

@Article{Todd:1955:MWN,
  author =       "John Todd",
  title =        "Motivation for working in numerical analysis",
  journal =      j-COMM-PURE-APPL-MATH,
  volume =       "8",
  number =       "1",
  pages =        "97--116",
  month =        feb,
  year =         "1955",
  CODEN =        "CPAMAT, CPMAMV",
  DOI =          "https://doi.org/10.1002/cpa.3160080107",
  ISSN =         "0010-3640 (print), 1097-0312 (electronic)",
  ISSN-L =       "0010-3640",
  MRclass =      "65.0X",
  MRnumber =     "70251",
  MRreviewer =   "G. E. Forsythe",
  bibdate =      "Fri Oct 20 08:38:37 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "0064.37402",
  acknowledgement = ack-nhfb,
  ajournal =     "Comm. Pure Appl. Math.",
  author-dates = "John Todd (16 May 1911--21 June 2007)",
  fjournal =     "Communications on Pure and Applied Mathematics (New
                 York)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
  keywords =     "characteristic roots (eigenvalues) of finite matrices;
                 game theory; integral equations; modified differences;
                 Monte Carlo; number of multiplications to evaluate a
                 polynomial; polynomial evaluation; quadrature; recent
                 activity in numerical analysis; sequence convergence
                 acceleration; theory of machines (automata)",
  remark-1 =     "This may be the earliest paper to note that a
                 polynomial of degree $n$ can be evaluated with fewer
                 than $n$ multiplications, but requiring more than $n$
                 additions. The normal Horner form requires $n$ multiply
                 and $n$ add operations: $ h = a_n $, $ h = x h + a_k $
                 (for $ k = n - 1 $ to $0$), and on modern hardware can
                 be conveniently evaluated in $n$ consecutive fused
                 multiply-add operations. However, the evaluation of the
                 altered forms often has terms of differing signs, and
                 may be subject to catastrophic leading digit loss, when
                 the original polynomial, if it had coefficients of the
                 same sign, might have been computed stably for $ x >
                 0$. In some cases, the new coefficients are complex,
                 even when those of the original polynomial are real
                 numbers. See also related publications
                 \cite{Ostrowski:1954:TPA, Todd:1954:MWN,
                 Motzkin:1955:EP, Motzkin:1955:ERF, Belaga:1958:SPI,
                 Pan:1959:CSC, Pan:1959:SCP, Floyd:1961:ACE,
                 Dorn:1962:GHR, Knuth:1962:EPC, Eisman:1963:PER,
                 Eve:1964:EP, Rice:1965:CPR, Winograd:1970:NMN,
                 Rabin:1972:FEP, Miller:1975:CCN, Knuth:1998:EP,
                 Kusterer:1979:SEP, Ceberio:2002:HRI}. Rice reports
                 extreme numerical instability of the Belaga and Motzkin
                 forms, and moderate instability of the Pan forms, while
                 the Chebyshev form is never unstable. Todd cites
                 Motzkin's work as ``to appear'', and those two
                 one-paragraph abstracts were received 12 November 1954
                 and published in March 1955, but Todd's paper has no
                 received date, so we cannot determine their relative
                 priority. Entry \cite{Ostrowski:1954:TPA} may be prior
                 art, but a copy of that work has not yet been located.
                 The quotation in entry \cite{Eve:1964:E} summarizes the
                 bounds on the number of add and multiply operations.",
  remark-2 =     "Knuth's treatment (Knuth:1962:EPC) concentrates on
                 operation counts, because the polynomial variable need
                 not be a real scalar floating-point number: it could be
                 complex, multiple precision, matrix, series, ..., where
                 multiplication is relatively expensive. Knuth remarks
                 on page 485 that ``numerical analysis of the accuracy
                 achieved \ldots{} is beyond the scope of this book: the
                 reader should be careful to investigate the accuracy of
                 any calculations undertaken with floating-point
                 arithmetic.'' On page 486, Knuth notes that the nested
                 form is often attributed to Horner:1819:XNM, but that
                 Isaac Newton used it in unpublished notes 150 years
                 earlier, and it was employed by the Chinese in the 13th
                 century CE.",
  remark-3 =     "The year of this paper is erroneously cited in
                 reference lists of several sources as 1951, rather than
                 the correct 1955.",
  ZBmath =       "3109832",
}

@Book{Achieser:1956:TA,
  author =       "N. I. Achieser",
  title =        "Theory of Approximation",
  publisher =    "Frederick Ungar Publishing Company",
  address =      "New York, NY, USA",
  pages =        "x + 307",
  year =         "1956",
  LCCN =         "QA221 .A533 1956",
  bibdate =      "Fri Oct 20 08:06:59 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "Translation of Russian original, Lek{\"e}t{\`\i}sii po
                 teorii approksima{\"e}t{\`\i}sii. Reprinted in
                 \cite{Achieser:1992:TA}.",
  subject =      "Mathematical analysis",
  tableofcontents = "Approximation Problems in Linear Normalized Spaces
                 \\
                 Formulation of the Principal Problem in the Theory of
                 Approximation / 1 \\
                 The Concept of Metric Space / 1 \\
                 The Concept of Linear Normalized Space / 2 \\
                 Examples of Linear Normalized Spaces / 3 \\
                 The Inequalities of Holder and Minkowski / 4 \\
                 Additional Examples of Linear Normalized Spaces / 7 \\
                 Hilbert Space / 8 \\
                 The Fundamental Theorem of Approximation Theory in
                 Linear Normalized Spaces / 10 \\
                 Strictly Normalized Spaces / 11 \\
                 An Example of Approximation in the Space $L^p$ / 12 \\
                 Geometric Interpretation / 13 \\
                 Separable and Complete Spaces / 14 \\
                 Approximation Theorems in Hilbert Space / 15 \\
                 An Example of Approximation in Hilbert Space / 19 \\
                 More About the Approximation Problem in Hilbert Space /
                 21 \\
                 Orthonormalized Vector Systems in Hilbert Space / 22
                 \\
                 Orthogonalization of Vector Systems / 23 \\
                 Infinite Orthonormalized Systems / 25 \\
                 An Example of a Non-Separable System / 29 \\
                 Weierstrass' First Theorem / 29 \\
                 Weierstrass' Second Theorem / 32 \\
                 The Separability of the Space C / 33 \\
                 The Separability of the Space $L^p$ / 34 \\
                 Generalization of Weierstrass' Theorem to the Space
                 $L^p$ / 37 \\
                 The Completeness of the Space $L^p$ / 38 \\
                 Examples of Complete Orthonormalized Systems in
                 L[superscript 2] / 40 \\
                 Muntz's Theorem / 43 \\
                 The Concept of the Linear Functional / 46 \\
                 F. Riesz's Theorem / 47 \\
                 A Criterion for the Closure of a Set of Vectors in
                 Linear Normalized Spaces / 49 \\
                 P. L. Tchebysheff's Domain of Ideas \\
                 Statement of the Problem / 51 \\
                 A Generalization of the Theorem of de la Vallee-Poussin
                 / 52 \\
                 The Existence Theorem / 53 \\
                 Tchebysheff's Theorem / 55 \\
                 A Special Case of Tchebysheff's Theorem / 57 \\
                 The Tchebysheff Polynomials of Least Deviation from
                 Zero / 57 \\
                 A Further Example of P. Tchebysheff's Theorem / 58 \\
                 An Example for the Application of the General Theorem
                 of de la Vallee-Poussin / 60 \\
                 An Example for the Application of P. L. Tchebysheff's
                 General Theorem / 62 \\
                 The Passage to Periodic Functions / 64 \\
                 An Example of Approximating with the Aid of Periodic
                 Functions / 66 \\
                 The Weierstrass Function / 66 \\
                 Haar's Problem / 67 \\
                 Proof of the Necessity of Haar's Condition / 68 \\
                 Proof of the Sufficiency of Haar's Condition / 69 \\
                 An Example Related to Haar's Problem / 72 \\
                 P. L. Tchebysheff's Systems of Functions / 73 \\
                 Generalization of P. L. Tchebysheff's Theorem / 74 \\
                 On a Question Pertaining to the Approximation of a
                 Continuous Function in the Space $L$ / 76 \\
                 A. A. Markoff's Theorem / 82 \\
                 Special Cases of the Theorem of A. A. Markoff / 85 \\
                 Elements of Harmonic Analysis \\
                 The Simplest Properties of Fourier Series / 89 \\
                 Fourier Series for Functions of Bounded Variation / 93
                 \\
                 The Parseval Equation for Fourier Series / 97 \\
                 Examples of Fourier Series / 98 \\
                 Trigonometric Integrals / 101 \\
                 The Riemann--Lebesgue Theorem / 103 \\
                 Plancherel's Theory / 104 \\
                 Watson's Theorem / 106 \\
                 Plancherel's Theorem / 108 \\
                 Fejer's Theorem / 110 \\
                 Integral-Operators of the Fejer Type / 113 \\
                 The Theorem of Young and Hardy / 116 \\
                 Examples of Kernels of the Fejer Type / 118 \\
                 The Fourier Transformation of Integrable Functions /
                 120 \\
                 The Faltung of two Functions / 122 \\
                 V. A. Stekloff's Functions / 123 \\
                 Multimonotonic Functions / 125 \\
                 Conjugate Functions / 126 \\
                 Certain Extremal Properties of Integral Transcendental
                 Functions of the Exponential Type \\
                 Integral Functions of the Exponential Type / 130 \\
                 The Borel Transformation / 132 \\
                 The Theorem of Wiener and Paley / 134 \\
                 Integral Functions of the Exponential Type which are
                 Bounded along the Real Axis / 137 \\
                 S. N. Bernstein's Inequality / 140 \\
                 B. M. Levitan's Polynomials / 146 \\
                 The Theorem of Fejer and Riesz. A Generalization of
                 This Theorem / 152 \\
                 A Criterion for the Representation of Continuous
                 Functions as Fourier--Stieltjes Integrals / 154 \\
                 Questions Regarding the Best Harmonic Approximation of
                 Functions Preliminary Remarks / 160 \\
                 The Modulus of Continuity / 161 \\
                 The Generalization to the Space $L^p$ ($p \geq 1$) /
                 162 \\
                 An Example of Harmonic Approximation / 165 \\
                 Some Estimates for Fourier Coefficients / 169 \\
                 More about V. A. Stekloff's Functions / 173 \\
                 Two Lemmas / 175 \\
                 The Direct Problem of Harmonic Approximation / 176 \\
                 A Criterion due to B. Sz.-Nagy / 183 \\
                 The Best Approximation of Differentiable Functions /
                 187 \\
                 Direct Observations Concerning Periodic Functions / 195
                 \\
                 Jackson's Second Theorem / 199 \\
                 The Generalized Fejer Method / 201 \\
                 Berstein's Theorem / 206 \\
                 Priwaloff's Theorem / 210 \\
                 Generalizations of Bernstein's Theorems to the Space
                 $L^p$ ($p \geq 1$) / 211 \\
                 The Best Harmonic Approximation of Analytic Functions /
                 214 \\
                 A Different Formulation of the Result of the Preceding
                 Section / 218 \\
                 The Converse of Bernstein's Theorem / 221 \\
                 Wiener's Theorem on Approximation \\
                 Wiener's Problem / 224 \\
                 The Necessity of Wiener's Condition / 224 \\
                 Some Definitions and Notation / 225 \\
                 Several Lemmas / 227 \\
                 The Wiener--Levy Theorem / 230 \\
                 Proof of the Sufficiency of Wiener's Condition / 233
                 \\
                 Wiener's General Tauber Theorem / 234 \\
                 Weakly Decreasing Functions / 235 \\
                 Remarks on the Terminology / 237 \\
                 Ikehara's Theorem / 238 \\
                 Carleman's Tauber Theorem / 241 \\
                 Various Addenda and Problems \\
                 Elementary Extremal Problems and Certain Closure
                 Criteria / 243 \\
                 Szego's Theorem and Some of Its Applications / 256 \\
                 Further Examples of Closed Sequences of Functions / 267
                 \\
                 The Caratheodory--Fejer Problem and Similar Problems /
                 270 \\
                 Solotareff's Problems and Related Problems / 280 \\
                 The Best Harmonic Approximation of the Simplest
                 Analytic Functions / 289 \\
                 Notes / 296 \\
                 Index / 306",
}

@InProceedings{Haynes:1956:EIE,
  author =       "John G. Haynes",
  editor =       "????",
  booktitle =    "{ACM'56: Proceedings of the 1956 11th ACM national
                 meeting}",
  title =        "Evaluation of incomplete elliptic integrals by
                 {Gaussian} integration",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "56--59",
  year =         "1956",
  DOI =          "https://doi.org/10.1145/800258.808948",
  bibdate =      "Fri Dec 21 08:53:15 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://dl.acm.org/ft_gateway.cfm?id=808948",
  acknowledgement = ack-nhfb,
}

@Book{Jeffreys:1956:MMP,
  author =       "Harold Jeffreys and Bertha {Swirles Jeffreys}",
  title =        "Methods of Mathematical Physics",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Third",
  pages =        "714",
  year =         "1956",
  LCCN =         "QA401 .J4 1956",
  bibdate =      "Thu Aug 17 10:48:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://en.wikipedia.org/wiki/Bertha_Swirles;
                 https://en.wikipedia.org/wiki/Harold_Jeffreys",
  acknowledgement = ack-nhfb,
  author-dates = "Sir Harold Jeffreys (22 April 1891--18 March 1989);
                 Lady Bertha Swirles Jeffreys (22 May 1903--18 December
                 1999)",
  remark =       "References to Douglas Hartree in",
  remark-1 =     "First edition 1946, second edition 1950, third edition
                 1956, first paperback edition 1972, reprinted 1978,
                 1980, 1988, 1992, 1999, 2001. Third edition preface is
                 dated April 1953. Second edition preface is dated 15
                 November 1948. First edition preface is dated 1946.
                 Reprinted in \cite{Jeffreys:1999:MMP}.",
  subject-dates = "Douglas Rayner Hartree (27 March 1897--12 February
                 1958)",
  tableofcontents = "Preface \\
                 Authors' Notes \\
                 1: The Real Variable \\
                 2: Scalars and Vectors \\
                 3: Tensors \\
                 4: Matrices \\
                 5: Multiple Integrals \\
                 6: Potential Theory \\
                 7: Operational Methods \\
                 8: Physical Applications of the Operational Method \\
                 9: Numerical Methods \\
                 10: Calculus of Variations \\
                 11: Functions of a Complex Variable \\
                 12: Contour Integration and Bromwich's Integral \\
                 13: Conformal Representation \\
                 14: Fourier's Theorem \\
                 15: The Factorial and Related Functions \\
                 16: Solution of Linear Differential Equation \\
                 17: Asymptotic Expansions \\
                 18: The Equations of Potential, Waves, and Heat
                 Conduction \\
                 19: Waves in One Dimension and Waves With Spherical
                 Symmetry \\
                 20: Conduction of Heat in One and Three Dimensions \\
                 21: Bessel Functions \\
                 22: Applications of Bessel Functions \\
                 23: The Confluent Hypergeometric Function \\
                 24: Legendre Functions and Associated Functions \\
                 25: Elliptic Functions \\
                 Notes \\
                 Appendix on Notation \\
                 Index",
}

@Article{Lehmer:1956:RRZ,
  author =       "D. H. Lehmer",
  title =        "On the roots of the {Riemann} zeta-function",
  journal =      j-ACTA-MATH,
  volume =       "95",
  number =       "1",
  pages =        "291--298",
  month =        dec,
  year =         "1956",
  CODEN =        "ACMAA8",
  DOI =          "https://doi.org/10.1007/BF02401102",
  ISSN =         "0001-5962 (print), 1871-2509 (electronic)",
  ISSN-L =       "0001-5962",
  MRclass =      "10.1X",
  MRnumber =     "0086082 (19,121a)",
  MRreviewer =   "L. Schoenfeld",
  bibdate =      "Mon Sep 28 16:18:23 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Acta Mathematica",
  journal-URL =  "http://link.springer.com/journal/11511",
  remark-1 =     "See \cite[references 38--39, page
                 54]{Bullynck:2015:CPT} for Turing's role in this work,
                 published two years after Turing's death in 1954.
                 Turing's incomplete work appears in
                 \cite{Turing:1953:SCR}.",
  remark-2 =     "From page 293: ``Plans to extend the work of
                 Titchmarsh [on the zeros of the Riemann zeta function]
                 by use of a differential analyzer were made in 1939 by
                 the late A. M. Turing. These were interrupted by the
                 war and later rendered obsolete by the advent of the
                 electronic digital computers.''",
  remark-3 =     "From page 293: ``In 1947 the writer programmed an
                 extension of the work of Titchmarsh [on the zeros of
                 the Riemann zeta function] for the ENIAC, the only
                 electronic computer then in operation. However, before
                 the program could be run, the ENIAC was drastically
                 modified thus rendering it useless for the problem.''",
  remark-4 =     "From page 293: ``In June 1950, Turing used the
                 Manchester University Mark 1 electronic digital
                 computer to examine the zeta-function for $24,937.96 <
                 t < 25,735.93$ (that is for $63 < \sqrt{\tau} < 6.4$)
                 and found in this region of the critical strip that
                 there are about 1070 simple zeros all with $a = 1/2$.
                 In another short run the validity of the Riemann
                 Hypothesis was verified between Titchmarsh's upper
                 limit of $t = 1468$ and $t = 1540$. Only some twenty
                 hours of machine time was used. Unfortunately no
                 further time was made available and these incomplete
                 results were published in 1953.''",
}

@InProceedings{Luke:1956:RFAa,
  author =       "Yudell L. Luke",
  editor =       "????",
  booktitle =    "{ACM'56: Proceedings of the 1956 11th ACM national
                 meeting}",
  title =        "On rational function approximations to the exponential
                 function with application to the practical solution of
                 linear differential difference equations with constant
                 coefficients",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "13--16",
  year =         "1956",
  DOI =          "https://doi.org/10.1145/800258.808937",
  bibdate =      "Fri Dec 21 08:53:15 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See errata and addenda \cite{Luke:1956:RFAb}.",
  URL =          "https://dl.acm.org/ft_gateway.cfm?id=808937",
  acknowledgement = ack-nhfb,
}

@InProceedings{Luke:1956:RFAb,
  author =       "Yudell L. Luke",
  editor =       "????",
  booktitle =    "{ACM'56: Proceedings of the 1956 11th ACM national
                 meeting}",
  title =        "On rational function approximations to the exponential
                 function with application to the practical solution of
                 linear differential difference equations with constant
                 coefficients: Errata and addenda",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "177--178",
  year =         "1956",
  DOI =          "https://doi.org/10.1145/800258.808979",
  bibdate =      "Fri Dec 21 08:53:15 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Luke:1956:RFAa}.",
  URL =          "https://dl.acm.org/ft_gateway.cfm?id=808979",
  acknowledgement = ack-nhfb,
}

@Book{Sneddon:1956:SFM,
  author =       "Ian Naismith Sneddon",
  title =        "Special Functions of Mathematical Physics and
                 Chemistry",
  volume =       "19",
  publisher =    "Oliver and Boyd",
  address =      "Edinburgh, UK",
  edition =      "Third",
  pages =        "viii + 164",
  year =         "1956",
  LCCN =         "QA1 U588 v. 19",
  bibdate =      "Sat Oct 30 18:41:48 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "University mathematical texts",
  acknowledgement = ack-nhfb,
  remark =       "See second edition \cite{Sneddon:1961:SFM} and third
                 edition \cite{Sneddon:1980:SFM}.",
  subject =      "Functions, Special",
}

@Book{Stratton:1956:SWF,
  author =       "Julius Adams Stratton",
  title =        "Spheroidal Wave Functions, Including Tables of
                 Separation Constants and Coefficients",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiii + 613",
  year =         "1956",
  LCCN =         "QA405 .S8",
  bibdate =      "Sat Apr 1 14:32:29 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1901--1994",
  subject =      "Wave mechanics; Spheroidal functions",
}

@Book{Flammer:1957:SWF,
  author =       "Carson Flammer",
  title =        "Spheroidal Wave Functions",
  publisher =    pub-STANFORD,
  address =      pub-STANFORD:adr,
  pages =        "ix + 220",
  year =         "1957",
  LCCN =         "QA405 .F55",
  bibdate =      "Sat Apr 1 14:32:29 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "A Stanford Research Institute monograph",
  acknowledgement = ack-nhfb,
  remark =       "The basis for this monograph was work done at Stanford
                 Research Institute for the United States Air Force
                 Cambridge Research Center under Contract AF 19
                 (604)-1296.",
  subject =      "Spheroidal functions",
}

@Article{Franklin:1957:CARb,
  author =       "Joel Franklin and Bernard Friedman",
  title =        "A convergent asymptotic representation for integrals",
  journal =      j-PROC-CAMBRIDGE-PHIL-SOC,
  volume =       "53",
  pages =        "612--619",
  year =         "1957",
  CODEN =        "PCPSA4",
  ISSN =         "0008-1981",
  MRclass =      "42.1X",
  MRnumber =     "0090691",
  MRreviewer =   "P. Henrici",
  bibdate =      "Tue Feb 06 15:03:36 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2F167020D3A1F98182882E99549E7751/S0305004100032667a.pdf/a-convergent-asymptotic-representation-for-integrals.pdf",
  abstract =     "This paper represents a new method for obtaining an
                 asymptotic representation for integrals of the form $
                 \int_0^\infty e^{-p x} x^{c - 1} f(x) \, d x $ when $p$
                 is large. It is shown that if $ f(x)$ satisfies certain
                 conditions this representation is also convergent.
                 Numerical calculations seem to show that the first term
                 of the representation gives a close approximation to
                 the value of the integral for a wide range of values of
                 $p$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Cambridge Philosophical Society.
                 Mathematical and physical sciences",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=PSP",
  remark =       "See applications in
                 \cite{Temme:2015:AMI,Navas-Palencia:2018:HPC}.",
}

@Article{Hitchcock:1957:PAB,
  author =       "A. J. M. Hitchcock",
  title =        "Polynomial Approximations to {Bessel} Functions of
                 Order Zero and One and to Related Functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "11",
  number =       "58",
  pages =        "86--88",
  month =        apr,
  year =         "1957",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Mon Feb 27 08:05:17 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2002156",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Kogbetliantz:1957:CEN,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of {$ e^N $} for $ - \infty < {N} < +
                 \infty $ Using an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "1",
  number =       "2",
  pages =        "110--115",
  month =        apr,
  year =         "1957",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.12.0110",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "68.0X",
  MRnumber =     "19,775d",
  bibdate =      "Tue Sep 06 20:55:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  reviewer =     "W. F. Freiberger",
}

@Article{Linskii:1957:CEF,
  author =       "V. S. Linski{\u{\i}}",
  title =        "Calculation of elementary functions on automatic
                 digital machines. ({Russian})",
  journal =      "Vy{\v{c}}isl. Mat.",
  volume =       "2",
  pages =        "90--119",
  year =         "1957",
  MRclass =      "68.00",
  MRnumber =     "21 \#982",
  MRreviewer =   "J. W. Carr, III",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Luke:1957:C,
  author =       "Yudell L. Luke",
  title =        "On the Computation of $ \log {Z} $ and $ \operatorname
                 {arc} \tan {Z} $",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "11",
  number =       "57",
  pages =        "16--18",
  month =        jan,
  year =         "1957",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1957-0084855-1",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Miller:1957:NGS,
  author =       "J. C. P. Miller",
  title =        "Note on the General Solution of the Confluent
                 Hypergeometric Equation",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "11",
  number =       "58",
  pages =        "97--99",
  month =        apr,
  year =         "1957",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Mon Feb 27 08:05:17 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2002156",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Southard:1957:ATW,
  author =       "Thomas H. Southard",
  title =        "Approximation and Table of the {Weierstrass} $ \wp $
                 Function in the Equianharmonic Case for Real Argument",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "11",
  number =       "58",
  pages =        "99--100",
  month =        apr,
  year =         "1957",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Mon Feb 27 08:05:17 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2002156",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Stegun:1957:GBF,
  author =       "Irene A. Stegun and Milton Abramowitz",
  title =        "Generation of {Bessel} Functions on High Speed
                 Computers",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "11",
  number =       "60",
  pages =        "255--257",
  month =        oct,
  year =         "1957",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1957-0093939-3",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{T:1957:CHS,
  author =       "C. B. T.",
  title =        "Comment: {T. H. Southard, \booktitle{Approximation and
                 table of the Weierstrass $ \wp $ function in the
                 equianharmonic case for real argument}. [MTAC, this
                 issue, p. 99--100]}",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "11",
  number =       "58",
  pages =        "110--110",
  month =        apr,
  year =         "1957",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Mon Feb 27 08:05:17 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2002157",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Wilkes:1957:PPE,
  author =       "Maurice V. Wilkes and David J. Wheeler and Stanley
                 Gill",
  title =        "The Preparation of Programs for an Electronic Digital
                 Computer",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  pages =        "xiv + 238",
  year =         "1957",
  LCCN =         "QA76.5 .W52 1957",
  bibdate =      "Mon Feb 10 09:42:47 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also first edition \cite{Wilkes:1951:PPE}.",
  URL =          "https://b-ok.org/book/3668116/b363ff",
  acknowledgement = ack-nhfb,
  remark-1 =     "According to \cite{Anderson:2019:SAM}, this book
                 discusses the computation of integer population counts
                 on the Electronic Delay Storage Automatic Calculator
                 (EDSAC) computer using a recursive divide-and-conquer
                 algorithm. See also somewhat negative 1958 review by
                 Fernando J. Corbat{\'o}
                 \cite{https://doi.org/10.1063/1.3062687}.
                 Floating-point arithmetic is discussed on pages 60,
                 90--91, and 135--137.",
  remark-2 =     "From page 5: ``Each storage location in the EDSAC
                 holds 17 binary digits. In words representing numbers,
                 the binary point is regarded as being to the right of
                 the extreme left-hand digit; this digit (the most
                 significant digit) is used as a sign indicator and is
                 referred to as the sign digit. \ldots{} the capacity of
                 the accumulator is 70 digits; there is, therefore,
                 plenty of room to hold the full 33-digit product of two
                 17-digit numbers. \ldots{} A negative number $-x$
                 (where $O < x \leq 1$) is represented by a $1$ in the
                 sign-digit position, followed by the digits of $(1 -
                 x)$; for example, $1.1100\ldots{}$ represents $-(1 -
                 3/4) = -1/4$. \ldots{}. Another way of explaining the
                 representation of negative numbers is to regard the
                 sign digit as an ordinary numerical digit, and to say
                 that $-x$ is stored as the number $(2 - x)$. Note in
                 particular that $1.0000\ldots{}$ represents $-1$.''
                 [Page 59 calls this a {\em True complements}
                 representation, distinguished from one's complement.]",
  remark-3 =     "From page 35: ``The EDSAC has a facility which enables
                 an even-numbered storage location and the following
                 odd-numbered storage to be used as a single storage
                 location holding 35 binary digits.'' [This suggests the
                 word size in 18, not 17 as page 5 suggests. The
                 Wikipedia article on the EDSAC reports: ``The EDSAC's
                 main memory consisted of 1024 locations, though only
                 512 locations were initially installed. Each contained
                 18 bits, but the topmost bit was always unavailable due
                 to timing problems, so only 17 bits were used.'']",
  remark-4 =     "From page 36: ``The multiplier register of the
                 arithmetical unit is of sufficient capacity to hold a
                 long number, and the accumulator is of sufficient
                 capacity to hold the complete (69) binary digit
                 [including the sign bit] product of two long
                 numbers.''",
  remark-5 =     "From page 36: ``In some calculations, long numbers may
                 not provide sufficient precision. In such cases, the
                 programmer may make use of what is known as
                 double-length or double-precision working, in which two
                 long storage locations are used to hold the digits of a
                 single number.'' [this would be a quad-word number
                 holding 69 bits, including the sign bit.].",
  remark-6 =     "From page 60: ``\ldots{} two double-length numbers,
                 each stored in two locations, can be added and the
                 result put in two locations in the store, by means of
                 six orders''.",
  remark-7 =     "From page 90: ``Each number is expressed in the form
                 $a \cdot 10^p$, where $-10 \leq a \leq 10$ and $63 \leq
                 p < 63$ and is represented in the store by $a \cdot
                 2^{-11} + p \cdot 2^{-6}$.''",
  remark-8 =     "From page 91: ``Numbers are expressed in the form $a
                 \cdot 10^p$, where $a$ and $p$ are packed into a single
                 storage location. The number of digits defining $p$ may
                 be varied from 4 to 15 by means of a preset parameter,
                 so that a suitable value for the permissible range of
                 variation of numbers may be selected for a given
                 calculation.''",
  remark-9 =     "From page 91: ``Although the use of floating-point
                 operation can simplify the programmer's task by
                 relieving him of undue preoccupation with scaling, it
                 must not be thought that it solves all his
                 difficulties. In particular, the loss of significant
                 digits resulting from the subtraction of a number from
                 a nearly equal number can have serious consequences
                 unless proper precautions are taken.''",
  tableofcontents = "CHAPTER 1. THE ELEMENTS OF PROGRAM DESIGN / 1 \\
                 1-1 Introduction / 1 \\
                 1-2 Types of automatic computing machine / 1 \\
                 1-3 The EDSAC / 3 \\
                 1-4 Store / 5 \\
                 1-5 Arithmetical unit / 5 \\
                 1-6 Form of numbers in the machine / 5 \\
                 1-7 Form of orders in the machine / 6 \\
                 1-8 Storage of orders / 6 \\
                 1-9 Written form of orders / 7 \\
                 1-10 Some simple examples / 7 \\
                 Exercises A / 9 \\
                 1-11 Jump orders / 9 \\
                 Exercises B / 11 \\
                 1-12 Repeated groups of orders / 11 \\
                 1-13 The use of the B-register / 15 \\
                 Exercises C / 18 \\
                 1-14 Equivalence between orders and numbers;
                 pseudo-orders / 18 \\
                 1-15 Use of the arithmetical unit for constructing or
                 modifying orders / 20 \\
                 1-16 The mix order / 23 \\
                 Exercises D / 24 \\
                 CHAPTER 2. SUBROUTINES / 25 \\
                 2-1 Introduction / 25 \\
                 2-2 Relative numbering of addresses / 25 \\
                 2-3 Internal and external forms of orders / 26 \\
                 2-4 Reading of orders from the input tape / 28 \\
                 2-5 Open and closed subroutines / 29 \\
                 2-6 Entering and leaving a closed subroutine / 29 \\
                 2-7 Closed B subroutines / 30 \\
                 2-8 Closed A subroutines / 31 \\
                 2-9 Use of library subroutines / 32 \\
                 Exercises E / 33 \\
                 2-10 Long numbers / 35 \\
                 2-11 Some further orders in the order code / 36 \\
                 2-12 Scale factors / 38 \\
                 2-13 Control combinations / 39 \\
                 Exercises F / 40 \\
                 2-14 Relative addresses in control combinations / 41
                 \\
                 2-15 Extension of the use of relative addresses / 41
                 \\
                 2-16 Setting of the constants to be added by terminal
                 code letters / 43 \\
                 2-17 Complete table of terminal code letters / 44 \\
                 2-18 Parameters / 45 \\
                 2-19 Preset parameters / 46 \\
                 2-20 Program parameters / 46 \\
                 2-21 Standard procedure for setting preset parameters /
                 46 \\
                 2-22 Interpretive subroutines / 47 \\
                 Exercises G / 49 \\
                 CHAPTER 3. PROGRAMMING FOR OTHER MACHINES / 51 \\
                 3-1 Introduction / 51 \\
                 3-2 Single-address codes / 52 \\
                 3-3 Multi-address codes / 53 \\
                 3-4 Multiplication and division / 56 \\
                 3-5 Source-destination codes / 57 \\
                 3-6 Representation of negative numbers / 59 \\
                 3-7 Miscellaneous facilities / 60 \\
                 3-8 Minimum-access coding / 61 \\
                 3-9 The evaluation of an order code / 63 \\
                 3-10 Use of an auxiliary store / 64 \\
                 CHAPTER 4. INPUT AND OUTPUT / 66 \\
                 4-1 Introduction / 66 \\
                 4-2 Input of numbers / 66 \\
                 4-3 Output of numbers / 67 \\
                 4-4 Input of orders / 69 \\
                 4-5 Recognition of the code letter S / 72 \\
                 4-6 Economy of input and output time / 72 \\
                 4-7 Some features of input systems used with other
                 machines / 73 \\
                 4-8 Punched tape / 73 \\
                 4-9 Punched cards / 75 \\
                 CHAPTER 5. THE LIBRARY OF SUBROUTINES / 80 \\
                 5-1 Introduction / 80 \\
                 5-2 Library catalog / 80 \\
                 5-3 Input subroutines / 81 \\
                 5-4 Output subroutines / 81 \\
                 5-5 Division subroutines / 82 \\
                 5-6 Trigonometric and other functions / 82 \\
                 5-7 The economization of a power series by the use of
                 Chebyshev polynomials / 83 \\
                 5-8 Quadrature / 86 \\
                 5-9 Integration of ordinary differential equations / 87
                 \\
                 5-10 Library subroutines Gl2 and G13: Runge--Kutta
                 processes / 88 \\
                 5-11 The independent variable / 88 \\
                 5-12 Definition of the Runge--Kutta--Gill process / 89
                 \\
                 5-13 Taylor-series method / 90 \\
                 5-14 Interpretive subroutines / 90 \\
                 5-15 Floating-point subroutines / 90 \\
                 CHAPTER 6. DIAGNOSIS OF ERRORS IN PROGRAM / 92 \\
                 6-1 Introduction / 92 \\
                 6-2 Proofreading of programs / 93 \\
                 6-3 Punching / 93 \\
                 6-4 Locating mistakes in a program- / 94 \\
                 6-5 Subroutines for checking programs / 96 \\
                 6-6 The development of a program / 97 \\
                 CHAPTER 7. EXAMPLES OF COMPLETE PROGRAMS FOR THE EDSAC
                 / 99 \\
                 EXAMPLE 1 Calculation of $e^{-\sin x}$ / 99 \\
                 EXAMPLE 2 The evaluation of a definite integral / 102
                 \\
                 EXAMPLE 3 Integration of an ordinary differential
                 equation / 108 \\
                 EXAMPLE 4 Evaluation of a Fourier transform / 113 \\
                 EXAMPLE 5 Evaluation of a definite integral / 118 \\
                 CHAPTER 8. AUTOMATIC PROGRAMMING / 126 \\
                 8-1 Introduction / 126 \\
                 8-2 Conversion versus interpretation / 127 \\
                 8-3 Assembly of a program / 127 \\
                 8-4 Floating addresses / 129 \\
                 8-5 Formula recognition / 136 \\
                 Part Two: SPECIFICATIONS OF EDSAC LIBRARY SUBROUTINES /
                 139 \\
                 CATEGORY A. Subroutines to carry out floating-point
                 arithmetic / 140 \\
                 CATEGORY B. Subroutines to perform arithmetical
                 operations on complex numbers / 142 \\
                 CATEGORY C. Error-diagnosis subroutines / 144 \\
                 CATEGORY D. Division subroutines / 146 \\
                 CATEGORY E. Exponential subroutines / 148 \\
                 CATEGORY F. General subroutines relating to functions /
                 148 \\
                 CATEGORY G. Subroutines for the integration of
                 differential equations / 150 \\
                 CATEGORY L. Subroutines for evaluating logarithms / 153
                 \\
                 CATEGORY M. Miscellaneous subroutines / 154 \\
                 CATEGORY N. Operations on double-length numbers / 156
                 \\
                 CATEGORY P. Print subroutines / 158 \\
                 CATEGORY Q. Quadrature subroutines / 162 \\
                 CATEGORY R. Input subroutines / 164 \\
                 CATEGORY s. Subroutines for evaluating fractional
                 powers / 168 \\
                 CATEGORY T. Subroutines for calculating trigonometric
                 functions / 169 \\
                 CATEGORY Z. Post-mortem routines / 170 \\
                 PART THREE: PROGRAMS OF SELECTED EDSAC LIBRARY
                 SUBROUTINES / 173 \\
                 APPENDIX 1. Input and output codes of the EDSAC / 212
                 \\
                 APPENDIX 2. Order code and controls of the EDSAC / 214
                 \\
                 APPENDIX 3. The initial input routine of the EDSAC /
                 218 \\
                 APPENDIX 4. Control combinations / 221 \\
                 APPENDIX 5. Specimen solutions to programming exercises
                 / 223 \\
                 BIBLIOGRAPHY / 233 \\
                 INDEX / 237",
}

@Article{Beattie:1958:TFZ,
  author =       "Curtis L. Beattie",
  title =        "Table of First 700 Zeros of {Bessel} Functions --- {$
                 J_l(x) $} and {$ J^{\prime }_l(x) $}",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "37",
  number =       "3",
  pages =        "689--697",
  month =        may,
  year =         "1958",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  MRclass =      "65.00",
  MRnumber =     "0093928 (20 \#448)",
  MRreviewer =   "J. C. P. Miller",
  bibdate =      "Tue Nov 9 11:15:54 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1958/BSTJ.1958.3703.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol37/bstj37-3-689.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}

@Article{Belaga:1958:SPI,
  author =       "{\`E}. G. Belaga",
  title =        "Some problems involved in the calculation of
                 polynomials",
  journal =      j-DOKL-AKAD-NAUK,
  volume =       "123",
  pages =        "775--777",
  year =         "1958",
  CODEN =        "DANKAS",
  ISSN =         "0002-3264",
  MRclass =      "65.00",
  MRnumber =     "105192",
  MRreviewer =   "John Todd",
  bibdate =      "Fri Oct 20 10:34:44 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Doklady Akademii Nauk SSSR",
  journal-URL =  "http://istina.msu.ru/journals/366838/",
  keywords =     "number of multiplications to evaluate a polynomial",
}

@Book{Bowman:1958:IBF,
  author =       "Frank Bowman",
  title =        "Introduction to {Bessel} Functions",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "x + 135",
  year =         "1958",
  LCCN =         "QA408 .B68i 1958",
  bibdate =      "Sat Jan 15 17:24:26 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  remark =       "An unabridged and unaltered republication of the first
                 edition.",
  subject =      "Bessel functions",
}

@Article{Dingle:1958:AEC,
  author =       "R. B. Dingle",
  title =        "Asymptotic Expansions and Converging Factors. {III}.
                 Gamma, Psi and Polygamma Functions, and {Fermi--Dirac}
                 and {Bose--Einstein} Integrals",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
  volume =       "244",
  number =       "1239",
  pages =        "484--490",
  day =          "22",
  month =        apr,
  year =         "1958",
  CODEN =        "PRLAAZ",
  ISSN =         "0080-4630",
  bibdate =      "Mon Jun 18 07:22:24 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/100264",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society of London. Series A,
                 Mathematical and physical sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/content/current",
}

@Article{Goldstein:1958:BFL,
  author =       "M. Goldstein and R. M. Thaler",
  title =        "{Bessel} Functions for Large Arguments",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "12",
  number =       "61",
  pages =        "18--26",
  month =        jan,
  year =         "1958",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1958-0102906-3",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Kogbetliantz:1958:CANa,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of Arctan {N} for $ - \infty < {N} < +
                 \infty $ Using an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "2",
  number =       "1",
  pages =        "43--53",
  month =        jan,
  year =         "1958",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.21.0043",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "65.3X",
  MRnumber =     "19,982e",
  bibdate =      "Wed Aug 31 13:40:00 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  reviewer =     "C. B. Haselgrove",
}

@Article{Kogbetliantz:1958:CANb,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of Arcsin {N} for $ 0 < {N} < 1 $ Using an
                 Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "2",
  number =       "3",
  pages =        "218--222",
  month =        jul,
  year =         "1958",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.23.0218",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "65.3X",
  MRnumber =     "19,1197c",
  bibdate =      "Wed Aug 31 13:41:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  reviewer =     "C. B. Haselgrove",
}

@Book{Lewin:1958:DAF,
  author =       "Leonard Lewin",
  title =        "Dilogarithms and Associated Functions",
  publisher =    "Macdonald",
  address =      "London, UK",
  pages =        "353",
  year =         "1958",
  LCCN =         "QA351 .L5",
  bibdate =      "Fri Jun 16 13:51:36 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "22-Jul-1919--13-Aug-2007",
  author-url =   "https://en.wikipedia.org/wiki/Leonard_Lewin_(telecommunications_engineer)",
  remark =       "Foreword by J. C. P. Miller",
  subject =      "Dilogarithms",
}

@Article{Wadey:1958:TSR,
  author =       "W. G. Wadey",
  title =        "Two Square-Root Approximations",
  journal =      j-CACM,
  volume =       "1",
  number =       "11",
  pages =        "13--14",
  month =        nov,
  year =         "1958",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/368932.368936",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:22 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Wadey58",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Wadey58",
}

@Article{Corbato:1959:GSB,
  author =       "Fernando J. Corbat{\'o} and Jack L. Uretsky",
  title =        "Generation of Spherical {Bessel} Functions in Digital
                 Computers",
  journal =      j-J-ACM,
  volume =       "6",
  number =       "3",
  pages =        "366--375",
  month =        jul,
  year =         "1959",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Mon Dec 05 20:07:17 1994",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "https://dl.acm.org/loi/jacm",
}

@Article{Davis:1959:LEI,
  author =       "P. J. Davis",
  title =        "{Leonhard Euler}'s integral: a historical profile of
                 the gamma function: In Memoriam: {Milton Abramowitz}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "66",
  number =       "10",
  pages =        "849--869",
  month =        dec,
  year =         "1959",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "00 (33.00)",
  MRnumber =     "MR0106810 (21 #5540)",
  bibdate =      "Mon Nov 24 20:57:26 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2309786",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{DiDonato:1959:NFC,
  author =       "A. R. DiDonato and A. V. Hershey",
  title =        "New Formulas for Computing Incomplete Elliptic
                 Integrals of the First and Second Kind",
  journal =      j-J-ACM,
  volume =       "6",
  number =       "4",
  pages =        "515--526",
  month =        oct,
  year =         "1959",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/320998.321005",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65.00",
  MRnumber =     "0107353",
  MRreviewer =   "F. Stallmann",
  bibdate =      "Mon Dec 05 20:10:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
}

@Book{Emde:1959:TEF,
  author =       "Fritz Emde",
  title =        "{Tafeln Elementarer Funktionen} ({German}) [Tables of
                 Elementary Functions]",
  publisher =    "B. T. Teubner",
  address =      "Leipzig, Germany and Berlin, Germany",
  edition =      "Third",
  pages =        "xii + 181",
  year =         "1959",
  LCCN =         "QA47 .E5",
  bibdate =      "Fri Jun 11 12:34:09 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://lccn.loc.gov/61020314",
  acknowledgement = ack-nhfb,
  author-dates = "1873--1951",
  language =     "German",
}

@Article{Gautschi:1959:EIL,
  author =       "W. Gautschi",
  title =        "Exponential integral $ \int_1^\infty e^{-x t} t^{-n}
                 \, d t $ for large values of $n$",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "62",
  number =       "3",
  pages =        "123--125",
  month =        mar,
  year =         "1959",
  DOI =          "https://doi.org/10.6028/jres.062.022",
  ISSN =         "0091-0635",
  bibdate =      "Sat Feb 18 14:39:27 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Research of the National Bureau of
                 Standards (1934)",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
}

@Article{Goldstein:1959:RTC,
  author =       "M. Goldstein and R. M. Thaler",
  title =        "Recurrence Techniques for the Calculation of {Bessel}
                 Functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "13",
  number =       "66",
  pages =        "102--108",
  month =        apr,
  year =         "1959",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1959-0105794-5",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Greenhill:1959:AEF,
  author =       "Alfred George Greenhill",
  title =        "The Applications of Elliptic Functions",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xi + 357",
  year =         "1959",
  bibdate =      "Wed Mar 15 08:21:33 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Greenhill:1892:AEF}.",
  acknowledgement = ack-nhfb,
  author-dates = "1847--1927",
  remark =       "Reprint of \cite{Greenhill:1892:AEF}.",
}

@Article{Kogbetliantz:1959:CSC,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of $ \sin {N} $, $ \cos {N} $, and $ {M} $
                 th Root of $ {N} $ Using an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "3",
  number =       "2",
  pages =        "147--152",
  month =        apr,
  year =         "1959",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.32.0147",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "65.00",
  MRnumber =     "21 \#964",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  reviewer =     "B. A. Chartres",
}

@Article{Kreyszig:1959:RUE,
  author =       "Erwin Kreyszig and John Todd",
  title =        "The radius of univalence of the error function",
  journal =      j-NUM-MATH,
  volume =       "1",
  pages =        "78--89",
  month =        dec,
  year =         "1959",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 20:47:18 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Longman:1959:STT,
  author =       "I. M. Longman",
  title =        "A Short Table of $ \int^\infty_x {J}_0 (t)t^{-n} d t $
                 and $ \int^\infty_x {J}_1 (t) t^{-n} d t $ (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "13",
  number =       "68",
  pages =        "306--311",
  month =        oct,
  year =         "1959",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1959-0108892-5",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 6-digit values for $ n = 1, 2, \ldots {},
                 22 $ and for $ x = 1, 2, \ldots {}, 10 $.",
}

@Article{Luke:1959:ECH,
  author =       "Yudell L. Luke",
  title =        "Expansion of the Confluent Hypergeometric Function in
                 Series of {Bessel} Functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "13",
  number =       "68",
  pages =        "261--271",
  month =        oct,
  year =         "1959",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1959-0107027-2",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Pan:1959:CSC,
  author =       "V. Ya. Pan",
  title =        "Certain schemes for the calculation of values of
                 polynomials with real coefficients",
  journal =      "Problemy Kibernetiki",
  volume =       "5",
  number =       "??",
  pages =        "17--29",
  month =        "????",
  year =         "1959",
  bibdate =      "Fri Oct 20 10:40:33 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Also available as English translation JPRS No.
                 11045.",
  acknowledgement = ack-nhfb,
  ajournal =     "Probl. Kibernetiki",
  keywords =     "number of multiplications to evaluate a polynomial",
  language =     "Russian",
  remark =       "Check: MathSciNet does not cover this volume, or
                 record this paper, and the year may be wrong (based on
                 available volume/year list entries). Cited in
                 \cite[ref. 5, p. 178]{Fike:1967:MEP}.",
}

@Article{Pan:1959:SCP,
  author =       "V. Ya. Pan",
  title =        "Schemes for the computation of polynomials with real
                 coefficients",
  journal =      j-DOKL-AKAD-NAUK,
  volume =       "127",
  number =       "2",
  pages =        "266--269",
  month =        "????",
  year =         "1959",
  CODEN =        "DANKAS",
  ISSN =         "0002-3264",
  bibdate =      "Fri Oct 20 10:38:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Doklady Akademii nauk SSSR",
  journal-URL =  "http://istina.msu.ru/journals/366838/",
  keywords =     "number of multiplications to evaluate a polynomial",
  language =     "Russian",
}

@Article{Sarafyan:1959:NMC,
  author =       "Diran Sarafyan",
  title =        "A New Method of Computation of Square Roots Without
                 Using Division",
  journal =      j-CACM,
  volume =       "2",
  number =       "11",
  pages =        "23--24",
  month =        nov,
  year =         "1959",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/368481.368511",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:24 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See comments \cite{Traub:1960:CNM}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Sarafyan59",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sarafyan59",
}

@Article{Sherry:1959:CGF,
  author =       "M. E. Sherry and S. Fulda",
  title =        "Calculation of Gamma Functions to High Accuracy (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "13",
  number =       "68",
  pages =        "314--315",
  month =        oct,
  year =         "1959",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1959-0108891-3",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@InProceedings{Stiefel:1959:NMT,
  author =       "Eduard L. Stiefel",
  title =        "Numerical methods of {Tchebycheff} approximation",
  crossref =     "Langer:1959:NAP",
  pages =        "217--232",
  year =         "1959",
  MRclass =      "65.00 (41.00)",
  MRnumber =     "0107961",
  MRreviewer =   "M. R. Hestenes",
  bibdate =      "Wed Sep 2 16:23:13 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)",
}

@Article{Strachey:1959:TSR,
  author =       "C. Strachey",
  title =        "On taking the square root of a complex number",
  journal =      j-COMP-J,
  volume =       "2",
  number =       "2",
  pages =        "89--89",
  month =        jul,
  year =         "1959",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/2.2.89",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:55:11 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/compj1950.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Volder:1959:CCT,
  author =       "Jack Volder",
  title =        "The {CORDIC} Computing Technique",
  journal =      "Proceedings of the Western Joint Computer Conference",
  pages =        "257--261",
  year =         "1959",
  DOI =          "https://doi.org/10.1145/1457838.1457886",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Graphics/siggraph/Pre.1975.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions",
}

@Article{Volder:1959:CTC,
  author =       "Jack E. Volder",
  title =        "The {CORDIC} Trigonometric Computing Technique",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-8",
  number =       "3",
  pages =        "330--334",
  month =        sep,
  year =         "1959",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1959.5222693",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:56:45 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222693",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Beam:1960:ACE,
  author =       "A. Beam",
  title =        "{Algorithm 14}: {Complex} exponential integral",
  journal =      j-CACM,
  volume =       "3",
  number =       "7",
  pages =        "406--406",
  month =        jul,
  year =         "1960",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/367349.367351",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:27 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\Ei(z)$; special functions",
  remark =       "Fullerton: 30-line Algol procedure incorrectly
                 labelled algorithm 13.",
}

@Article{Haimovici:1960:MRE,
  author =       "Corina Haimovici",
  title =        "A method of representing elementary functions in
                 algebras of finite order. ({Romanian})",
  journal =      "An. {\c{S}}ti. Univ. ``Al. I. Cuza'' Ia{\c{s}}i
                 Sec{\c{t}} I. (N.S.)",
  volume =       "6",
  pages =        "507--515",
  year =         "1960",
  MRclass =      "26.00",
  MRnumber =     "24 \#A1342",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Harumi:1960:VTN,
  author =       "Kasabur{\^o} Harumi and Shigetoshi Katsura and John W.
                 {Wrench, Jr.}",
  title =        "Values of {$ \frac {2}{\pi } \int^\infty_0 \Big (\frac
                 {\sin t}{t} \Big)^n d t $} (in {Technical Notes and
                 Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "14",
  number =       "72",
  pages =        "379--379",
  month =        oct,
  year =         "1960",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1960-0122010-7",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 10-digit table for $ n = 1, 2, \ldots {},
                 30 $.",
}

@InCollection{Kogbetliantz:1960:GEF,
  author =       "E. G. Kogbetliantz",
  title =        "Generation of elementary functions",
  crossref =     "Ralston:1960:MMD",
  pages =        "7--35",
  year =         "1960",
  MRclass =      "68.00 (65.00)",
  MRnumber =     "22 \#8681",
  MRreviewer =   "J. C. P. Miller",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Lang:1960:ECC,
  author =       "H. A. Lang",
  title =        "On the Evaluation of Certain Complex Elliptic
                 Integrals (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "14",
  number =       "70",
  pages =        "195--199",
  month =        apr,
  year =         "1960",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1960-0112241-4",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Lebedev:1960:GMT,
  author =       "A. V. (Aleksandr Vasil'evich) Lebedev and R. M. (Rimma
                 Maksimova) Fedorova and Nina Mikhollovna Burunova",
  title =        "A Guide to Mathematical Tables",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "xlvi + 586",
  year =         "1960",
  LCCN =         "Z6654.T3 L42",
  bibdate =      "Mon Feb 13 17:12:14 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "English edition prepared by D. G. Fry from the Russian
                 original.",
  acknowledgement = ack-nhfb,
  subject =      "Mathematics; Tables; Indexes",
  tableofcontents = "Front Cover \\
                 A Guide to Mathematical Tables \\
                 Copyright Page \\
                 Translator's Preface \\
                 Preface \\
                 Index to the Section Headings in the Table of Contents
                 of the Guide and the Supplement \\
                 Table of Contents \\
                 Part One: Description of the Tables \\
                 1. Powers, Rational and Algebraic Functions \\
                 Positive Whole Powers \\
                 Fractional Positive Powers \\
                 Reciprocals (Negative Whole and Fractional Powers) \\
                 Rational Functions \\
                 Algebraic Functions \\
                 Complex Numbers and Their Powers \\
                 2. Trigonometric Functions. Various Values Connected
                 With the Circle and the Sphere \\
                 Natural Values of Trigonometric Functions \\
                 Various Expressions Containing Trigonometric Functions
                 \\
                 Derivatives and Powers of Trigonometric Functions \\
                 Reciprocal Trigonometric Functions of A Complex
                 Variable \\
                 Geometric Quantities \\
                 Tables For Converting From One Angular Measure to
                 Another \\
                 3. Exponential and Hyperbolic Functions \\
                 Exponential Functions \\
                 Hyperbolic Functions \\
                 Expressions Containing Trigonometric and Hyperbolic
                 Functions \\
                 Inverse Hyperbolic Functions \\
                 4. Logarithms \\
                 Common Logarithms and Antilogarithms \\
                 Natural Logarithms \\
                 Logarithms to Base 2 \\
                 5. Factorials, Euler Integrals and Related Functions
                 \\
                 Factorials \\
                 the Gamma Function \\
                 the Psi Function and Its Derivatives \\
                 the Beta Function \\
                 Certain Constants \\
                 6. Sine and Cosine Integrals, Exponential and
                 Logarithmic Integrals and Related Functions \\
                 Sine and Cosine Integrals \\
                 Hyperbolic Sine and Cosine Integrals \\
                 Exponential Integral \\
                 Logarithmic Integral \\
                 Generalised and Composite Integral Functions \\
                 Integral Functions of Complex Argument \\
                 7. Probability Integrals and Related Functions \\
                 Functions of the Distribution of Probability and
                 Related Functions \\
                 Probability Integrals and Expressions Containing
                 Probability Integrals \\
                 Tables in Which the Integral Serves As the Argument \\
                 Probability Integrals of Complex Argument \\
                 Derivatives of Various Orders of Probability
                 Distribution Functions \\
                 Zeros of Probability Integrals \\
                 Logarithms of Probability Integrals \\
                 Fresnel Integrals and Related Functions \\
                 8. Elliptic Integrals and Elliptic Functions \\
                 Moduli of the Integrals \\
                 Complete Elliptic Integrals \\
                 Incomplete Elliptic Integrals \\
                 Elliptic Functions \\
                 Theta Functions \\
                 9. Legendre Functions and Polynomials \\
                 Legendre Polynomials and Legendre Functions of the
                 First Kind \\
                 Associated Legendre Functions of the First Kind \\
                 Roots of Legendre Functions \\
                 Various Expressions Containing Legendre Functions \\
                 10. Cylinder Functions \\
                 Cylinder Functions of the First and Second Kinds of
                 Real Argument \\
                 Riccati--Bessel Functions \\
                 Lommel Functions of Two Real Variables \\
                 Cylinder Functions of the Third Kind (Hankel Functions)
                 \\
                 Cylinder Functions of the First and Second Kinds of
                 Imaginary Argument \\
                 Lommel Functions of Two Imaginary Variables \\
                 Cylinder Functions of Complex Argument \\
                 Thomson Functions",
}

@Manual{Maehly:1960:ACD,
  author =       "Hans J. Maehly",
  title =        "Approximations for the {Control Data 1604}",
  organization = inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "ii + 44",
  day =          "15",
  month =        jan,
  year =         "1960",
  bibdate =      "Tue Nov 06 00:39:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.bitsavers.org/pdf/cdc/1604/Approximations_For_The_Control_Data_1604_Mar60.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "$\arctan(x)$; $\cos(x)$; $\exp(x)$; $\log(x)$;
                 $\sin(x)$; $\sqrt(x)$; $\tan(x)$; CDC 1604",
}

@Article{Philip:1960:FI,
  author =       "J. R. Philip",
  title =        "The function $ \operatorname {inverfc} \theta $",
  journal =      j-AUSTRALIAN-J-PHYS,
  volume =       "13",
  number =       "1",
  pages =        "13--20",
  month =        mar,
  year =         "1960",
  CODEN =        "AUJPAS",
  DOI =          "https://doi.org/10.1071/PH600013",
  ISSN =         "0004-9506 (print), 1446-5582 (electronic)",
  ISSN-L =       "0004-9506",
  MRnumber =     "22 \9626",
  bibdate =      "Tue Sep 11 20:53:59 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "135.28302",
  abstract =     "The function inverfc $ \theta $ arises in certain
                 differential equations when concentration is taken as
                 an independent variable. It enters into a general
                 method of exact solution of the concentration-dependent
                 diffusion equation. An account is given of the
                 properties of this function, and of its derivatives and
                 integrals. The function\par

                  $$ B(\theta) = (2 / \pi^{1 / 2}) \exp [ -
                 (\operatorname {inverfc} \theta)^2] $$

                 \noindent is intimately connected with the first
                 integral of inverfc $ \theta $ and with its
                 derivatives. Tables of $ \operatorname {inverfc} \theta
                 $ and $ B(\theta) $ are given.",
  acknowledgement = ack-nhfb,
  fjournal =     "Australian Journal of Physics",
  journal-URL =  "http://www.publish.csiro.au/ph/content/allissues",
}

@Book{Rainville:1960:SF,
  author =       "Earl David Rainville",
  title =        "Special Functions",
  publisher =    pub-MACMILLAN,
  address =      pub-MACMILLAN:adr,
  pages =        "xii + 365",
  year =         "1960",
  ISBN =         "0-8284-0258-2",
  ISBN-13 =      "978-0-8284-0258-3",
  LCCN =         "QA331 R15; QA351 .R3 1971",
  bibdate =      "Mon Sep 3 16:04:28 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Reprinted in 1971.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  remark =       "Based upon the lectures on special functions which
                 \ldots{} [the author has] been giving at the University
                 of Michigan since 1946. Fullerton: All traditional
                 functions and polynomials are discussed in some
                 detail.",
  shorttableofcontents = "1: Infinite Products \\
                 2: The Gamma and Beta Functions \\
                 3: Asymptotic Series \\
                 4: The Hypergeometric Function \\
                 5: Generalized Hypergeometric Functions \\
                 6: Bessel Functions \\
                 7: The Confluent Hypergeometric Function \\
                 8: Generating Functions \\
                 9: Orthogonal Polynomials \\
                 10: Legendre Polynomials \\
                 11: Hermite Polynomials \\
                 12: Laguerre Polynomials \\
                 13: The Sheffer Classification and Related Topics \\
                 14: Pure Recurrence Relations \\
                 15: Symbolic Relations \\
                 16: Jacobi Polynomials \\
                 17: Ultraspherical and Gegenbauer Polynomials \\
                 18: Other Polynomial Sets \\
                 19: Elliptic Functions \\
                 20: Theta Functions \\
                 21: Jacobian Elliptic Functions \\
                 Bibliography \\
                 Index",
  subject =      "Functions, Special",
  tableofcontents = "1: Infinite Products \\
                 1. Introduction / 1 \\
                 2. Definition of an infinite product / 1 \\
                 3. A necessary condition for convergence . / 2 \\
                 4. The associated series of logarithms / 2 \\
                 5. Absolute convergence / 3 \\
                 6. Uniform convergence / 5 \\
                 \\
                 2: The Gamma and Beta Functions \\
                 7. The Euler or Mascheroni constant $\gamma$ / 8 \\
                 8. The Gamma function / 9 \\
                 9. A series for $\Gamma'(z) / \Gamma(z)$ / 10 \\
                 10. Evaluation of $\Gamma(1)$ and $\Gamma'(1)$ / 10 \\
                 11. The Euler product for $\Gamma(z)$ / 11 \\
                 12. The difference equation $\Gamma(z + 1) = z
                 \Gamma(z)$ / 12 \\
                 13. The order symbols $o$ and $O$ / 12 \\
                 14. Evaluation of certain infinite products / 13 \\
                 15. Euler's integral for $\Gamma(z)$ / 15 \\
                 16. The Beta function / 18 \\
                 17. The value of $\Gamma(z) \Gamma(1 - z)$ / 19 \\
                 18. The factorial function / 22 \\
                 19. Legendre's duplication formula / 23 \\
                 20. Gauss' multiplication theorem / 24 \\
                 21. A summation formula due to Euler / 26 \\
                 22. The behavior of $\log \Gamma(z)$ for large $|z|$ /
                 29 \\
                 \\
                 3: Asymptotic Series \\
                 23. Definition of an asymptotic expansion / 33 \\
                 24. Asymptotic expansions about infinity / 36 \\
                 25. Algebraic properties / 38 \\
                 26. Term-by-term integration / 39 \\
                 27. Uniqueness / 40 \\
                 28. Watson's lemma / 41 \\
                 \\
                 4: The Hypergeometric Function \\
                 29. The function $F(a, b; c; z)$ / 45 \\
                 30. A simple integral form / 47 \\
                 31. $F(a, b; c; 1)$ as a function of the parameters /
                 48 \\
                 32. Evaluation of $F(a, b; c; 1)$ / 48 \\
                 33. The contiguous function relations / 50 \\
                 34. The hypergeometric differential equation / 53 \\
                 35. Logarithmic solutions of the hypergeometric
                 equation / 54 \\
                 36. $F(a, b; c; 2)$ as a function of its parameters /
                 55 \\
                 37. Elementary series manipulations / 56 \\
                 38. Simple transformations / 58 \\
                 39. Relation between functions of $z$ and $1 - z$ / 61
                 \\
                 40. A quadratic transformation / 63 \\
                 41. Other quadratic transformations / 65 \\
                 42. A theorem due to Kummer / 68 \\
                 43. Additional properties / 68 \\
                 \\
                 5: Generalized Hypergeometric Functions \\
                 44. The function $_pF_q$ / 73 \\
                 45. The exponential and binomial functions / 74 \\
                 46. A differential equation / 74 \\
                 47. Other solutions of the differential equation / 76
                 \\
                 48. The contiguous function relations / 80 \\
                 49. A simple integral / 85 \\
                 50. The $_pF_q$ with unit argument / 85 \\
                 51. Saalsch{\"u}tz' theorem / 86 \\
                 52. Whipple's theorem / 88 \\
                 53. Dixon's theorem / 92 \\
                 54. Contour integrals of Barnes' type / 94 \\
                 55. The Barnes integrals and the function $_pF_q$ / 98
                 \\
                 56. A useful integral / 102 \\
                 \\
                 6: Bessel Functions \\
                 57. Remarks / 108 \\
                 58. Definition of $J_n(z)$ / 108 \\
                 59. Bessel's differential equation / 109 \\
                 60. Differential recurrence relations / 110 \\
                 61. A pure recurrence relation / 111 \\
                 62. A generating function / 112 \\
                 63. Bessel's integral / 114 \\
                 64. Index half an odd integer 114 , \\
                 65. Modified Bessel functions / 116 \\
                 66. Neumann polynomials / 116 \\
                 67. Neumann series / 119 \\
                 \\
                 7: The Confluent Hypergeometric Function \\
                 68. Basic properties of the $_1F_1$ / 123 \\
                 69. Kummer's first formula / 124 \\
                 70. Kummer's second formula / 125 \\
                 \\
                 8: Generating Functions \\
                 71. The generating function concept / 129 \\
                 72. Generating functions of the form $G(2 x t - t^2)$ /
                 131 \\
                 73. Sets generated by $e^t \psi(x t)$ / 132 \\
                 74. The generating functions $A(t) \exp[-x t / (1 -
                 t)]$ / 135 \\
                 75. Another class of generating functions / 137 \\
                 76. Boas and Buck generating functions / 140 \\
                 77. An extension / 143 \\
                 \\
                 9: Orthogonal Polynomials \\
                 78. Simple sets of polynomials / 147 \\
                 79. Orthogonality / 147 \\
                 80. An equivalent condition for orthogonality / 148 \\
                 81. Zeros of orthogonal polynomials / 149 \\
                 82. Expansion of polynomials / 150 \\
                 83. The three-term recurrence relation / 151 \\
                 84. The Christoffel--Darboux formula / 153 \\
                 85. Normalization; Bessel's inequality / 155 \\
                 \\
                 10: Legendre Polynomials \\
                 86. A generating function / 157 \\
                 87. Differential recurrence relations / 158 \\
                 88. The pure recurrence relation / 159 \\
                 89. Legendre's differential equation / 160 \\
                 90. The Rodrigues formula / 161 \\
                 91. Bateman's generating function / 162 \\
                 92. Additional generating functions / 163 \\
                 93. Hypergeometric forms of $P_n(x)$ / 163 \\
                 94. Brafman's generating functions / 167 \\
                 95. Special properties of $P_n(x)$ / 168 \\
                 96. More generating functions / 169 \\
                 97. Laplace's first integral form / 171 \\
                 98. Some bounds on $P_n(z)$ / 172 \\
                 99. Orthogonality / 173 \\
                 100. An expansion theorem / 176 \\
                 101. Expansion of $x^n$ / 179 \\
                 102. Expansion of analytic functions / 181 \\
                 \\
                 11: Hermite Polynomials \\
                 103. Definition of $H_n(x)$ / 187 \\
                 104. Recurrence relations / 188 \\
                 105. The Rodrigues formula / 189 \\
                 106. Other generating functions / 190 \\
                 107. Integrals / 190 \\
                 108. The Hermite polynomial as a $_2F_0$ / 191 \\
                 109. Orthogonality / 191 \\
                 110. Expansion of polynomials / 193 \\
                 111. More generating functions / 196 \\
                 \\
                 12: Laguerre Polynomials \\
                 112. The polynomial $L_n^{(\alpha)}(x)$ / 200 \\
                 113. Generating functions / 201 \\
                 114. Recurrence relations / 202 \\
                 115. The Rodrigues formula / 203 \\
                 116. The differential equation / 204 \\
                 117. Orthogonality / 204 \\
                 118. Expansion of polynomials / 206 \\
                 119. Special properties / 209 \\
                 120. Other generating functions / 211 \\
                 121. The simple Laguerre polynomials / 213 \\
                 \\
                 13: The Sheffer Classification and Related Topics \\
                 122. Differential operators and polynomial sets / 218
                 \\
                 123. Sheffer's $A$-type classification / 221 \\
                 124. Polynomials of Sheffer $A$-type zero / 222 \\
                 195. An extension of Sheffer's classification / 226 \\
                 126. Polynomials of $\sigma$-type zero / 228 \\
                 \\
                 14: Pure Recurrence Relations \\
                 127. Sister Celine's technique / 233 \\
                 128. A mild extension / 240 \\
                 \\
                 15: Symbolic Relations \\
                 129. Notation / 246 \\
                 130. Symbolic relations among classical polynomials /
                 247 \\
                 131. Polynomials of symbolic form $L_n(y(x))$ / 249 \\
                 \\
                 16: Jacobi Polynomials \\
                 132. The Jacobi polynomials / 254 \\
                 133. Bateman's generating function / 256 \\
                 134. The Rodrigues formula / 257 \\
                 135. Orthogonality / 258 \\
                 136. Differential recurrence relations / 261 \\
                 137. The pure recurrence relation / 263 \\
                 138. Mixed relations / 263 \\
                 139. Appell's functions of two variables / 265 \\
                 140. An elementary generating function / 269 \\
                 141. Brafman's generating functions / 271 \\
                 142. Expansion in series of polynomials / 272 \\
                 \\
                 17: Ultraspherical and Gegenbauer Polynomials \\
                 143. Definitions / 276 \\
                 144. The Gegenbauer polynomials / 277 \\
                 145. The ultraspherical polynomials / 283 \\
                 \\
                 18: Other Polynomial Sets \\
                 146. Bateman's $Z_n(x)$ / 285 \\
                 147. Rice's $H_n(\zeta, p, v)$ / 287 \\
                 148. Bateman's $F_n(z)$ / 289 \\
                 149. Sister Celine's polynomials / 290 \\
                 150. Bessel polynomials / 293 \\
                 151. Bedient's polynomials / 297 \\
                 152. Shively's pseudo-Laguerre and other polynomials /
                 298 \\
                 153. Bernoulli polynomials / 299 \\
                 154. Euler polynomials / 300 \\
                 155. Tchebicheff polynomials / 301 \\
                 \\
                 19: Elliptic Functions \\
                 156. Doubly periodic functions / 305 \\
                 157. Elliptic functions / 306 \\
                 158. Elementary properties / 306 \\
                 159. Order of an elliptic function / 308 \\
                 160. The Weierstrass function $P(z)$ / 309 \\
                 161. Other elliptic functions / 311 \\
                 162. A differential equation for $P(z)$ / 311 \\
                 163. Connection with elliptic integrals / 313 \\
                 \\
                 20: Theta Functions \\
                 164. Definitions / 314 \\
                 165. Elementary properties / 315 \\
                 166. The basic property table / 316 \\
                 167. Location of zeros / 319 \\
                 168. Relations among squares of theta functions / 322
                 \\
                 169. Pseudo addition theorems / 325 \\
                 170. Relation to the heat equation / 328 \\
                 171. The relation $\theta_1' = \theta_2 \theta_3
                 \theta_4$ / 329 \\
                 172. Infinite products / 332 \\
                 173. The value of $G$ / 334 \\
                 \\
                 21: Jacobian Elliptic Functions \\
                 174. A differential equation involving theta functions
                 / 339 \\
                 175. The function $\sn(u)$ / 342 \\
                 176. The functions $\cn(u)$ and $\dn(u)$ / 343 \\
                 177. Relations involving squares / 344 \\
                 178. Relations involving derivatives / 345 \\
                 179. Addition theorems / 347 \\
                 \\
                 Bibliography / 349 \\
                 \\
                 Index / 359",
}

@Article{Sarafyan:1960:DCS,
  author =       "Diran Sarafyan",
  title =        "Divisionless computation of square roots through
                 continued squaring",
  journal =      j-CACM,
  volume =       "3",
  number =       "5",
  pages =        "319--321",
  month =        may,
  year =         "1960",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/367236.367267",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.00",
  MRnumber =     "22\#8639",
  bibdate =      "Fri Nov 25 18:19:26 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions",
  ZMreviewer =   "M. Lotkin",
}

@Article{Sholander:1960:AEE,
  author =       "Marlow Sholander",
  title =        "Analytical expressions and elementary functions",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "67",
  number =       "3",
  pages =        "213--214",
  month =        mar,
  year =         "1960",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26.00",
  MRnumber =     "22 \#9553",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2309678",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Book{Slater:1960:CHF,
  author =       "Lucy Joan Slater",
  title =        "Confluent hypergeometric functions",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "247",
  year =         "1960",
  LCCN =         "QA351 .S56",
  bibdate =      "Sat Oct 30 21:01:55 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  remark =       "Fullerton: Discussion of properties and 7 decimal
                 place tables of $_1 F_1 (a; b; x)$.",
  subject =      "Hypergeometric functions",
}

@Article{Traub:1960:CNM,
  author =       "J. F. Traub",
  title =        "Comments on a recent paper [{``A New Method of
                 Computation of Square Roots Without Using
                 Division''}]",
  journal =      j-CACM,
  volume =       "3",
  number =       "2",
  pages =        "86--86",
  month =        feb,
  year =         "1960",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/366959.366989",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:25 MST 2005",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Sarafyan:1959:NMC}.",
  abstract =     "Mr. Diran Sarafyan, in his paper \booktitle{A New
                 Method of Computation of Square Roots Without Using
                 Divisions} (Communications, Nov. 1959) gave a way of
                 computing square roots which converges faster than the
                 standard Newton method. His technique can be
                 generalized as follows.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Traub60",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60",
}

@Article{Ward:1960:CCE,
  author =       "Morgan Ward",
  title =        "The Calculation of the Complete Elliptic Integral of
                 the Third Kind",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "67",
  number =       "3",
  pages =        "205--213",
  month =        mar,
  year =         "1960",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2309677",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Tue Feb 6 16:32:27 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2309677",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Book{Warmus:1960:TEF,
  author =       "Mieczys{\l}aw Warmus",
  title =        "Tables of elementary functions",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "vii + 567",
  year =         "1960",
  LCCN =         "QA55 .W3 1960",
  MRclass =      "65.05",
  MRnumber =     "23 \#B1141",
  MRreviewer =   "J. C. P. Miller",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Pa{\'n}stwowe Wydawnictwo Naukowe, Warsaw. Separately
                 bound table of proportional parts, 30 pp.",
  acknowledgement = ack-nhfb,
}

@Article{Wynn:1960:RAF,
  author =       "Peter Wynn",
  title =        "The Rational Approximation of Functions which are
                 Formally Defined by a Power Series Expansion",
  journal =      j-MATH-COMPUT,
  volume =       "14",
  number =       "70",
  pages =        "147--186",
  month =        apr,
  year =         "1960",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Barakat:1961:EIG,
  author =       "Richard Barakat",
  title =        "Evaluation of the Incomplete Gamma Function of
                 Imaginary Argument by {Chebyshev} Polynomials",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "73",
  pages =        "7--11",
  month =        jan,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Boersma:1961:TFR,
  author =       "J. Boersma",
  title =        "Two Formulas Relating to Elliptic Integrals of the
                 Third Kind (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "75",
  pages =        "296--298",
  month =        jul,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Bowman:1961:IEF,
  author =       "Frank Bowman",
  title =        "Introduction to Elliptic Functions with Applications",
  volume =       "922",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "115",
  year =         "1961",
  LCCN =         "QA343 .B76 1961",
  bibdate =      "Wed Mar 15 06:50:49 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "Unabridged and corrected republication of
                 \cite{Bowman:1953:IEF}.",
}

@Article{Cheney:1961:TNA,
  author =       "E. W. Cheney and H. L. Loeb",
  title =        "Two new algorithms for rational approximation",
  journal =      j-NUM-MATH,
  volume =       "3",
  number =       "1",
  pages =        "72--75",
  month =        dec,
  year =         "1961",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01386002",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 19:01:15 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Corrington:1961:ACE,
  author =       "Murlan S. Corrington",
  title =        "Applications of the Complex Exponential Integral",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "73",
  pages =        "1--6",
  month =        jan,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Ehrling:1961:NCI,
  author =       "G. Ehrling",
  title =        "On the Numerical Computation of Incomplete Elliptic
                 Integrals",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "1",
  number =       "1",
  pages =        "8--14",
  month =        mar,
  year =         "1961",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01961946",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:06 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=1&spage=8",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Fields:1961:EHF,
  author =       "Jerry L. Fields and Jet Wimp",
  title =        "Expansions of Hypergeometric Functions in
                 Hypergeometric Functions",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "76",
  pages =        "390--395",
  month =        oct,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Floyd:1961:ACE,
  author =       "Robert W. Floyd",
  title =        "An algorithm for coding efficient arithmetic
                 operations",
  journal =      j-CACM,
  volume =       "4",
  number =       "1",
  pages =        "42--51",
  month =        jan,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/366062.366082",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:30 MST 2005",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/Compiler.Lins.bib;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Robert W. Floyd (8 June 1936--25 September 2001)",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Description of binary subdivision method for computing
                 $n$-th powers in $ O(\log_2 (n))$ operations, as
                 referenced in \cite{Knuth:1962:EPC}.",
}

@Article{Froberg:1961:RCA,
  author =       "Carl-Erik Fr{\"o}berg",
  title =        "Rational {Chebyshev} Approximations of Elementary
                 Functions",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "1",
  number =       "4",
  pages =        "256--262",
  month =        dec,
  year =         "1961",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01933243",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:07 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See erratum \cite{Froberg:1963:ERC}.",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=4&spage=256",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "elementary functions",
}

@Article{Gautschi:1961:RCR,
  author =       "Walter Gautschi",
  title =        "Recursive Computation of the Repeated Integrals of the
                 Error Function",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "75",
  pages =        "227--232",
  month =        jul,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Gray:1961:BFI,
  author =       "Marion C. Gray",
  title =        "{Bessel} functions of integral order and complex
                 argument",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "169--169",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355578.366318",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "33.25",
  MRnumber =     "27\#1636",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The FORTRAN II source language [1, 2] places rather
                 severe restrictions on the form a subscript may take,
                 primarily because of the manner in which indices are
                 incremented in iterative loops. In the process of
                 constructing a compiler for a medium-sized (8008-word
                 memory) computer which will accept the FORTRAN II
                 source language, it became clear that the ``recursive
                 address calculation'' scheme, as used in the FORTRAN
                 compilers to minimize object-program running time, was
                 probably not the best one to use. This system,
                 described in some detail by Samelson and Bauer [3],
                 requires that the subscript expression be a linear
                 function of the subscripting variable. The alternative,
                 which requires complete evaluation of the ``storage
                 mapping function'', is usually rejected because of the
                 time required for the object program to perform the
                 necessary address calculation.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Bessel functions; special functions",
}

@Article{Herndon:1961:ABF,
  author =       "John R. Herndon",
  title =        "{Algorithm 57}: {Ber} or {Bei} Function",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "181--181",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355578.366476",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "bei functions; ber functions; special functions",
  remark =       "Fullerton: 20-line Algol procedure that only sums
                 series.",
}

@Article{Herndon:1961:ACEa,
  author =       "John R. Herndon",
  title =        "{Algorithm 55}: {Complete} elliptic integral of the
                 first kind",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "180--180",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355578.366454",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}

@Article{Herndon:1961:ACEb,
  author =       "John R. Herndon",
  title =        "{Algorithm 56}: {Complete} elliptic integral of the
                 second kind",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "180--181",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355578.366474",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}

@Article{Herndon:1961:AEC,
  author =       "John R. Herndon",
  title =        "{Algorithm 46}: {Exponential} of a Complex Number",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "178--178",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355578.366356",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\exp(z)$; $e^z$; elementary functions",
}

@Article{Herndon:1961:AGF,
  author =       "John R. Herndon",
  title =        "{Algorithm 54}: {Gamma} function for range $1$ to
                 $2$",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "180--180",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://dl.acm.org/doi/10.1145/355578.366453",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\Gamma(x)$; special functions",
}

@Article{Herndon:1961:ASN,
  author =       "J. R. Herndon",
  title =        "{Algorithm 49}: {Spherical} {Neumann} Function",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "179--179",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355578.355579",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Coleman:1978:RSN}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Neumann functions; special functions",
}

@Book{Hochstadt:1961:SFM,
  author =       "Harry Hochstadt",
  title =        "Special functions of mathematical physics",
  publisher =    pub-HRW,
  address =      pub-HRW:adr,
  pages =        "viii + 81",
  year =         "1961",
  ISBN =         "0-236-73011-8",
  ISBN-13 =      "978-0-236-73011-7",
  LCCN =         "QA351 H65 1961",
  bibdate =      "Sat Oct 30 18:01:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "Reprinted 1966.",
}

@Article{Landau:1961:PSW,
  author =       "H. J. Landau and H. O. Pollak",
  title =        "Prolate spheroidal wave functions, {Fourier} analysis
                 and uncertainty. {II}",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "40",
  number =       "1",
  pages =        "65--84",
  month =        jan,
  year =         "1961",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  MRclass =      "33.27",
  MRnumber =     "0140733 (25 \#4147)",
  MRreviewer =   "I. Marx",
  bibdate =      "Tue Nov 9 11:15:54 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1961/BSTJ.1961.4001.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol40/bstj40-1-65.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}

@Article{Luke:1961:EHF,
  author =       "Yudell L. Luke and Richard L. Coleman",
  title =        "Expansion of Hypergeometric Functions in Series of
                 Other Hypergeometric Functions",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "75",
  pages =        "233--237",
  month =        jul,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Rader:1961:CAC,
  author =       "P. J. Rader and Henry C. {Thacher, Jr.}",
  title =        "Certification of {Algorithm 14 [not 13]}: {Complex}
                 exponential integral",
  journal =      j-CACM,
  volume =       "4",
  number =       "2",
  pages =        "105--105",
  month =        feb,
  year =         "1961",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:30 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\Ei(z)$; special functions",
  remark =       "Fullerton: It's accurate but sometimes slow.",
}

@Article{Slepian:1961:PSW,
  author =       "D. Slepian and H. O. Pollak",
  title =        "Prolate spheroidal wave functions, {Fourier} analysis
                 and uncertainty. {I}",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "40",
  number =       "1",
  pages =        "43--63",
  month =        jan,
  year =         "1961",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  MRclass =      "33.27",
  MRnumber =     "0140732 (25 \#4146)",
  MRreviewer =   "I. Marx",
  bibdate =      "Tue Nov 9 11:15:54 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1961/BSTJ.1961.4001.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol40/bstj40-1-43.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}

@Book{Sneddon:1961:SFM,
  author =       "Ian Naismith Sneddon",
  title =        "Special Functions of Mathematical Physics and
                 Chemistry",
  publisher =    "Oliver and Boyd",
  address =      "Edinburgh, UK",
  edition =      "Ssecond",
  pages =        "184",
  year =         "1961",
  LCCN =         "QA331 .S65 1961",
  bibdate =      "Sat Oct 30 21:22:03 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "University mathematical texts",
  acknowledgement = ack-nhfb,
  remark =       "See first edition \cite{Sneddon:1956:SFM} and third
                 edition {Sneddon:1980:SFM}",
}

@Article{Spielberg:1961:ECF,
  author =       "Kurt Spielberg",
  title =        "Efficient Continued Fraction Approximations To
                 Elementary Functions",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "76",
  pages =        "409--417",
  month =        oct,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.20",
  MRnumber =     "MR0134842 (24 \#B894)",
  MRreviewer =   "M. E. Rose",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Thacher:1961:ISR,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "Iterated Square Root Expansions for the Inverse Cosine
                 and Inverse Hyperbolic Cosine",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "76",
  pages =        "399--403",
  month =        oct,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Weingarten:1961:TGC,
  author =       "Harry Weingarten and A. R. {Di Donato}",
  title =        "A Table of Generalized Circular Error",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "74",
  pages =        "169--173",
  month =        apr,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Werner:1961:CAG,
  author =       "Helmut Werner and Robert Collinge",
  title =        "{Chebyshev} Approximations to the Gamma Function (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "74",
  pages =        "195--197",
  month =        apr,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Wojcicki:1961:ABF,
  author =       "Maria E. Wojcicki",
  title =        "{Algorithm 44}: {Bessel} Functions Computed
                 Recursively",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "177--178",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355578.366341",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Bessel functions; special functions",
}

@Article{Albrecht:1962:FKM,
  author =       "J. Albrecht",
  title =        "{Fehlerschranken und Konvergenzbeschleunigung bei
                 einer monotonen oder alternierenden Iterationsfolge}.
                 ({German}) [{Error} Bounds and Convergence Acceleration
                 with a Monotone or Alternating Iteration Sequence]",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "196--208",
  month =        dec,
  year =         "1962",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon Oct 18 01:28:20 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "convergence acceleration",
  language =     "German",
}

@Article{Arscott:1962:BRI,
  author =       "F. M. Arscott",
  title =        "Book Review: {{\booktitle{Introduction to Elliptic
                 Functions with Applications}} (F. Bowman)}",
  journal =      j-SIAM-REVIEW,
  volume =       "4",
  number =       "4",
  pages =        "408--408",
  month =        "????",
  year =         "1962",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1004109",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:04:56 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/4/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "October 1962",
}

@TechReport{Blanch:1962:TRR,
  author =       "Gertrude Blanch and Donald S. Clemm",
  title =        "Tables Relating to the Radial {Mathieu} Functions,
                 Vols. 1 \& 2",
  type =         "Report",
  institution =  "Aeronautical Research Labs. U. S. Government Printing
                 Office",
  address =      "Washington, DC, USA",
  year =         "1962",
  bibdate =      "Fri Oct 29 21:37:53 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Gertrude Blanch (1897--1996)",
  citedby =      "Fullerton:1980:BEM",
  remark =       "Fullerton: 7-place tables.",
}

@Article{Boersma:1962:CLF,
  author =       "J. Boersma",
  title =        "On the Computation of {Lommel}'s Functions of Two
                 Variables (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "16",
  number =       "78",
  pages =        "232--238",
  month =        apr,
  year =         "1962",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Lommel's functions are infinite sums
                 involving Bessel functions $ J_{\nu - 2m}(x) $.",
}

@Article{Cantor:1962:LEF,
  author =       "D. Cantor and G. Estrin and R. Turn",
  title =        "Logarithmic and Exponential Function Evaluation in a
                 Variable Structure Digital Computer",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-11",
  number =       "2",
  pages =        "155--164",
  month =        apr,
  year =         "1962",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1962.5219348",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 09:11:49 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219348",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Christiansen:1962:APC,
  author =       "S{\o}ren Christiansen",
  title =        "{Algol} Programming: Contribution no. 3: Calculation
                 of complementary {Fresnel} integrals",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "2",
  number =       "3",
  pages =        "192--194",
  year =         "1962",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Mon Nov 16 14:34:20 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  journal-URL =  "http://link.springer.com/journal/10543",
  remark =       "Fullerton: A 50-line Algol procedure is given. It
                 calculates $ \int_x^\infty \cos (t) / \sqrt {2 \pi t}
                 \, d t $ and $ \int_x^\infty \sin (t) / \sqrt {2 \pi t}
                 \, d t $.",
}

@Article{Cundiff:1962:AEA,
  author =       "John L. Cundiff",
  title =        "{Algorithm 88}: {Evaluation} of Asymptotic Expression
                 for the {Fresnel} Sine and Cosine Integrals",
  journal =      j-CACM,
  volume =       "5",
  number =       "5",
  pages =        "280--280",
  month =        may,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:38 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "C(x); S(x); special functions",
  remark =       "Fullerton: Can be used with algorithms 89 and 90.
                 30-line Algol procedure.",
}

@Article{Cundiff:1962:AEFa,
  author =       "John L. Cundiff",
  title =        "{Algorithm 89}: {Evaluation} of the {Fresnel} Sine
                 Integral",
  journal =      j-CACM,
  volume =       "5",
  number =       "5",
  pages =        "280--280",
  month =        may,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:38 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "S(x); special functions",
  remark =       "Fullerton: 20-line Algol procedure that must be used
                 with algorithm 88.",
}

@Article{Cundiff:1962:AEFb,
  author =       "John L. Cundiff",
  title =        "{Algorithm 90}: {Evaluation} of the {Fresnel} Cosine
                 Integral",
  journal =      j-CACM,
  volume =       "5",
  number =       "5",
  pages =        "281--281",
  month =        may,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:38 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "C(x); special functions",
  remark =       "Fullerton: 20-line Algol procedure that must be used
                 with algorithm 88.",
}

@Article{DiDonato:1962:MCC,
  author =       "A. R. DiDonato and M. P. Jarnagin",
  title =        "A Method for Computing the Circular Coverage
                 Function",
  journal =      j-MATH-COMPUT,
  volume =       "16",
  number =       "79",
  pages =        "347--355",
  month =        jul,
  year =         "1962",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@TechReport{DiDonato:1962:MCG,
  author =       "A. R. DiDonato and M. P. Jamagin",
  title =        "A Method for Computing the Generalized Circular Error
                 Function and the Circular Coverage Function",
  type =         "NWL Report",
  number =       "1768",
  institution =  "Naval Surface Weapons Center",
  address =      "Dahlgren, VA 22448, USA",
  day =          "23",
  month =        jan,
  year =         "1962",
  bibdate =      "Wed Nov 12 15:56:35 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Dorn:1962:GHR,
  author =       "William S. Dorn",
  title =        "Generalizations of {Horner}'s rule for polynomial
                 evaluation",
  journal =      j-IBM-JRD,
  volume =       "6",
  number =       "2",
  pages =        "239--245",
  month =        apr,
  year =         "1962",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.62.0239",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "65.50",
  MRnumber =     "24 \#B2541",
  bibdate =      "Tue Sep 11 16:10:28 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
                 http://www.research.ibm.com/journal/",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392358",
  ZMnumber =     "128.37202",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  reviewer =     "D. H. Lehmer",
}

@Article{Fraser:1962:CRA,
  author =       "W. Fraser and J. F. Hart",
  title =        "On the computation of rational approximations to
                 continuous functions",
  journal =      j-CACM,
  volume =       "5",
  number =       "7",
  pages =        "401--403",
  month =        jul,
  year =         "1962",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/368273.368578",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:39 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\abs(x)$; $\cos(x)$; $\Gamma(1+x)$; $\sin(x)$;
                 elementary functions; Remes algorithm; special
                 functions",
  remark =       "This paper outlines the Remes algorithm for ``for
                 finding polynomial approximations to the determination
                 of `best' rational approximations.''. It also gives
                 approximations for starting values of Newton--Raphson
                 iterations for $ \abs (x) $, $ \cos (x) $, $ \Gamma (1
                 + x) $, and $ \sin (x) $.",
}

@Article{Hansen:1962:SRV,
  author =       "Eldon R. Hansen and Merrell L. Patrick",
  title =        "Some Relations and Values for the Generalized
                 {Riemann} Zeta Function",
  journal =      j-MATH-COMPUT,
  volume =       "16",
  number =       "79",
  pages =        "265--274",
  month =        jul,
  year =         "1962",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Jefferson:1962:RAI,
  author =       "David K. Jefferson",
  title =        "Remark on {Algorithm 73}: {Incomplete} elliptic
                 integrals",
  journal =      j-CACM,
  volume =       "5",
  number =       "10",
  pages =        "514--514",
  month =        oct,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:41 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}

@Article{Knuth:1962:ECP,
  author =       "Donald E. Knuth",
  title =        "{Euler}'s Constant to $ 1271 $ Places",
  journal =      j-MATH-COMPUT,
  volume =       "16",
  number =       "79",
  pages =        "275--281",
  month =        jul,
  year =         "1962",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1962-0148255-X",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "10.41",
  MRnumber =     "26 #5763",
  bibdate =      "Fri Mar 22 18:03:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database; MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Knuth:1962:EPC,
  author =       "Donald E. Knuth",
  title =        "Evaluation of polynomials by computer",
  journal =      j-CACM,
  volume =       "5",
  number =       "12",
  pages =        "595--599",
  month =        dec,
  year =         "1962",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355580.369074",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "68.00 (12.00)",
  MRnumber =     "27 #970",
  bibdate =      "Thu Dec 08 11:11:03 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  note =         "See letter \cite{Knuth:1963:LEE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "The author reports that Motzkin (1962) showed that
                 Horner's rule for polynomial evaluation may not be
                 optimal, and develops the idea further for arbitrary
                 polynomials, but also observes that the coefficients of
                 the revised polynomials may be difficult to find. He
                 also asks about, but does not answer, the question of
                 error analysis of the various methods.",
}

@Article{Landau:1962:PSW,
  author =       "H. J. Landau and H. O. Pollak",
  title =        "Prolate spheroidal wave functions, {Fourier} analysis
                 and uncertainty. {III}. {The} dimension of the space of
                 essentially time- and band-limited signals",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "41",
  number =       "4",
  pages =        "1295--1336",
  month =        jul,
  year =         "1962",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  MRclass =      "33.28 (94.10)",
  MRnumber =     "0147686 (26 \#5200)",
  MRreviewer =   "I. Marx",
  bibdate =      "Tue Nov 9 11:15:54 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1962/BSTJ.1962.4104.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol41/bstj41-4-1295.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}

@Article{Merner:1962:AAC,
  author =       "J. N. Merner",
  title =        "{ACM Algorithm 149}: Complete Elliptic Integral",
  journal =      j-CACM,
  volume =       "5",
  number =       "12",
  pages =        "605",
  month =        dec,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Skovgaard:1978:RCE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Thacher:1962:CAB,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "Certification of {Algorithm 57}: {$ \operatorname
                 {ber} $} or {$ \operatorname {bei} $} function",
  journal =      j-CACM,
  volume =       "5",
  number =       "8",
  pages =        "438--438",
  month =        aug,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:40 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "bei functions; ber functions; special functions",
  remark =       "Fullerton: The algorithm is inaccurate for large
                 $x$.",
}

@Article{Thacher:1962:CAH,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "Certification of {Algorithms 191 and 192,
                 Hypergeometric and Confluent Hypergeometric
                 Functions}",
  journal =      j-CACM,
  volume =       "7",
  number =       "4",
  pages =        "244--244",
  month =        apr,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Oct 30 11:27:28 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: An error in a comment is noted.",
}

@Article{Wimp:1962:PEB,
  author =       "Jet Wimp",
  title =        "Polynomial Expansions of {Bessel} Functions and Some
                 Associated Functions",
  journal =      j-MATH-COMPUT,
  volume =       "16",
  number =       "80",
  pages =        "446--458",
  month =        oct,
  year =         "1962",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  note =         "See corrigendum \cite{Wimp:1972:CPE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Wynn:1962:AAP,
  author =       "P. Wynn",
  title =        "An Arsenal of {ALGOL} Procedures for Complex
                 Arithmetic",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "2",
  number =       "4",
  pages =        "232--255",
  month =        dec,
  year =         "1962",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01940171",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:07 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=2&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=2&issue=4&spage=232",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "ALGOL; complex arithmetic; confluence hypergeometric
                 function; continued fractions; incomplete beta
                 function; incomplete gamma function; Stieltjes
                 $S$-fractions; Weber parabolic cylinder function",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Barakat:1963:CES,
  author =       "Richard Barakat and Agnes Houston",
  title =        "{Chebyschev} Expansion of the Sine and Cosine
                 Integrals",
  journal =      j-J-MATH-PHYS-MIT,
  volume =       "42",
  number =       "1--4",
  pages =        "331--333",
  month =        apr,
  year =         "1963",
  CODEN =        "JMPHA9",
  DOI =          "https://doi.org/10.1002/sapm1963421331",
  ISSN =         "0097-1421",
  ISSN-L =       "0097-1421",
  bibdate =      "Sat Aug 19 13:36:07 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib",
  URL =          "https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1963421331",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Math. Phys. (MIT)",
  fjournal =     "Journal of Mathematics and Physics (MIT)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590",
  onlinedate =   "April 1963",
}

@Article{Burgoyne:1963:AKF,
  author =       "F. D. Burgoyne",
  title =        "Approximations to {Kelvin} Functions (in {Technical
                 Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "17",
  number =       "83",
  pages =        "295--298",
  month =        jul,
  year =         "1963",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 9-digit approximations.",
}

@Article{Carlitz:1963:IEF,
  author =       "L. Carlitz",
  title =        "The Inverse of the Error Function",
  journal =      j-PAC-J-MATH,
  volume =       "13",
  number =       "2",
  pages =        "459--470",
  year =         "1963",
  CODEN =        "PJMAAI",
  ISSN =         "0030-8730 (print), 1945-5844 (electronic)",
  ISSN-L =       "0030-8730",
  bibdate =      "Thu Sep 13 21:30:05 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://pjm.math.berkeley.edu/pjm;
                 http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.pjm/1103035736&view=body&content-type=pdf_1",
  acknowledgement = ack-nhfb,
  fjournal =     "Pacific Journal of Mathematics",
  journal-URL =  "http://msp.org/pjm",
}

@Article{Clenshaw:1963:ASF,
  author =       "C. W. Clenshaw and G. F. Miller and M. Woodger",
  title =        "Algorithms for Special Functions {I}",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "403--419",
  month =        dec,
  year =         "1963",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Fri Sep 16 10:21:31 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  remark =       "Fullerton: ALGOL 60 procedures with accuracy $ \approx
                 10^{-15} $ for $ \exp $, $ \ln $, $ \sin $, $ \cos $, $
                 \tan $, $ \arcsin $, $ \arctan $, $ \gamma $, $ \Ei $
                 and $ \erf $. See G. F. Miller (1965) for
                 corrections.",
}

@Article{Eisman:1963:PER,
  author =       "S. H. Eisman",
  title =        "Polynomial Evaluation Revisited",
  journal =      j-CACM,
  volume =       "6",
  number =       "7",
  pages =        "384--385",
  month =        jul,
  year =         "1963",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/366663.366668",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:47 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Erdelyi:1963:AEC,
  author =       "A. Erd{\'e}lyi and M. Wyman",
  title =        "The asymptotic evaluation of certain integrals",
  journal =      j-ARCH-RAT-MECH-ANAL,
  volume =       "14",
  number =       "1",
  pages =        "217--260",
  month =        jan,
  year =         "1963",
  CODEN =        "AVRMAW",
  DOI =          "https://doi.org/10.1007/BF00250704",
  ISSN =         "0003-9527 (print), 1432-0673 (electronic)",
  ISSN-L =       "0003-9527",
  bibdate =      "Sat Feb 18 14:53:08 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/BF00250704",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for rational mechanics and analysis",
  journal-URL =  "http://link.springer.com/journal/205",
  keywords =     "incomplete gamma function",
}

@Article{Eve:1963:SAI,
  author =       "J. Eve",
  title =        "Starting Approximations for the Iterative Calculation
                 of Square Roots",
  journal =      j-COMP-J,
  volume =       "6",
  number =       "3",
  pages =        "274--276",
  month =        nov,
  year =         "1963",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/6.3.274",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:30 MST 2012",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://comjnl.oxfordjournals.org/content/6/3.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/compj1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Several starting approximations are given which, in
                 conjunction with a well-known iterative process, lead
                 to square root approximations, with a relative error in
                 the range $ (2^{-55}, 2^{-45}) $, at the expense of
                 three divisions. More accurate approximations are given
                 which require in addition a single multiplication.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Fettis:1963:AMH,
  author =       "Henry E. Fettis",
  title =        "{Algorithm 163}: {Modified} {Hankel} function",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "161--162",
  month =        apr,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:46 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Hankel functions; special functions",
  remark =       "Fullerton: A 25-line Algol procedure for $ e^x K_p(x)
                 $.",
}

@Article{Froberg:1963:APC,
  author =       "Carl-Erik Fr{\"o}berg",
  title =        "{Algol} Programming: Contribution no. 5: Computation
                 of the {Fermi} function",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "3",
  number =       "2",
  pages =        "141--142",
  year =         "1963",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Mon Nov 16 14:36:22 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  journal-URL =  "http://link.springer.com/journal/10543",
  remark =       "Fullerton: The Fermi function depends on several
                 physical parameters of the atomic nucleus.",
}

@Article{Froberg:1963:ERC,
  author =       "C.-E. Fr{\"o}berg",
  title =        "Erratum: {``Rational Chebyshev Approximations of
                 Elementary Functions'' [BIT {\bf 1}(4), 1961, p. 261,
                 line 12]}",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "3",
  number =       "1",
  pages =        "68--68",
  month =        mar,
  year =         "1963",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01963538",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:07 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=3&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Froberg:1961:RCA}.",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=3&issue=1&spage=68",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "elementary functions",
}

@InProceedings{Gautschi:1963:RCS,
  author =       "Walter Gautschi",
  editor =       "????",
  booktitle =    "{The University of Michigan Engineering Summer
                 Conferences, Numerical Analysis, Summer 1963}",
  title =        "Recursive computation of special functions",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "1963",
  bibdate =      "Fri Aug 21 11:08:35 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Gray:1963:AFI,
  author =       "Malcolm D. Gray",
  title =        "{Algorithm 213}: {Fresnel} Integrals",
  journal =      j-CACM,
  volume =       "6",
  number =       "10",
  pages =        "617--617",
  month =        oct,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:49 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See certification \cite{Gray:1964:CAF} and related
                 remark \cite{Gray:1963:RAE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "C(x); S(x); special functions",
}

@Article{Gray:1963:RAE,
  author =       "Malcolm D. Gray",
  title =        "Remark on Algorithms 88, 89, and 90 evaluation of the
                 {Fresnel} integrals",
  journal =      j-CACM,
  volume =       "6",
  number =       "10",
  pages =        "618--618",
  month =        oct,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:49 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "C(x); S(x); special functions",
  remark =       "Fullerton: An error is noted.",
}

@Article{Hofsommer:1963:NCE,
  author =       "D. J. Hofsommer and R. van de Riet",
  title =        "On the numerical calculation of elliptic integrals of
                 the first and second kind and the elliptic functions of
                 {Jacobi}",
  journal =      j-NUM-MATH,
  volume =       "5",
  pages =        "291--302",
  month =        dec,
  year =         "1963",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon Oct 18 01:28:20 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Ibbetson:1963:AG,
  author =       "D. Ibbetson",
  title =        "{Algorithm 209}: {Gauss}",
  journal =      j-CACM,
  volume =       "6",
  number =       "10",
  pages =        "616--616",
  month =        oct,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:49 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Knuth:1963:LEE,
  author =       "Donald E. Knuth",
  title =        "Letter to the {Editor}: {Evaluation} of polynomials by
                 computer",
  journal =      j-CACM,
  volume =       "6",
  number =       "2",
  pages =        "51--51",
  month =        feb,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Dec 26 16:31:38 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Knuth:1962:EPC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Lee-Whiting:1963:EFC,
  author =       "G. E. Lee-Whiting",
  title =        "Erratum: ``{Formulas} for Computing Incomplete
                 Elliptic Integrals of the First and Second Kinds''",
  journal =      j-J-ACM,
  volume =       "10",
  pages =        "412--412",
  year =         "1963",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Sat Dec 10 15:59:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Lee-Whiting:1963:FCI}.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
  xxmonth =      "none",
  xxnumber =     "none",
}

@Article{Lee-Whiting:1963:FCI,
  author =       "G. E. Lee-Whiting",
  title =        "Formulas for Computing Incomplete Elliptic Integrals
                 of the First and Second Kinds",
  journal =      j-J-ACM,
  volume =       "10",
  number =       "2",
  pages =        "126--130",
  month =        apr,
  year =         "1963",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Sat Nov 05 22:55:28 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Lee-Whiting:1963:EFC}.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
}

@Book{Ljusternik:1963:MVF,
  author =       "L. A. Ljusternik and O. A. {\v{C}}ervonenkis and A. R.
                 Janpol{\'s}ki{{\u{\i}}}",
  title =        "{{\cyr Matematicheski{\u{\i}}analiz. Vychislenie
                 {\`e}lementarnykh funktsi{\u{\i}}}}. [Mathematical
                 analysis. {Computation} of the elementary functions]",
  publisher =    "Gosudarstv. Izdat. Fiz-Mat. Lit.",
  address =      "Moscow, USSR",
  pages =        "247",
  year =         "1963",
  MRclass =      "65.25",
  MRnumber =     "28 \#1733",
  MRreviewer =   "John Todd",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Ludwig:1963:AIB,
  author =       "Oliver G. Ludwig",
  title =        "{Algorithm 179}: {Incomplete} beta ratio",
  journal =      j-CACM,
  volume =       "6",
  number =       "6",
  pages =        "314--314",
  month =        jun,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:47 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Pike:1976:RIB,Bosten:1974:RAI}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: This algorithm is the basis for a modern
                 treatment by Bosten and Battiste.",
}

@Article{Meyer:1963:CAI,
  author =       "Noelle A. Meyer",
  title =        "Certification of {Algorithm 73}: {Incomplete} elliptic
                 integrals",
  journal =      j-CACM,
  volume =       "6",
  number =       "2",
  pages =        "69--69",
  month =        feb,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:44 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}

@Article{Newman:1963:ICS,
  author =       "J. N. Newman and W. Frank",
  title =        "An Integral Containing the Square of a {Bessel}
                 Function",
  journal =      j-MATH-COMPUT,
  volume =       "17",
  number =       "81",
  pages =        "64--70",
  month =        jan,
  year =         "1963",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: The integral $ I_n^m(x) = \int_0^{\pi / 2}
                 \frac {J_n^2(x \cos (\theta))}{(x \cos (\theta))^{2m}}
                 \, d \theta $, where $m$ and $n$ are either integers or
                 half integers, is considered.",
}

@Article{Peuizulaev:1963:AEF,
  author =       "{\v{S}}. I. Pe{\u{\i}}zulaev",
  title =        "An approximation by elementary functions.
                 ({Russian})",
  journal =      "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz.",
  volume =       "3",
  pages =        "769--770",
  year =         "1963",
  MRclass =      "41.30",
  MRnumber =     "28 \#398",
  MRreviewer =   "D. D. Stancu",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Relph:1963:AAH,
  author =       "A. P. Relph",
  title =        "{ACM Algorithm 191}: Hypergeometric",
  journal =      j-CACM,
  volume =       "6",
  number =       "7",
  pages =        "388--389",
  month =        jul,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:32:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See certification \cite{Koppelaar:1974:CRA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Relph:1963:ACH,
  author =       "A. P. Relph",
  title =        "{Algorithm 192}: {Confluent} hypergeometric",
  journal =      j-CACM,
  volume =       "6",
  number =       "7",
  pages =        "388--388",
  month =        jul,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:47 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: 30-line Algol procedure for complex args.
                 The work of Luke supersedes this.",
}

@Article{Relph:1963:AH,
  author =       "A. P. Relph",
  title =        "{Algorithm 191}: {Hypergeometric}",
  journal =      j-CACM,
  volume =       "6",
  number =       "7",
  pages =        "388--388",
  month =        jul,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:47 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See certification \cite{Koppelaar:1974:CRA}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: 30-line Algol procedure. The work of Luke
                 is better.",
}

@Article{Rutishauser:1963:BQG,
  author =       "H. Rutishauser",
  title =        "{Betrachtungen zur Quadratwurzeliteration}. ({German})
                 [{Considerations} on square root iteration]",
  journal =      j-MONAT-MATH,
  volume =       "67",
  pages =        "452--464",
  year =         "1963",
  CODEN =        "MNMTA2",
  DOI =          "https://doi.org/10.1007/BF01295091",
  ISSN =         "0026-9255 (print), 1436-5081 (electronic)",
  ISSN-L =       "0026-9255",
  MRclass =      "65.50",
  MRnumber =     "158532",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Mon Aug 24 21:56:15 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Heinz Rutishauser (30 January 1918--10 November
                 1970)",
  fjournal =     "Monatshefte f{\"u}r Mathematik",
  journal-URL =  "http://link.springer.com/journal/605",
  language =     "German",
}

@Book{Sneddon:1963:SFM,
  author =       "Ian Naismith Sneddon",
  title =        "{Spezielle Funktionen der mathematischen Physik und
                 Chemie. Mathematische Formelsammlung II}. ({German})
                 [Special {functions} of mathematical physics and
                 chemistry. {Mathematical} formula collection {II}]",
  volume =       "54",
  publisher =    pub-BIBLIO-INST,
  address =      pub-BIBLIO-INST:adr,
  pages =        "166",
  year =         "1963",
  LCCN =         "QA351 .S6415",
  bibdate =      "Sat Oct 30 21:22:03 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "B. I.-Hochschultaschenb{\"u}cher",
  acknowledgement = ack-nhfb,
  language =     "German",
  remark =       "German translation of \cite{Sneddon:1961:SFM}.",
  subject =      "Functions; Mathematical physics",
}

@Article{Stern:1963:CSR,
  author =       "T. E. Stern and R. M. Lerner",
  title =        "A circuit for the square root of the sum of the
                 squares",
  journal =      j-PROC-IEEE,
  volume =       "51",
  number =       "4",
  pages =        "593--596",
  month =        apr,
  year =         "1963",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  summary =      "A piecewise-linear network can produce an output
                 proportional to the square root of the sum of the
                 squares of a set of input voltages, using resistors and
                 diodes alone. The required relationship between
                 voltages can be represented by a multi- \ldots{}",
}

@Article{Sweeney:1963:CEC,
  author =       "Dura W. Sweeney",
  title =        "On the Computation of {Euler}'s Constant",
  journal =      j-MATH-COMPUT,
  volume =       "17",
  number =       "82",
  pages =        "170--178",
  month =        apr,
  year =         "1963",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1963-0160308-X",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 3566 digits should be enough.",
}

@Article{Thacher:1963:ACEa,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "{Algorithm 165}: {Complete} elliptic integrals",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "163--164",
  month =        apr,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:46 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}

@Article{Thacher:1963:CACa,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "Certification of {Algorithm 55}: {Complete} elliptic
                 integral of the first kind",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "166--167",
  month =        apr,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:46 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}

@Article{Thacher:1963:CACb,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "Certification of {Algorithm 149}: {Complete} elliptic
                 integral",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "166--167",
  month =        apr,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:46 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}

@Book{Tocher:1963:AS,
  author =       "K. D. Tocher",
  title =        "The Art of Simulation",
  publisher =    "Van Nostrand",
  address =      "Princeton, NJ, USA",
  pages =        "viii + 184",
  year =         "1963",
  LCCN =         "TA177 .T6",
  bibdate =      "Sat Dec 16 17:47:12 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Simulation methods",
}

@Article{vandeRiet:1963:CAI,
  author =       "R. P. van de Riet",
  title =        "Certification of {Algorithm 73}: {Incomplete} elliptic
                 integrals",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "167--167",
  month =        apr,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:46 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}

@Article{Werner:1963:AFI,
  author =       "H. Werner and G. Raymann",
  title =        "An Approximation to the {Fermi} Integral {$ F_{1 /
                 2}(x) $}",
  journal =      j-MATH-COMPUT,
  volume =       "17",
  number =       "82",
  pages =        "193--194",
  month =        apr,
  year =         "1963",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2003641",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Relative errors of $ 5 \times 10^{-4} $.",
}

@Article{Whittlesey:1963:IGF,
  author =       "John R. B. Whittlesey",
  title =        "Incomplete Gamma Functions for Evaluating {Erlang}
                 Process Probabilities",
  journal =      j-MATH-COMPUT,
  volume =       "17",
  number =       "81",
  pages =        "11--17",
  month =        jan,
  year =         "1963",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@InCollection{Abramowitz:1964:CWF,
  author =       "Milton Abramowitz",
  title =        "{Coulomb} Wave Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "537--554",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@InCollection{Abramowitz:1964:SFR,
  author =       "Milton Abramowitz",
  title =        "{Struve} Functions and Related Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "495--502",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@Article{Aiken:1964:PAC,
  author =       "H. H. Aiken and A. G. Oettinger and T. C. Bartee",
  title =        "Proposed automatic calculating machine",
  journal =      j-IEEE-SPECTRUM,
  volume =       "1",
  number =       "8",
  pages =        "62--69",
  month =        aug,
  year =         "1964",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1964.6500770",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Tue Jan 14 11:14:17 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  abstract =     "Here presented is the memorandum that 20 years ago
                 initiated a series of events whose revolutionary
                 implications are only beginning to manifest themselves
                 a description of the first large-scale general-purpose
                 automatic digital computer. Twenty years ago, on August
                 7, 1944, Mark I, the first large-scale general-purpose
                 automatic digital computer ever to be put in operation
                 was dedicated at Harvard University by James B. Conant,
                 then president of Harvard, and the late Thomas J.
                 Watson, founder of IBM.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  remark =       "Pages 66--69 discuss computation of the elementary
                 functions with minimal intermediate storage: recipes
                 are given for integral and fractional power, log,
                 exponential, trigonometric, inverse trigonometric,
                 hyperbolic, and inverse hyperbolic. Mention is also
                 made of the probability integral, elliptic functions,
                 and Bessel functions, but the text says they will be
                 discussed later (meaning, in a future publication). The
                 methods involve recurrences and series summations, and
                 thus, can be regarded as precision independent.",
  xxnote =       "Previously unpublished memorandum written by Aiken and
                 dated by an unknown recipient as 4 November 1937.
                 Reprinted in \cite[\S 5.1]{Randell:1982:ODC}.",
}

@InCollection{Antosiewicz:1964:BFF,
  author =       "H. A. Antosiewicz",
  title =        "{Bessel} Functions of Fractional Order",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "435--478",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@InCollection{Blanch:1964:MF,
  author =       "Gertrude Blanch",
  title =        "{Mathieu} Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "721--750",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1897--1996",
  citedby =      "Fullerton:1980:BEM",
}

@Article{Bray:1964:CAGa,
  author =       "T. A. Bray",
  title =        "Certification of {Algorithm 225}: {Gamma} function
                 with controlled accuracy",
  journal =      j-CACM,
  volume =       "7",
  number =       "10",
  pages =        "586--586",
  month =        oct,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:56 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\Gamma(x)$; special functions",
  remark =       "Fullerton: No corrections were necessary.",
}

@Article{Burgoyne:1964:GTF,
  author =       "F. D. Burgoyne",
  title =        "Generalized Trigonometric Functions (in {Technical
                 Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "18",
  number =       "86",
  pages =        "314--316",
  month =        apr,
  year =         "1964",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Cody:1964:DPS,
  author =       "William J. {Cody, Jr.}",
  title =        "Double-Precision Square Root for the {CDC-3600}",
  journal =      j-CACM,
  volume =       "7",
  number =       "12",
  pages =        "715--718",
  month =        dec,
  year =         "1964",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355588.365122",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:57 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In January of 1960, the late Hans J. Maehly completed
                 a summary of approximations to the elementary functions
                 for the CDC-1604 computer. The approximations and
                 techniques suggested by Maehly are equally applicable
                 to the second large computer in the CDC line, the 3600.
                 Unlike the 1604, however, the 3600 has built-in
                 double-precision floating-point arithmetic. The present
                 work, largely inspired by the successes of Maehly and
                 his associates, concerns the extension of one of
                 Maehly's ideas to a double-precision subroutine for the
                 3600.",
  acknowledgement = ack-nhfb # "\slash " # ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$sqrt(x)$; CDC 3600; elementary functions;
                 floating-point arithmetic",
}

@Article{Cowgill:1964:LEB,
  author =       "D. Cowgill",
  title =        "Logic Equations for a Built-In Square Root Method",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-13",
  number =       "2",
  pages =        "156--157",
  month =        apr,
  year =         "1964",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1964.263791",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:56:59 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038119",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Curtiss:1964:EIB,
  author =       "C. F. Curtiss",
  title =        "Expansions of Integrals of {Bessel} Functions of Large
                 Order",
  journal =      j-J-MATH-PHYS,
  volume =       "5",
  number =       "4",
  pages =        "561--564",
  month =        apr,
  year =         "1964",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.1704149",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Oct 28 08:40:12 MDT 2011",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1960.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v5/i4/p561_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  onlinedate =   "22 December 2004",
  pagecount =    "4",
}

@Article{Cyvin:1964:AGF,
  author =       "S. J. Cyvin and B. N. Cyvin",
  title =        "{Algorithm 225}: {Gamma} function with controlled
                 accuracy",
  journal =      j-CACM,
  volume =       "7",
  number =       "5",
  pages =        "295--295",
  month =        may,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:53 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\Gamma(x)$; special functions",
  remark =       "Fullerton: 30-line Algol procedure based on
                 out-of-date method.",
}

@Article{Cyvin:1964:AND,
  author =       "S. J. Cyvin",
  title =        "{Algorithm 226}: {Normal} distribution function",
  journal =      j-CACM,
  volume =       "7",
  number =       "5",
  pages =        "295--295",
  month =        may,
  year =         "1964",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/364099.364315",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:53 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "probability functions",
}

@InCollection{Davis:1964:GFR,
  author =       "Philip J. Davis",
  title =        "Gamma Function and Related Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "253--294",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@Article{Eve:1964:EP,
  author =       "J. Eve",
  title =        "The evaluation of polynomials",
  journal =      j-NUM-MATH,
  volume =       "6",
  number =       "1",
  pages =        "17--21",
  month =        dec,
  year =         "1964",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01386049",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon Oct 18 20:10:40 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "number of multiplications to evaluate a polynomial",
  remark =       "From the first two paragraphs: ``Ostrowski [5] has
                 shown that the $ 2 n $ operations required by this
                 algorithm [Horner's] are minimal for $ n \leq 4 $.
                 Motzkin [4] (see also Todd [8]) and Knuth [3] have
                 given methods whereby polynomials with $ 4 \leq n \leq
                 6 $ can be evaluated in $ [(1 / 2)(n + 3)] $
                 multiplications and not more than $ n + 1 $ additions.
                 Similar methods effecting a reduction in the number of
                 multiplications have been described by Pan [6] for $ n
                 \leq 12 $. Each of these methods is valid only for a
                 particular value of $n$.\par A general method due to
                 Pan [7] applicable to all polynomials with $ n \geq 5 $
                 results in an evaluation involving $ [(1 / 2) (n + 4)]
                 $ multiplications and $ n + 1 $ additions. Knuth has
                 also given a method applicable to all polynomials with
                 $ n \geq 3 $ in which $ n + 1 $ additions are required
                 while the number of multiplications varies between $
                 [(1 / 2) (n + 3)] $ and approximately $ (3 / 4)n $.''",
}

@TechReport{Fisherkeller:1964:TCE,
  author =       "M. A. Fisherkeller and W. J. {Cody, Jr.}",
  title =        "Tables of the Complete Elliptic Integrals $ {K} $, $
                 {K}' $, $ {E} $, and $ {E}' $",
  type =         "Technical Memo",
  number =       "ANL AMD 71",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  pages =        "14",
  year =         "1964",
  bibdate =      "Thu Nov 17 10:44:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See review by John W. Wrench in Mathematics of
                 Computation, {\bf 19}(89--92), 342, 1965.",
  acknowledgement = ack-nhfb,
}

@Article{Gargantini:1964:RCA,
  author =       "I. Gargantini and T. Pomentale",
  title =        "Rational {Chebyshev} approximations to the {Bessel}
                 function integrals {$ K i_s(x) $}",
  journal =      j-CACM,
  volume =       "7",
  number =       "12",
  pages =        "727--730",
  month =        dec,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.25",
  MRnumber =     "31\#863",
  bibdate =      "Fri Nov 25 18:19:57 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The second Remes algorithm is used to approximate the
                 integrals $ K i_s $ by rational functions. The related
                 coefficients for the approximations of $ K i_1, K i_2,
                 K i_3 $ are given for different precisions.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Bessel functions; Kis(x); special functions",
  remark =       "Fullerton: Approximations for repeated integrals $
                 \operatorname {Ki}_s(x) $ of $ K(x) $ for $ s = 1, 2, 3
                 $ are given for accuracies down to $ 10^{-5} $ for $ s
                 = 1 $ and to $ 10^{-7} $ for $ s = 2, 3 $.",
}

@Article{Gautschi:1964:AAB,
  author =       "W. Gautschi",
  title =        "{ACM Algorithm 236}: {Bessel} Functions of the First
                 Kind [{S17}]",
  journal =      j-CACM,
  volume =       "7",
  number =       "8",
  pages =        "479--480",
  month =        aug,
  year =         "1964",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355586.355587",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:55 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Skovgaard:1975:RBF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$J_n(x)$; Bessel functions of the first kind; special
                 functions",
}

@Article{Gautschi:1964:AGF,
  author =       "Walter Gautschi",
  title =        "{Algorithm 221}: {Gamma} functions",
  journal =      j-CACM,
  volume =       "7",
  number =       "3",
  pages =        "143--143",
  month =        mar,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:52 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\Gamma(x)$; special functions",
}

@Article{Gautschi:1964:AIB,
  author =       "Walter Gautschi",
  title =        "{Algorithm 222}: {Incomplete} beta functions ratios",
  journal =      j-CACM,
  volume =       "7",
  number =       "3",
  pages =        "143--143",
  month =        mar,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:52 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "beta functions; special functions",
  remark =       "Fullerton: 200-line Algol procedure.",
}

@Article{Gautschi:1964:CAI,
  author =       "Walter Gautschi",
  title =        "Certification of {Algorithm 222}: {Incomplete} beta
                 function ratios",
  journal =      j-CACM,
  volume =       "7",
  number =       "4",
  pages =        "244--244",
  month =        apr,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:53 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "beta functions; special functions",
  remark =       "Fullerton: A typographical error is noted.",
}

@InCollection{Gautschi:1964:EFF,
  author =       "Walter Gautschi",
  title =        "Error Function and {Fresnel} Integrals",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "295--330",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@InCollection{Gautschi:1964:EIR,
  author =       "Walter Gautschi and William F. Cahill",
  title =        "Exponential Integral and Related Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "227--252",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@Article{Gray:1964:CAF,
  author =       "Malcolm Gray",
  title =        "Certification of {Algorithm 213}: {Fresnel}
                 integrals",
  journal =      j-CACM,
  volume =       "7",
  number =       "11",
  pages =        "661--661",
  month =        nov,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:56 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Gray:1963:AFI,Gray:1963:RAE}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "C(x); S(x); special functions",
  remark =       "Fullerton: Several corrections are given.",
}

@InCollection{Haynsworth:1964:BEP,
  author =       "Emilie V. Haynsworth and Karl Goldberg",
  title =        "{Bernoulli} and {Euler} Polynomials, {Riemann Zeta}
                 Function",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "803--820",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@InCollection{Hochstrasser:1964:OP,
  author =       "Urs W. Hochstrasser",
  title =        "Orthogonal Polynomials",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "771--802",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@Article{Hummer:1964:EDF,
  author =       "David G. Hummer",
  title =        "Expansions of {Dawson}'s Function in a Series of
                 {Chebyshev} Polynomials (in {Technical Notes and Short
                 Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "18",
  number =       "86",
  pages =        "317--319",
  month =        apr,
  year =         "1964",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Almost l5-digit approximations.",
}

@Article{Lanczos:1964:PAG,
  author =       "Cornelius Lanczos",
  title =        "A Precision Approximation of the Gamma Function",
  journal =      j-SIAM-J-NUM-ANALYSIS-B,
  volume =       "1",
  number =       "1",
  pages =        "86--96",
  month =        "????",
  year =         "1964",
  DOI =          "https://doi.org/10.1137/0701008",
  ISSN =         "0887-459X (print), 1095-7170 (electronic)",
  ISSN-L =       "0887-459X",
  MRclass =      "33.15",
  MRnumber =     "0176115 (31 \#390)",
  MRreviewer =   "S. C. van Veen",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2949767",
  ZMnumber =     "Zbl 0136.05201",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Society for Industrial and Applied
                 Mathematics: Series B, Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/loi/sjnaam.1",
}

@Article{Lotsch:1964:AFI,
  author =       "Helmut Lotsch and Malcolm Gray",
  title =        "{Algorithm 244}: {Fresnel} Integrals [{S20}]",
  journal =      j-CACM,
  volume =       "7",
  number =       "11",
  pages =        "660--661",
  month =        nov,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:56 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This procedure computes the Fresnel sine and cosine
                 integrals $ C(w) = \int_0^\infty \cos [(\pi / 2)t^2] \,
                 d t $ and $ S(w) = \int_0^w \sin [(\pi / 2)t^2] \, d t
                 $. It is a modification of Algorithm 213 (Comm. ACM, 6
                 (Oct. 1963), 617) such that the accuracy, expressed by
                 \textit{eps}, is improved. eps can arbitrarily be
                 chosen up to $ \textit {eps} = 10^{-6} $ for a computer
                 with sufficient word length as, for example, the
                 Burroughs B5000 which has 11--12 significant digits.
                 Referring to the formulas of Algorithm 213: if $ |w| <
                 \sqrt {(26.20 / \pi)} $ the series expansions $ C(w) $
                 and $ S(w) $ are terminated when the absolute value of
                 the relative change in two successive terms is $ \leq
                 \textit {eps} $. If $ |w| \geq \sqrt {(26.20 / \pi)} $
                 the series $ Q(x) $ and $ P(x) $ are terminated when
                 the absolute value of the terms is $ \leq \textit {eps}
                 / 2 $. However, this truncation point is not
                 necessarily valid for the range $ \sqrt {(26.20 / \pi)}
                 \leq |w| < \sqrt {(28.50 / \pi)} $ when $ \textit {eps}
                 = 10^{-6} $, since the asymptotic series must be
                 terminated before arriving at the minimum. In this
                 range the ignored terms of the series expansions are $
                 < 3 \times 10^6 $, and for larger arguments $ < 10^{-6}
                 $. This accuracy may be improved if desired: the
                 switch-over point from the regular to the asymptotic
                 series expansions has to be displaced to larger
                 arguments.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "C(x); Fresnel integrals; S(x); special functions",
  remark =       "Fullerton: 100-line Algol procedure.",
}

@InCollection{Lowan:1964:SWF,
  author =       "Arnold N. Lowan",
  title =        "Spheroidal Wave Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "751--770",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@InCollection{Luke:1964:IBF,
  author =       "Yudell L. Luke",
  title =        "Integrals of {Bessel} Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "479--494",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@Book{Meinardus:1964:AFI,
  author =       "Gunter Meinardus",
  title =        "{Approximation von Funktionen und ihre numerische
                 Behandlung}. ({German}) [{Approximation} of functions
                 and their numerical treatment]",
  volume =       "4",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 180",
  year =         "1964",
  DOI =          "https://doi.org/10.1007/978-3-642-85646-4",
  ISBN =         "3-540-03219-3, 3-642-85646-2, 3-642-85647-0 (print)",
  ISBN-13 =      "978-3-540-03219-9, 978-3-642-85646-4,
                 978-3-642-85647-1 (print)",
  LCCN =         "QA320 .M4",
  bibdate =      "Thu Oct 19 17:00:27 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Springer tracts in natural philosophy",
  abstract =     "[numerous OCR errors to be corrected] Erst in den
                 letzten Jahren hat sich derjenige Tell der
                 Approximations theorie, der sich auf numerische
                 Fragestellungen anwenden l{\"a}{\ss}t, starker
                 entwickelt. Das Prinzip der in einem gewissen Sinne
                 besten Ann{\"a}herung von Funktionen gewann
                 insbesondere durch die Verwendung elektronischer
                 Rechenmaschinen an Bedeutung. Einige der theoretischen
                 Grundlagen, die zur Behandlung der auftretenden
                 Probleme herange zogen werden mussen, finden sich
                 verstreut in wenigen Buchern. Der weitaus gro{\ss}te
                 Teil der theoretischen und praktischen Untersuchungen
                 ist jedoch nur in den Originalarbeiten nachzulesen.
                 Hieraus ergab sich die Zielsetzung des vorliegenden
                 Buches: Es sollte eine Zusammen stellung der
                 wesentlichen Ergebnisse der Approximationstheorie
                 gegeben werden, die einerseits ein rasches Eindringen
                 in die modernen Entwicklungen dieses Gebietes
                 ermoglicht und andererseits eine gewisse
                 Vollst{\"a}ndigkeit auf dem Problemkreis der
                 Tschebyscheff-Approximationen bietet, womit keineswegs
                 gemeint ist, da{\ss} eine vollst{\"a}ndige Literatur
                 {\"u}bersicht angestrebt wurde. Die Auswahl erfolgte
                 stets nach dem immer noch subjektiven Gesichtspunkt der
                 Bedeutung f{\"u}r die Anwendungen. Dies gilt z. B. auch
                 f{\"u}r die asymptotischen Untersuchungen des {\S} 3,
                 denn ich bin der Meinung, da{\ss} man sich auch
                 beinumerischen Approximationen {\"u}ber die, wenigstens
                 asymptotisch zu erwartende Genauigkeit Gedanken machen
                 sollte. Fast ausschlie{\ss}lich habe ich mich auf die
                 Theorie der gleich m{\"a}{\ss}igen Approximation
                 beschr{\"a}nkt, da diese die weitaus gro{\ss}te
                 praktische Bedeutung besitzt. Das erste Kapitel
                 behandelt lineare Approximationen. Der {\S} 3
                 enth{\"a}lt wohl den heute k{\"u}rzesten Zugang zur
                 linearen Theorie.",
  acknowledgement = ack-nhfb,
  author-dates = "1926--",
  language =     "German",
  subject =      "Aproximaciones",
  tableofcontents = "I Lineare Approximationen \\
                 I.1. Das allgemeine lineare Approximationsproblem \\
                 I.2. Dichte Systeme \\
                 I.3. Allgemeine Theorie linearer
                 Tschebyscheff-Approximationen \\
                 I.4. Spezielle Tschebyscheff-Approximationen \\
                 I.5. Absch{\"a}tzungen der Gr{\"o}{\ss}enordnung des
                 Fehlers bei trigonometrischer und bei polynomialer
                 Approximation \\
                 I.6. Polynomapproximationen \\
                 I.7. Numerische Verfahren bei linearen
                 Tschebyscheff-Approximationen \\
                 II Nicht-lineare Approximationen \\
                 II.8. Allgemeine Theorie nicht-linearer
                 Tschebyscheff-Approximationen \\
                 II.9. Rationale Approximationen \\
                 II.10. Exponentialapproximationen",
}

@InCollection{Miller:1964:PCF,
  author =       "J. C. P. Miller",
  title =        "Parabolic Cylinder Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "685--720",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@InCollection{Milne-Thomson:1964:EI,
  author =       "L. M. Milne-Thomson",
  title =        "Elliptic Integrals",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "587--626",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@InCollection{Milne-Thomson:1964:JEF,
  author =       "L. M. Milne-Thomson",
  title =        "{Jacobian} Elliptic Functions and Theta Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "567--586",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@Article{Morelock:1964:AAE,
  author =       "J. C. Morelock",
  title =        "{ACM} Algorithm 229: Elementary Functions by Continued
                 Fractions",
  journal =      j-CACM,
  volume =       "7",
  number =       "5",
  pages =        "296",
  month =        may,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:32:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@InCollection{Oberhettinger:1964:HF,
  author =       "Frtiz Oberhettinger",
  title =        "Hypergeometric Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "555--566",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@InCollection{Olver:1964:BFI,
  author =       "F. W. J. Olver",
  title =        "{Bessel} Functions of Integer Order",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "355--434",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@Article{Schmidt:1964:AEC,
  author =       "Paul W. Schmidt",
  title =        "Asymptotic Expansion of Certain Integrals Containing
                 the {Bessel} Function {$ J_0 (x) $}",
  journal =      j-J-MATH-PHYS,
  volume =       "5",
  number =       "8",
  pages =        "1183--1184",
  month =        aug,
  year =         "1964",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.1704223",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Oct 28 08:40:15 MDT 2011",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1960.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v5/i8/p1183_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  onlinedate =   "22 December 2004",
  pagecount =    "2",
}

@Article{Simauti:1964:AFS,
  author =       "Takakazu Simauti",
  title =        "Approximation formulas for some elementary functions",
  journal =      "Comment. Math. Univ. St. Paul.",
  volume =       "12",
  pages =        "23--35",
  year =         "1964",
  CODEN =        "COMAAC",
  ISSN =         "0010-258X",
  MRclass =      "65.25",
  MRnumber =     "28 \#5552",
  MRreviewer =   "John Todd",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Slater:1964:CHF,
  author =       "Lucy Joan Slater",
  title =        "Confluent Hvpergeometric Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "503--536",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@Article{Slepian:1964:PSW,
  author =       "David Slepian",
  title =        "Prolate Spheroidal Wave Functions, {Fourier} Analysis
                 and Uncertainty --- {IV}: Extensions to Many
                 Dimensions; Generalized Prolate Spheroidal Functions",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "43",
  number =       "6",
  pages =        "3009--3057",
  month =        nov,
  year =         "1964",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  MRclass =      "33.28",
  MRnumber =     "0181766 (31 \#5993)",
  MRreviewer =   "J. Meixner",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1964/BSTJ.1964.4306.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol43/bstj43-6-3009.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}

@InCollection{Southard:1964:WER,
  author =       "Thomas H. Southard",
  title =        "{Weierstrass} Elliptic and Related Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "627--684",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@InCollection{Stegun:1964:LF,
  author =       "Irene A. Stegun",
  title =        "{Legendre} Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "331--354",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@InCollection{Stegun:1964:MF,
  author =       "Irene A. Stegun",
  title =        "Miscellaneous Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "997--1010",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  keywords =     "Clausen's integral; Clebsch--Gordan coefficients;
                 Debye function; Dilogarithm (Spence's integral);
                 Einstein function; Planck function; Sievert and related
                 integrals",
  remark =       "Fullerton: Debye, Planck and Einstein functions.
                 Sievert and related integrals. Dilogarithm (Spence's
                 integral). Clausen's integral. Clebsch--Gordan
                 coefficients.",
}

@Article{Wengert:1964:SAD,
  author =       "R. E. Wengert",
  title =        "A simple automatic derivative evaluation program",
  journal =      j-CACM,
  volume =       "7",
  number =       "8",
  pages =        "463--464",
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Math/auto.diff.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "A procedure for automatic evaluation of total and
                 partial derivatives of arbitrary algebraic functions is
                 presented. The numerical values of derivatives are
                 computed without developing analytic expressions for
                 the derivatives. The function is decomposed into a
                 sequence of elementary expressions A library is
                 provided for differentiating of elementary functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "computer program.; differentiation arithmetic; point
                 algorithm",
  referred =     "[Bell65a]; [Carl86a]; [Corl88a]; [Garc91a]; [Irim91a];
                 [Kala83b]; [Laws88a]; [Laws91a]; [Neid87a]; [Neid89a];
                 [Ostr71a]; [Pfei87a]; [Tesf91a]; [Voli85a]; [Wexl87a];
                 [Wilk64a].",
}

@InCollection{Zelen:1964:PF,
  author =       "Marvin Zelen and Norman C. Severo",
  title =        "Probability Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "925--996",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@InCollection{Zucker:1964:ETF,
  author =       "Ruth Zucker",
  title =        "Elementary Transcendental Functions. {Logarithmic},
                 Exponential, Circular and Hyperbolic Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "65--226",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@Article{Bingulac:1965:ACG,
  author =       "S. P. Bingulac and E. A. Humo",
  title =        "Analog Computer Generation of {Bessel} Functions of
                 Arbitrary Order",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "6",
  pages =        "886--889",
  month =        dec,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264084",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:41 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038609",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Braess:1965:MIG,
  author =       "Dietrich Braess",
  title =        "{Monotone Iterationsfolgen bei Gleichungssystemen mit
                 fehlerhaften Koeffizienten und
                 Iterationsbeschleunigung}. ({German}) [{Monotone}
                 Iteration Sequences for Equation Systems with
                 Coefficients Having Errors, and Iteration
                 Acceleration]",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "1",
  pages =        "32--41",
  month =        feb,
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon Oct 18 01:28:20 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "convergence acceleration",
  language =     "German",
}

@Article{Bulirsch:1965:NCEa,
  author =       "R. Bulirsch",
  title =        "Numerical calculation of elliptic integrals and
                 elliptic functions",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "1",
  pages =        "78--90",
  month =        feb,
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon Oct 18 20:10:40 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Handbook Series Special functions",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Bulirsch:1965:NCEb,
  author =       "R. Bulirsch",
  title =        "Numerical calculation of elliptic integrals and
                 elliptic functions. {II}",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "4",
  pages =        "353--354",
  month =        aug,
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 16:12:48 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Christiansen:1965:APE,
  author =       "S. Christiansen",
  title =        "{Algol} programming: Error Integral with Complex
                 Argument",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "5",
  number =       "4",
  pages =        "287--293",
  month =        dec,
  year =         "1965",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01937509",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:09 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=4&spage=287",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  journal-URL =  "http://link.springer.com/journal/10543",
  remark =       "Fullerton: A 75-line Algol procedure with maximum
                 absolute error about $ 2 \times 10^{-6} $ is given for
                 $ w(z) = e^{-z^2} \erfc ( - i z) $.",
}

@Article{Cochran:1965:ZHF,
  author =       "J. A. Cochran",
  title =        "The zeros of {Hankel} functions as functions of their
                 order",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "3",
  pages =        "238--250",
  month =        jun,
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon Oct 18 10:06:00 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Cody:1965:CAC,
  author =       "W. J. {Cody, Jr.}",
  title =        "{Chebyshev} Approximations for the Complete Elliptic
                 Integrals {$K$} and {$E$}",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "89--92",
  pages =        "105--112",
  month =        apr,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.05",
  MRnumber =     "30\#1601",
  bibdate =      "Fri Oct 23 11:10:16 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Cody:1966:CCA}.",
  URL =          "http://www.jstor.org/stable/2004103",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Relative errors down to $ 4 \times 10^{-18}
                 $.",
}

@Article{Cody:1965:CPE,
  author =       "W. J. {Cody, Jr.}",
  title =        "{Chebyshev} Polynomial Expansions of Complete Elliptic
                 Integrals",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "89--92",
  pages =        "249--259",
  month =        apr,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.25",
  MRnumber =     "31\#2820",
  bibdate =      "Fri Oct 23 11:10:33 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2003350",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 25-digit approximations.",
}

@Article{Combet:1965:CBT,
  author =       "M. Combet and H. {Van Zonneveld} and L. Verbeek",
  title =        "Computation of the Base Two Logarithm of Binary
                 Numbers",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "6",
  pages =        "863--867",
  month =        dec,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264080",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:41 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038605",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Dahlquist:1965:CAP,
  author =       "Germund Dahlquist and Sven-{\AA}ke Gustafson and
                 K{\'a}roly Sikl{\'o}si",
  title =        "Convergence Acceleration from the Point of View of
                 Linear Programming",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "5",
  number =       "1",
  pages =        "1--16",
  month =        mar,
  year =         "1965",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01975719",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  bibdate =      "Wed Jan 4 18:52:08 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=1&spage=1",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "convergence acceleration",
}

@Article{Fettis:1965:CEI,
  author =       "Henry E. Fettis",
  title =        "Calculation of Elliptic Integrals of the Third Kind by
                 Means of {Gauss}' Transformation",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "89",
  pages =        "97--104",
  month =        apr,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2004102",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Fields:1965:RAG,
  author =       "Jerry L. Fields",
  title =        "Rational Approximations to Generalized Hypergeometric
                 Functions",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "92",
  pages =        "606--624",
  month =        oct,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Franke:1965:NEE,
  author =       "Charles H. Franke",
  title =        "Numerical Evaluation of the Elliptic Integral of the
                 Third Kind (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "91",
  pages =        "494--496",
  month =        jul,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Fraser:1965:SMC,
  author =       "W. Fraser",
  title =        "A Survey of Methods for Computing Minimax and
                 Near-Minimax Polynomial Approximations for Functions of
                 a Single Independent Variable",
  journal =      j-J-ACM,
  volume =       "12",
  number =       "3",
  pages =        "295--314",
  month =        jul,
  year =         "1965",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321281.321282",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Thu Nov 03 08:47:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Methods are described for the derivation of minimax
                 and near-minimax polynomial approximations. For minimax
                 approximations techniques are considered for both
                 analytically defined functions and functions defined by
                 a table of values. For near-minimax approximations
                 methods of determining the coefficients of the
                 Fourier--Chebyshev expansion are first described. These
                 consist of the rearrangement of the coefficients of a
                 power polynomial, and also direct determination of the
                 coefficients from the integral which defines them, or
                 the differential equation which defines the function.
                 Finally there is given a convenient modification of an
                 interpolation scheme which finds coefficients of a
                 near-minimax approximation without requiring numerical
                 integration or the numerical solution of a system of
                 equations.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
}

@Article{Gautschi:1965:ALF,
  author =       "W. Gautschi",
  title =        "{Algorithm 259}: {Legendre} Functions for Arguments
                 Larger than One [{S16}]",
  journal =      j-CACM,
  volume =       "8",
  number =       "8",
  pages =        "488--492",
  month =        aug,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:01 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Jansen:1977:RLF}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Legendre functions; special functions",
  remark =       "Fullerton: Long Algol procedures for the associated
                 Legendre functions of the first and second kinds: $
                 P_a^n(x) $ and $ Q_n^m $.",
}

@Article{Gautschi:1965:CAS,
  author =       "Walter Gautschi",
  title =        "Certification of {Algorithm 236} [{S17}]: {Bessel}
                 functions of the first kind",
  journal =      j-CACM,
  volume =       "8",
  number =       "2",
  pages =        "105--106",
  month =        feb,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:58 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$J_n(x)$; Bessel functions of the first kind; special
                 functions",
}

@Article{Gunn:1965:ASa,
  author =       "J. H. Gunn",
  title =        "{Algorithm 260}: {6-$J$} symbols",
  journal =      j-CACM,
  volume =       "8",
  number =       "8",
  pages =        "492--492",
  month =        aug,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:01 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: Short Algol procedure.",
}

@Article{Gunn:1965:ASb,
  author =       "J. H. Gunn",
  title =        "{Algorithm 261}: {9-$J$} symbols",
  journal =      j-CACM,
  volume =       "8",
  number =       "8",
  pages =        "492--493",
  month =        aug,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:01 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: Short Algol procedure.",
}

@Article{Gunn:1965:AZV,
  author =       "J. H. Gunn",
  title =        "{Algorithm 252} [{Z}]: {Vector} coupling or
                 {Clebsch--Gordan} coefficients",
  journal =      j-CACM,
  volume =       "8",
  number =       "4",
  pages =        "217--217",
  month =        apr,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:59 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: Short Algol procedure.",
}

@Article{Heatley:1965:ETT,
  author =       "A. H. Heatley",
  title =        "An Extension of the Table of the {Toronto} Function
                 (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "89",
  pages =        "118--123",
  month =        apr,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Some 5 and 7-digit values.",
}

@Article{James:1965:GSR,
  author =       "Wendy James and P. Jarratt",
  title =        "The Generation of Square Roots on a Computer with
                 Rapid Multiplication Compared with Division (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "91",
  pages =        "497--500",
  month =        jul,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Kazangapov:1965:REF,
  author =       "A. N. Kazangapov",
  title =        "Representation of elementary function in the system of
                 residual classes. ({Russian})",
  journal =      "Izv. Akad. Nauk Kazah. SSR Ser. Fiz.-Mat. Nauk",
  volume =       "3",
  pages =        "79--84",
  year =         "1965",
  MRclass =      "65.25",
  MRnumber =     "33 \#5090",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{King:1965:LED,
  author =       "R. King",
  title =        "Letter to the {Editor}: On the Double-Precision Square
                 Root Routine",
  journal =      j-CACM,
  volume =       "8",
  number =       "4",
  pages =        "202",
  month =        apr,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions; floating-point
                 arithmetic",
}

@Book{Lebedev:1965:SFT,
  author =       "N. N. (Nikola{\u\i}i Nikolaevich) Lebedev",
  title =        "Special Functions and Their Applications",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xii + 308",
  year =         "1965",
  LCCN =         "QA351 .L3613",
  bibdate =      "Sat Apr 1 14:42:46 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Revised English edition translated and edited by
                 Richard A. Silverman.",
  series =       "Selected Russian publications in the mathematical
                 sciences",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Mathematical physics",
}

@Book{Lyusternik:1965:HCE,
  author =       "L. A. Lyusternik and O. A. Chervonenkis and A. R.
                 Yanpol{\'s}kii",
  title =        "Handbook for Computing Elementary Functions",
  volume =       "76",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "xiii + 251",
  year =         "1965",
  LCCN =         "QA221.L513",
  MRclass =      "65.25",
  MRnumber =     "32 \#584",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Translated from the Russian by G. J. Tee. Translation
                 edited by K. L. Stewart.",
  series =       "International series of monographs on pure and applied
                 mathematics",
  acknowledgement = ack-nhfb,
}

@Article{MacLaren:1965:APN,
  author =       "M. D. MacLaren",
  title =        "{Algorithm 272}: {Procedure} for the Normal
                 Distribution Functions [{S15}]",
  journal =      j-CACM,
  volume =       "8",
  number =       "12",
  pages =        "789--790",
  month =        dec,
  year =         "1965",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/365691.365957",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:03 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remarks \cite{Hill:1967:RAS,MacLaren:1968:RAP}.",
  abstract =     "The procedure gives $ \Phi (a) = \sqrt {1 / (2 \pi)}
                 \int_{- \infty }^a \exp ( - t^2 / 2) \, d t $ and $
                 \Phi *(a) = 2 (\Phi (|a|) - 0.5) = \sqrt {2 / \pi }
                 \int_0^{|a|} \exp ( - t^2 / 2) \, d t $.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "probability functions",
}

@Article{Maklovic:1965:IIC,
  author =       "S. T. Maklovi{\v{c}}",
  title =        "Investigation of integrals containing {Bessel} and
                 elementary functions. ({Russian})",
  journal =      "Ki{\v{s}}inev. Gos. Univ. U{\v{c}}en. Zap.",
  volume =       "82",
  pages =        "75--81",
  year =         "1965",
  MRclass =      "33.25",
  MRnumber =     "34 \#387",
  MRreviewer =   "H. A. Lauwerier",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Markman:1965:RZF,
  author =       "B. Markman",
  title =        "The {Riemann} Zeta Function",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "5",
  number =       "2",
  pages =        "138--141",
  year =         "1965",
  bibdate =      "Sat Oct 30 08:53:17 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  journal-URL =  "http://link.springer.com/journal/10543",
  remark =       "Fullerton: A 25-line Algol procedure for evaluating $
                 \zeta (s) $ for all $ s \neq 1 $ is given.",
}

@Article{Medhurst:1965:EI,
  author =       "R. G. Medhurst and J. H. Roberts",
  title =        "Evaluation of the Integral $ {I}_n(b) = \frac {2}{\pi
                 } \int^\infty_0 \bigg (\frac {\sin x}{x} \bigg)^n \cos
                 (b x) d x $",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "89",
  pages =        "113--117",
  month =        apr,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Metze:1965:MSR,
  author =       "Gernot Metze",
  title =        "Minimal Square Rooting",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "2",
  pages =        "181--185",
  month =        apr,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.263963",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038397",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Miller:1965:ASF,
  author =       "G. F. Miller",
  title =        "Algorithms for Special Functions {II}",
  journal =      j-NUM-MATH,
  volume =       "7",
  pages =        "194--196",
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Fri Sep 16 10:22:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  remark =       "Fullerton: Corrections and simplifications of the $
                 \sin $, $ \cos $ and $ \tan $ routines given in paper
                 I. See Clenshaw (1963).",
  xxmonth =      "(none)",
  xxnumber =     "(none)",
}

@Article{Nemeth:1965:CEF,
  author =       "G. N{\'e}meth",
  title =        "{Chebyshev} expansions for {Fresnel} integrals",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "4",
  pages =        "310--312",
  month =        aug,
  year =         "1965",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01436524",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 20:47:18 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  remark =       "Fullerton: Two series of 12-digit coefficients are
                 given to cover the range $ 0 \leq x < \infty $.",
}

@Article{Rice:1965:CPR,
  author =       "John R. Rice",
  title =        "On the Conditioning of Polynomial and Rational Forms",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "5",
  pages =        "426--435",
  month =        oct,
  year =         "1965",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01436257",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.99",
  MRnumber =     "MR0189283 (32 \#6710)",
  MRreviewer =   "James H. Wilkinson",
  bibdate =      "Sun Oct 16 17:22:04 GMT 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/nummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "number of multiplications to evaluate a polynomial",
}

@Article{Slepian:1965:EAP,
  author =       "David Slepian and Estelle Sonnenblick",
  title =        "Eigenvalues associated with prolate spheroidal wave
                 functions of zero order",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "44",
  number =       "8",
  pages =        "1745--1759",
  month =        oct,
  year =         "1965",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  MRclass =      "65.25",
  MRnumber =     "0183103 (32 \#585)",
  MRreviewer =   "R. Nicolovius",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1965/BSTJ.1965.4408.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol44/bstj44-8-1745.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}

@Article{Slepian:1965:SAE,
  author =       "David Slepian",
  title =        "Some Asymptotic Expansions for Prolate Spheroidal Wave
                 Functions",
  journal =      "J. Math. and Physics {XLIV(2)}",
  volume =       "??",
  number =       "??",
  pages =        "99--140",
  month =        jun,
  year =         "1965",
  bibdate =      "Sat Oct 30 10:46:38 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/mathscinet/search/publications.html?pg1=IID&s1=189661",
  acknowledgement = ack-nhfb,
  author-dates = "1923--2007",
  citedby =      "Fullerton:1980:BEM",
  remark =       "Fullerton: Several complicated expansions are derived
                 and presented.",
}

@Article{Swarztrauber:1965:LED,
  author =       "P. N. Swarztrauber",
  title =        "Letter to the {Editor}: On the Double-Precision Square
                 Root Routine",
  journal =      j-CACM,
  volume =       "8",
  number =       "4",
  pages =        "202",
  month =        apr,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Aug 31 14:02:19 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions; floating-point
                 arithmetic",
}

@Article{Thompson:1965:AEI,
  author =       "G. T. Thompson",
  title =        "The Asymptotic Expansion of the Integrals Psi and Chi
                 in Terms of {Tchebycheff} Polynomials (in {Technical
                 Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "92",
  pages =        "661--663",
  month =        oct,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Doppler Broadening",
}

@Book{Clenshaw:1966:CSB,
  author =       "C. W. Clenshaw and Susan M. Picken",
  title =        "{Chebyshev} series for {Bessel} functions of
                 fractional order",
  volume =       "8",
  publisher =    pub-HMSO,
  address =      pub-HMSO:adr,
  pages =        "iii + 53",
  year =         "1966",
  MRclass =      "33.25",
  MRnumber =     "203095",
  MRreviewer =   "L. J. Slater",
  bibdate =      "Sun Nov 12 06:18:24 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "National Physical Laboratory. Mathematical tables",
  acknowledgement = ack-nhfb,
  author-dates = "Charles William Clenshaw (15 March 1926--23 September
                 2004)",
  xxpages =      "51",
  xxpages =      "iii + 54",
}

@Article{Cody:1966:CCA,
  author =       "W. J. {Cody, Jr.}",
  title =        "Corrigenda: ``{Chebyshev} Approximations for the
                 Complete Elliptic Integrals $ {K} $ and $ {E} $''",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "93",
  pages =        "207--207",
  month =        jan,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Fri Oct 23 11:13:58 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Cody:1965:CAC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Doring:1966:CZC,
  author =       "Boro Doring",
  title =        "Complex Zeros of Cylinder Functions",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "94",
  pages =        "215--222",
  month =        apr,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Fike:1966:SAS,
  author =       "C. T. Fike",
  title =        "Starting Approximations for Square Root Calculation on
                 {IBM System\slash 360}",
  journal =      j-CACM,
  volume =       "9",
  number =       "4",
  pages =        "297--299",
  month =        apr,
  year =         "1966",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/365278.365556",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See letter \cite{Fike:1967:LER}.",
  abstract =     "Several starting approximations for square root
                 calculation by Newton's method are presented in a form
                 to facilitate their use in IBM System/360 square root
                 routines. These approximations include several for the
                 range [1/16, 1], which is the interval of primary
                 interest on IBM System/360.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions; IBM S/360",
}

@Article{Filippi:1966:BEE,
  author =       "S. Filippi",
  title =        "{Die Berechnung einiger elementarer transzendenter
                 Funktionen mit Hilfe des Richardson-Algorithmus}
                 \toenglish {The Computation of Some Elementary
                 Transcendental Functions by Means of the Richardson
                 Algorithm} \endtoenglish",
  journal =      j-COMPUTING,
  volume =       "1",
  number =       "2",
  pages =        "127--132",
  month =        jun,
  year =         "1966",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/BF02342622",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Gautschi:1966:AD,
  author =       "Walter Gautschi",
  title =        "{Algorithm 282}: {Derivatives} of $ e^x / x $, $ \cos
                 (x) / x $, and $ \sin (x) / x $",
  journal =      j-CACM,
  volume =       "9",
  number =       "4",
  pages =        "272--272",
  month =        apr,
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:05 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Gautschi:1970:RAD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\cos(x)/x$; $\sin(x)/x$; $e^x/x$; elementary
                 functions",
}

@Article{Gautschi:1966:ARC,
  author =       "Walter Gautschi",
  title =        "{Algorithm 292}: {Regular} {Coulomb} Wave Functions",
  journal =      j-CACM,
  volume =       "9",
  number =       "11",
  pages =        "793--795",
  month =        nov,
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:10 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Coulomb wave functions; special functions",
}

@Article{Glasser:1966:ESI,
  author =       "M. L. Glasser",
  title =        "Evaluation of Some Integrals Involving the $ \psi
                 $-Function (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "94",
  pages =        "332--333",
  month =        apr,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Gustafson:1966:CAM,
  author =       "Sven-{\AA}ke Gustafson",
  title =        "Convergence Acceleration by Means of Numerical
                 Quadrature",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "6",
  number =       "2",
  pages =        "117--128",
  month =        jun,
  year =         "1966",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01933103",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  bibdate =      "Wed Jan 4 18:52:09 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=6&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=2&spage=117",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "convergence acceleration",
}

@Article{Hart:1966:CAR,
  author =       "Roger G. Hart",
  title =        "A Close Approximation Related to the Error Function
                 (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "96",
  pages =        "600--602",
  month =        oct,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Hastings:1966:RCB,
  author =       "C. W. Hastings",
  title =        "{R66-78} Computation of the Base Two Logarithm of
                 Binary Number",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-15",
  number =       "6",
  pages =        "956--957",
  month =        dec,
  year =         "1966",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1966.264517",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 05:46:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038956",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Book{Jurimae:1966:KFT,
  author =       "E. J{\"u}rim{\"a}e",
  title =        "Kompleksmuutuja funktsioonide teooria. {I}:
                 Elementaarsed funktsioonid. ({Estonian}) [Theory of
                 functions of a complex variable. {I}: Elementary
                 functions]",
  publisher =    "Tartu Riiklik {\"U}likool",
  address =      "Tartu, Estonia",
  pages =        "131",
  year =         "1966",
  MRclass =      "30.00",
  MRnumber =     "40 \#5827a",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Kogbetliantz:1966:GEF,
  author =       "E. G. Kogbetliantz",
  title =        "Generation of Elementary Functions",
  crossref =     "Ralston:1960:MMD",
  pages =        "7--35",
  year =         "1966",
  bibdate =      "Sat Dec 09 14:09:27 1995",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}

@TechReport{Kuki:1966:CAE,
  author =       "H. Kuki",
  title =        "Comments on the {ANL} Evaluation of the {OS\slash 360
                 FORTRAN} Math Function Library",
  type =         "????",
  number =       "SSD 169, C4773",
  institution =  "SHARE Secretary Distribution",
  address =      "????",
  pages =        "47--53",
  year =         "1966",
  bibdate =      "Wed Feb 14 19:13:50 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Larssen:1966:CAC,
  author =       "Gerhard Meidell Larssen",
  title =        "Certification of {Algorithm 56}: {Complete} elliptic
                 integral of the second kind",
  journal =      j-CACM,
  volume =       "9",
  number =       "1",
  pages =        "12--12",
  month =        jan,
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:04 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}

@Article{Mechel:1966:CMB,
  author =       "Fr. Mechel",
  title =        "Calculation of the Modified {Bessel} Functions of the
                 Second Kind with Complex Argument",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "95",
  pages =        "407--412",
  month =        jul,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Nellis:1966:REE,
  author =       "W. J. Nellis and B. C. Carlson",
  title =        "Reduction and Evaluation of Elliptic Integrals",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "94",
  pages =        "223--231",
  month =        apr,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Pike:1966:ALG,
  author =       "M. C. Pike and I. D. Hill",
  title =        "{Algorithm 291}: {Logarithm} of Gamma Function",
  journal =      j-CACM,
  volume =       "9",
  number =       "9",
  pages =        "684--684",
  month =        sep,
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:09 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\log(\Gamma(x))$; special functions",
  remark =       "Fullerton: Short Algol procedure valid only for $ x >
                 0 $. Accurate to 10 digits.",
}

@TechReport{Price:1966:NAR,
  author =       "James F. Price",
  title =        "Numerical Analysis and Related Literature for
                 Scientific Computer Users",
  type =         "Mathematical Note",
  number =       "456 (D1-82-0517)",
  institution =  "Mathematics Research Laboratory, Boeing Scientific
                 Research Laboratories",
  address =      "Seattle, WA, USA",
  edition =      "Second",
  pages =        "ix + 191",
  month =        mar,
  year =         "1966",
  bibdate =      "Mon Jun 18 06:55:22 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.dtic.mil/dtic/tr/fulltext/u2/632244.pdf",
  abstract =     "The Second Edition of this annotated bibliography
                 lists the contents of over 150 books in English on
                 numerical analysis and related literature. It is meant
                 for the general scientific computer user and not for
                 the research numerical analyst; the descriptions and
                 suggestions are given with this in mind. It is expected
                 that the most useful section will be the 27-page index
                 which tells in which books various topics may be found.
                 There is also a section describing how to look up
                 further information on such topics which may be found
                 in the literature.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Introduction / iv \\
                 I. Numerical Procedures in Books / 1 \\
                 II. How to Find What You Want / 157 \\
                 A. Bibliographies, lists of books, abstracting journals
                 / 157 \\
                 B. Looking for Tables of Various Functions / 161 \\
                 C. Keeping Up with Some of the New Literature / 163 \\
                 III. Subject Index / 165",
}

@Book{Slater:1966:GHF,
  author =       "Lucy Joan Slater",
  title =        "Generalized Hypergeometric Functions",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xiii + 273",
  year =         "1966",
  LCCN =         "QA351 .S565",
  bibdate =      "Sat Oct 30 21:01:55 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Hypergeometric functions",
}

@Article{Takenaga:1966:EIG,
  author =       "Roy Takenaga",
  title =        "On the Evaluation of the Incomplete Gamma Function (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "96",
  pages =        "606--610",
  month =        oct,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Thompson:1966:ESI,
  author =       "Rory Thompson",
  title =        "Evaluation of $ {I}_n(b) = 2 \pi^{-1} \int^\infty_0
                 \big (\frac {sin x}{x} \big)^n \cos (b x) d x $ and of
                 Similar Integrals (in {Technical Notes and Short
                 Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "94",
  pages =        "330--332",
  month =        apr,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Tolke:1966:PFT,
  author =       "Friedrich T{\"o}lke",
  title =        "{Praktische Funktionenlehre. 2. Theta-Funktionen und
                 spezielle Weierstrasssche Funktionen}. ({German})
                 [{Practical} functional theory. 2. {Theta} functions
                 and special {Weierstrass} functions]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "vii + 248",
  year =         "1966",
  ISBN =         "",
  ISBN-13 =      "",
  LCCN =         "????",
  bibdate =      "Mon Feb 13 19:01:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@TechReport{Tricomi:1966:RUS,
  author =       "F. G. Tricomi",
  title =        "Lectures on the use of special functions by
                 calculations with electronic computers",
  type =         "Lecture Series",
  number =       "47",
  institution =  "The Institute for Fluid Dynamics and Applied
                 Mathematics, University of Maryland, College Park",
  address =      "College Park, MD, USA",
  year =         "1966",
  bibdate =      "Tue Mar 14 18:48:58 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Book{Watson:1966:TTB,
  author =       "G. N. Watson",
  title =        "A Treatise on the Theory of {Bessel} Functions",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Second",
  pages =        "vi + 804",
  year =         "1966",
  ISBN =         "0-521-09382-1",
  ISBN-13 =      "978-0-521-09382-8",
  LCCN =         "QA 408 W33t 1966",
  bibdate =      "Fri Nov 24 13:53:35 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matched-field-proc.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  alias =        "Watson 66a",
  sthbib =       "M2 Wat 82 55",
}

@Article{Wood:1966:DBI,
  author =       "Van E. Wood and R. P. Kenan and M. L. Glasser",
  title =        "{Doppler} Broadening Integrals (in {Technical Notes
                 and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "96",
  pages =        "610--611",
  month =        oct,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Anonymous:1967:CAP,
  author =       "Anonymous",
  title =        "Convergence acceleration from the point of view of
                 linear programming",
  journal =      j-BIT,
  volume =       "7",
  number =       "3",
  pages =        "256--256",
  month =        sep,
  year =         "1967",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01939269",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:10 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=7&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=7&issue=3&spage=256",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "convergence acceleration",
}

@Article{Bond:1967:AAF,
  author =       "Gillian Bond and M. L. V. Pitteway",
  title =        "{Algorithm 301}: {Airy} Function",
  journal =      j-CACM,
  volume =       "10",
  number =       "5",
  pages =        "291--292",
  month =        may,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:13 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Airy functions; special functions",
  remark =       "Fullerton: 100-line Algol program for $ \operatorname
                 {Ai} $, $ \operatorname {Bi} $. and their
                 derivatives.",
}

@Article{Cody:1967:CAN,
  author =       "W. J. Cody and K. E. Hillstrom",
  title =        "{Chebyshev} Approximations for the Natural Logarithm
                 of the Gamma Function",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "98",
  pages =        "198--203",
  month =        apr,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Relative errors down to $ 10^{-17} $.",
}

@Article{Cody:1967:CRC,
  author =       "W. J. Cody and Henry C. {Thacher, Jr.}",
  title =        "Corrigendum: ``{Rational Chebyshev approximations for
                 Fermi--Dirac integrals of orders $ - 1 / 2 $, $ 1 / 2
                 $, and $ 3 / 2 $''}",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "99",
  pages =        "525--525",
  month =        jul,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon Sep 26 19:36:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Cody:1967:RCA}.",
  URL =          "http://www.jstor.org/stable/2003289",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  xxmonth =      "(none)",
}

@Article{Cody:1967:LEA,
  author =       "William J. {Cody, Jr.}",
  title =        "Letter to the {Editor}: Another Aspect of Economical
                 Polynomials",
  journal =      j-CACM,
  volume =       "10",
  number =       "9",
  pages =        "531--531",
  month =        sep,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363566.363577",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Nov 17 10:20:03 1994",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Fike:1967:MEP}.",
  abstract =     "In his paper ``Methods of Evaluating Polynomial
                 Approximations in Function Evaluation Routines'' [Comm.
                 ACM 10, (March 1967)], C. T. Fike fails to discuss one
                 very important aspect of the ``economical'' methods for
                 polynomials. Since these evaluation methods involve a
                 decreased number of arithmetic operations over the
                 usual Horner's method (or at least replace a
                 multiplication by an addition) the implication is that
                 they are faster to execute. Dr. Fike points out that
                 these methods can be poorly conditioned for particular
                 polynomials, thus requiring extended precision or
                 fixed-point arithmetic to maintain accuracy and costing
                 more in time than Horner's method. But even if we
                 assume the methods are well conditioned, the need to
                 store away and retrieve intermediate results in some
                 machines with only one floating-point arithmetic
                 register can wipe out the time savings effected by a
                 reduction in the number of arithmetic operations. On
                 many of today's high-performance computers the time
                 required to store away and retrieve a result is about
                 the same as the time required for a floating-point
                 addition. It is no longer sufficient to estimate the
                 efficiency of a method by a count of arithmetic
                 operations alone.",
  acknowledgement = ack-wjc # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic",
}

@Article{Cody:1967:RCA,
  author =       "W. J. Cody and Henry C. {Thacher, Jr.}",
  title =        "Rational {Chebyshev} approximations for {Fermi--Dirac}
                 integrals of orders $ - 1 / 2 $, $ 1 / 2 $, and $ 3 / 2
                 $",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "97",
  pages =        "30--40",
  month =        jan,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon Sep 26 19:23:19 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Cody:1967:CRC}.",
  URL =          "http://www.jstor.org/stable/2003468",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Relative errors down to $ 10^{-9} $.",
}

@Article{DiDonato:1967:ECI,
  author =       "A. R. DiDonato and M. P. Jarnagin",
  title =        "The Efficient Calculation of the Incomplete
                 Beta-Function Ratio for Half-Integer Values of the
                 Parameters $ a, b $",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "100",
  pages =        "652--662",
  month =        oct,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Fair:1967:RAI,
  author =       "Wyman G. Fair and Yudell L. Luke",
  title =        "Rational Approximations to the Incomplete Elliptic
                 Integrals of the First and Second Kinds",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "99",
  pages =        "418--422",
  month =        jul,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Fettis:1967:MCI,
  author =       "Henry E. Fettis",
  title =        "More on the Calculation of the Integral $ {I}_n(b) =
                 \frac {2}{\pi } \int^\infty_0 \big (\frac {\sin x}{x}
                 \big)^n \cos b x \, d x $ (in {Technical Notes and
                 Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "100",
  pages =        "727--730",
  month =        oct,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Fike:1967:LER,
  author =       "C. T. Fike",
  title =        "Letter to the {Editor}: {A} rational approximation
                 optimal by {Moursund}'s criterion",
  journal =      j-CACM,
  volume =       "10",
  number =       "11",
  pages =        "683--684",
  month =        nov,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363790.363795",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:16 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Moursund:1967:OSV,Fike:1966:SAS}",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "elementary function; square root",
  remark =       "Gives a starting value for $ \sqrt {x} $ ($x$ on $ [1
                 / 16, 1]$) of $ R*(x) = 1.68212586 - 1.28977371 / (x +
                 0.84106293)$, with an error of $ 2^{-12.496}$.",
}

@Article{Fike:1967:MEP,
  author =       "C. T. Fike",
  title =        "Methods of Evaluating Polynomial Approximations in
                 Function Evaluation Routines",
  journal =      j-CACM,
  volume =       "10",
  number =       "3",
  pages =        "175--178",
  month =        mar,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363162.363200",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:12 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See remark on efficiency \cite{Cody:1967:LEA}.",
  abstract =     "The method of nested multiplication is commonly used
                 in function evaluation routines to evaluate
                 approximation polynomials. New polynomial evaluation
                 methods have been developed in recent years which
                 require fewer multiplications than nested
                 multiplication and may therefore be preferable for use
                 in function evaluation routines. Although some of these
                 methods do not appear to be practically useful because
                 of rounding-error difficulties, several methods of
                 evaluating low-degree polynomials have been found to be
                 satisfactory. Three such methods are described and
                 illustrated.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  received =     "August 1966 (revised December 1966)",
}

@Article{Friedland:1967:AAV,
  author =       "Paul Friedland",
  title =        "{Algorithm 312}: {Absolute} Value and Square Root of a
                 Complex Number",
  journal =      j-CACM,
  volume =       "10",
  number =       "10",
  pages =        "665--665",
  month =        oct,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363717.363780",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:15 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\abs(z)$; $\sqrt(z)$; elementary functions",
}

@Article{Gautschi:1967:CAT,
  author =       "Walter Gautschi",
  title =        "Computational Aspects of Three-Term Recurrence
                 Relations",
  journal =      j-SIAM-REVIEW,
  volume =       "9",
  number =       "1",
  pages =        "24--82",
  month =        jan,
  year =         "1967",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1009002",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:05:42 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/9/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://link.aip.org/link/?SIR/9/24/1",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  keywords =     "Bessel functions; continued fractions; Coulomb wave
                 functions; Fourier coefficients; incomplete beta
                 functions; incomplete gamma functions; Legendre
                 functions; Sturm--Liouville boundary value problems;
                 three-term recurrence relations",
  onlinedate =   "January 1967",
  remark =       "This paper is frequently cited in later work on
                 continued fractions, three-term recurrence relations,
                 and special functions.",
}

@Article{Goldstein:1967:CSB,
  author =       "Max Goldstein and C. W. Clenshaw and Susan M. Picken",
  title =        "{Chebyshev} Series for {Bessel} Functions of
                 Fractional Order",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "99",
  pages =        "509--??",
  month =        jul,
  year =         "1967",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2003271",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Sun Nov 12 09:25:35 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Charles William Clenshaw (15 March 1926--23 September
                 2004)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "TO DO: Why is this missing from journal bibliography
                 file, mathcomp1970.bib?",
}

@Article{Gunn:1967:ACW,
  author =       "J. H. Gunn",
  title =        "{Algorithm 300}: {Coulomb} Wave Functions",
  journal =      j-CACM,
  volume =       "10",
  number =       "4",
  pages =        "244--245",
  month =        apr,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:12 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Vos:1973:RAC}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Coulomb wave functions; special functions",
  remark =       "Fullerton: 150-line Algol procedure that is superseded
                 by other routines in the physics literature.",
}

@Article{Hill:1967:ACS,
  author =       "I. D. Hill and M. C. Pike",
  title =        "{Algorithm 299}: {Chi}-Squared Integral",
  journal =      j-CACM,
  volume =       "10",
  number =       "4",
  pages =        "243--244",
  month =        apr,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:12 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Hill:1985:RCS,elLozy:1976:RAC}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "chi-squared; probability functions",
  remark =       "Fullerton: Short Algol procedure.",
}

@Article{Hill:1967:ANCa,
  author =       "I. D. Hill and S. A. Joyce",
  title =        "{Algorithm 304}: {Normal} Curve Integral",
  journal =      j-CACM,
  volume =       "10",
  number =       "6",
  pages =        "374--375",
  month =        jun,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363332.363411",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:13 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remarks \cite{Hill:1967:RAS,Bergson:1968:ACR}.",
  abstract =     "{\tt normal(x,upper)} calculates the curve, i.e., tail
                 area of the standardized normal curve, i.e., $ (1 /
                 \sqrt {2 \pi }) \int \exp ( - t^2 / 2) \, d t $. If
                 {\tt upper} is {\tt true}, the limits of integration
                 are $x$ and $ \infty $. If {\tt upper} is {\tt false},
                 the limits of integration are $ - \infty $ and $x$.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "probability functions",
  remark =       "Fullerton: 75-line Algol procedure that is superseded
                 by numerous $ \erf $ routines.",
}

@Article{Hill:1967:RAS,
  author =       "I. D. Hill and S. A. Joyce",
  title =        "Remarks on {Algorithm 123} [{S15}]: {Real} error
                 function, {{\tt ERF(x)}}; {Algorithm 180} [{S15}]:
                 {Error} Function --- Large $ {X} $; {Algorithm 181}
                 [{S15}]: {Complementary} Error Function --- Large $ {X}
                 $; {Algorithm 209} [{S15}]: {Gauss}; {Algorithm 226}
                 [{S15}]: {Normal} Distribution Function; {Algorithm
                 272} [{S15}]: {Procedure} for the Normal Distribution
                 Functions; {Algorithm 304} [{S15}]: {Normal} Curve
                 Integral",
  journal =      j-CACM,
  volume =       "10",
  number =       "6",
  pages =        "377--378",
  month =        jun,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363332.365433",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:13 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See
                 \cite{Cyvin:1964:AND,MacLaren:1965:APN,Hill:1967:ANCa}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\erf(x)$; $\erfc(x)$; probability functions; special
                 functions",
}

@Article{Kilpatrick:1967:CIP,
  author =       "J. E. Kilpatrick and Shigetoshi Katsura and Yuji
                 Inoue",
  title =        "Calculations of Integrals of Products of {Bessel}
                 Functions",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "99",
  pages =        "407--412",
  month =        jul,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Knuth:1967:CTE,
  author =       "Donald E. Knuth and Thomas J. Buckholtz",
  title =        "Computation of Tangent, {Euler}, and {Bernoulli}
                 Numbers",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "100",
  pages =        "663--688",
  month =        oct,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.25",
  MRnumber =     "36 #4787",
  bibdate =      "Fri Mar 22 18:03:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database; MathSciNet database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: The first 119. 120 and 250 tangent, Euler
                 and Bernoulli numbers, respectively.",
}

@Book{MacRobert:1967:SHE,
  author =       "Thomas Murray MacRobert and Ian Naismith Sneddon",
  title =        "Spherical harmonics; an elementary treatise on
                 harmonic functions, with applications",
  volume =       "98",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  edition =      "Third",
  pages =        "xviii + 349",
  year =         "1967",
  LCCN =         "QA406 .M3 1967",
  bibdate =      "Sat Oct 30 21:22:03 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series of monographs in pure and applied
                 mathematics",
  acknowledgement = ack-nhfb,
  author-dates = "1884--1962",
  subject =      "Spherical harmonics",
}

@Book{Meinardus:1967:AFT,
  author =       "G{\"u}nter Meinardus",
  title =        "Approximation of functions: Theory and numerical
                 methods",
  volume =       "13",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 198",
  year =         "1967",
  ISBN =         "0-387-03985-6, 3-540-03985-6",
  ISBN-13 =      "978-0-387-03985-5, 978-3-540-03985-3",
  ISSN =         "0081-3877",
  LCCN =         "QA221 .M3813",
  bibdate =      "Thu Oct 19 17:07:54 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Springer Tracts in Natural Philosophy",
  URL =          "http://catalogue.bnf.fr/ark:/12148/cb37378349d",
  acknowledgement = ack-nhfb,
  author-dates = "(1926--2007)",
  remark =       "Translation by Larry L. Schumaker of
                 \cite{Meinardus:1964:AFI}.",
  subject =      "Approximation theory; Numerical analysis; Th{\'e}orie
                 de l'approximation; Analyse num{\'e}rique; Fonctions
                 (math{\'e}matiques); Approximation, Th{\'e}orie de l';
                 Analyse num{\'e}rique; Approximation theory; Numerical
                 analysis; Approximation; Funktion; Mathematik",
  tableofcontents = "Part I. Linear Approximation \\
                 1. The General Linear Approximation Problem / 1 \\
                 1.1. Statement of the Problem. Existence Theorem / 1
                 \\
                 1.2. Strictly Convex Spaces. Hilbert Space / 2 \\
                 1.3. Maximal Linear Functionals / 4 \\
                 2. Dense Systems / 5 \\
                 2.1. A General Criterion of Banach / 5 \\
                 2.2. Approximation Theorems of Weierstrass and Muntz /
                 6 \\
                 2.3. Approximation Theorems in the Complex Plane / 10
                 \\
                 3. General Theory of Linear Tchebycheff Approximation /
                 13 \\
                 3.1. Fundamentals. The Theorem of Kolmogoroff / 13 \\
                 3.2. The Haar Uniqueness Theorem. Linear Functionals
                 and Alternants / 16 \\
                 3.3. Further Uniqueness Results / 24 \\
                 3.4. Invariants / 26 \\
                 3.5. Vector-valued Functions / 28 \\
                 4. Special Tchebycheff Approximations / 28 \\
                 4.1. Tchebycheff Systems / 28 \\
                 4.2. Tchebycheff Polynomials / 31 \\
                 4.3. The Function ?? / 33 \\
                 4.4. A Problem of Bernstein and Achieser / 36 \\
                 4.5 Zolotareff's Problem / 41 \\
                 5. Estimating the Magnitude of Error in Trigonometric
                 and Polynomial Approximation / 45 \\
                 5.1. Projection Operators. Linear Polynomial Operators
                 / 45 \\
                 5.2. The Connection between Trigonometric and
                 Polynomial Approximation / 45 \\
                 5.3. The Fej{\'e}r Operator / 47 \\
                 5.4. The Korovkin Operators / 50 \\
                 5.5. The Theorems of D. Jackson / 52 \\
                 5.6. The Theorems of Bernstein and Zygmund / 57 \\
                 5.7. Supplements / 65 \\
                 6. Approximation by Polynomials and Related Functions /
                 72 \\
                 6.1. Foundations / 72 \\
                 6.2. Upper Bounds for En (??) / 77 \\
                 6.3. Lower Bounds for En (??) / 82 \\
                 6.4. Dependence of the Approximation on the Interval /
                 85 \\
                 6.5. Regular Haar Systems / 87 \\
                 6.6. Asymptotic Results / 90 \\
                 6.7. Results for tho Alternants / 101 \\
                 7. Numerical Methods for Linear Tchebycheff
                 Approximation / 105 \\
                 7.1. The Iterative Methods of Remez / 105 \\
                 7.2. Initial Approximations / 116 \\
                 7.3. Direct Methods / 122 \\
                 7.4. Discretization. Other Methods / 124 \\
                 Part II. Non-linear Approximation \\
                 8. General Theory of Non-linear Tchebycheff
                 Approximation / 131 \\
                 8.1. Survey of the Problem. A Generalization of the
                 Kolmogoroff Theorem / 131 \\
                 8.2. The Haar Uniqueness Theorem. Alternants / 141 \\
                 8.3. The Investigations of Rice / 148 \\
                 8.4. The Newton Iteration Method / 149 \\
                 8.5. H-Sets / 153 \\
                 9. Rational Approximation / 154 \\
                 9.1. Existence. Invariants. A Theorem of Walsh / 154
                 \\
                 9.2. Theorems on Alternants. Anomalies. Continuity.
                 Examples / 160 \\
                 9.3. Asymptotic Results. Small Intervals / 167 \\
                 9.4. Numerical Methods / 170 \\
                 10. Exponential Approximation / 176 \\
                 10.1. The Results of Rice / 176 \\
                 10.2. An Anomaly Theorem. Constructive Methods / 179
                 \\
                 11. Segment Approximation / 183 \\
                 11.1. Statement of the Problem. Hypotheses / 183 \\
                 11.2. The principle of Lawson / 184 \\
                 H.3. Equidegree Polynomial Approximation / 188 \\
                 Bibliography / 189 \\
                 Subject Index / 197",
}

@Article{Moody:1967:ADF,
  author =       "William T. Moody",
  title =        "Approximations for the Psi (Digamma) Function (in
                 Technical Notes and Short Notices)",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "97",
  pages =        "112--112",
  month =        jan,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Moursund:1967:OSV,
  author =       "David G. Moursund",
  title =        "Optimal starting values for {Newton--Raphson}
                 calculation of $ \sqrt {x} $",
  journal =      j-CACM,
  volume =       "10",
  number =       "7",
  pages =        "430--432",
  month =        jul,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363427.363454",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.25",
  MRnumber =     "39\#2297",
  bibdate =      "Thu Sep 1 10:15:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See letter \cite{Fike:1967:LER}.",
  abstract =     "The problem of obtaining starting values for the
                 Newton-Raphson calculation of $ \sqrt {x} $ on a
                 digital computer is considered. It is shown that the
                 conventionally used best uniform approximations to $
                 \sqrt {x} $ do not provide optimal starting values. The
                 problem of obtaining optimal starting values is stated,
                 and several basic results are proved. A table of
                 optimal polynomial starting values is given.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions",
  remark =       "Title of article has incorrect $ \sqrt (x^{1 / 2}) $:
                 the article discusses computation of {\tt sqrt(x)}.",
}

@Article{Olver:1967:BSS,
  author =       "F. W. J. Olver",
  title =        "Bounds for the Solutions of Second-Order Linear
                 Difference Equations [{Anger--Weber} and {Struve}
                 Functions]",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "71B",
  number =       "4",
  pages =        "161--166",
  month =        oct,
  year =         "1967",
  ISSN =         "0091-0635",
  bibdate =      "Sat Oct 30 09:37:44 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Fullerton: Truncation error estimates of an earlier
                 published algorithm.",
}

@Article{Olver:1967:NSS,
  author =       "F. W. J. Olver",
  title =        "Numerical solution of second-order linear difference
                 equations",
  journal =      j-J-RES-NATL-BUR-STAND-B,
  volume =       "71B",
  number =       "2--3",
  pages =        "111--129",
  month =        apr,
  year =         "1967",
  CODEN =        "JNBBAU",
  DOI =          "https://doi.org/10.6028/jres.071B.018",
  ISSN =         "0022-4340",
  MRclass =      "65.70",
  MRnumber =     "221789",
  MRreviewer =   "G. N. Lance",
  bibdate =      "Sun Nov 5 09:03:34 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://nvlpubs.nist.gov/nistpubs/jres/71B/jresv71Bn2-3p111_A1b.pdf",
  abstract =     "A new algorithm is given for computing the solution of
                 any second-order linear difference equation which is
                 applicable when simple recurrence procedures cannot be
                 used because of instability. Compared with the
                 well-known Miller algorithm the new method has the
                 advantages of (i) automatically determining the correct
                 number of recurrence steps. (ii) applying to
                 inhomogeneous difference equations, (iii) enabling more
                 powerful error analyses to be constructed.\par

                 The method is illustrated by numerical computations,
                 including error analyses of Anger--Weber, Struve, and
                 Bessel functions, and the solution of a differential
                 equation in Chebyshev series",
  acknowledgement = ack-nhfb,
  author-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards. Section B. Mathematics and Mathematical
                 Physics",
  journal-URL =  "http://www.nist.gov/nvl/jrespastpapers.cfm",
  keywords =     "Chebyshev series; difference equations; error
                 analysis; Miller algorithm. recurrence methods; special
                 functions",
}

@Article{Pike:1967:RAI,
  author =       "M. C. Pike and I. D. Hill",
  title =        "Remark on {Algorithm 179}: {Incomplete} {Beta} ratio",
  journal =      j-CACM,
  volume =       "10",
  number =       "6",
  pages =        "375--376",
  month =        jun,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:13 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$B(z,w)$; beta function; special functions",
  remark =       "Fullerton: Corrections to an Algol procedure.",
}

@Article{Pitteway:1967:RAA,
  author =       "M. L. V. Pitteway",
  title =        "Remark on {Algorithm 301}: {Airy} function",
  journal =      j-CACM,
  volume =       "10",
  number =       "7",
  pages =        "453--453",
  month =        jul,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:14 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Airy functions; special functions",
  remark =       "Fullerton: Corrections to an Algol procedure.",
}

@Book{Sen:1967:TSF,
  author =       "Bibhutibhusan Sen",
  title =        "A treatise on special functions, for scientists and
                 engineers",
  publisher =    "Allied Publishers",
  address =      "Bombay, India",
  pages =        "164",
  year =         "1967",
  LCCN =         "QA351 .S45",
  bibdate =      "Fri Oct 29 21:30:38 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Spherical harmonics",
}

@Book{Tolke:1967:PFE,
  author =       "Friedrich T{\"o}lke",
  title =        "{Praktische Funktionenlehre. 4. Elliptische
                 Integralgruppen und Jacobische elliptische Funktionen
                 im Komplexen}. ({German}) [{Practical} functional
                 theory. 4. {Elliptical} integral groups and {Jacobian}
                 elliptic functions in the complex plane]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 191",
  year =         "1967",
  DOI =          "https://doi.org/10.1007/978-3-662-36381-2",
  ISBN =         "3-662-36381-X, 3-662-35552-3 (print), 3-662-36381-X
                 (e-book)",
  ISBN-13 =      "978-3-662-36381-2, 978-3-662-35552-7 (print),
                 978-3-662-36381-2 (e-book)",
  LCCN =         "????",
  bibdate =      "Mon Feb 13 19:01:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/content/978-3-662-36381-2",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Book{Tolke:1967:PFJ,
  author =       "Friedrich T{\"o}lke",
  title =        "{Praktische Funktionenlehre. 3. Jacobische elliptische
                 Funktionen, Legendresche elliptische Normalintegrale
                 und spezielle Weierstrasssche Zeta- und
                 Sigma-Funktionen}. ({German}) [{Practical} functional
                 theory. 3. {Jacobian} elliptic functions, Legendre
                 elliptical normal Integrals and special {Weierstrass}
                 zeta- and sigma functions]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 180",
  year =         "1967",
  DOI =          "https://doi.org/10.1007/978-3-662-36379-9",
  ISBN =         "3-642-50264-4, 3-662-36379-8, 3-662-35550-7 (print),
                 3-662-36379-8 (e-book)",
  ISBN-13 =      "978-3-642-50264-4, 978-3-662-36379-9,
                 978-3-662-35550-3 (print), 978-3-662-36379-9 (e-book)",
  LCCN =         "????",
  bibdate =      "Mon Feb 13 19:01:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/content/978-3-662-36379-9",
  acknowledgement = ack-nhfb,
  language =     "German",
  tableofcontents = "5 Jacobische elliptische Funktionen und
                 zugeh{\"o}rige logarithmische Ableitungen \\
                 108. Definitionen \\
                 109. Funktionalgleichungen \\
                 110. Periodenverhalten und Substitutionen \\
                 111. Funktionswerte an den Stellen $ 0, \pm
                 \frac{1}{2}, \pm \frac{ix}{2}, \pm \frac{1}{2}, \pm
                 \frac{ix}{2} $ bzw. $ 0, \pm K, \pm iK', \pm K \pm iK'
                 $ \\
                 112. Trigonometrische und hyperbolische
                 Reihenentwicklungen \\
                 113. Potenzreihen-Entwicklungen \\
                 114. Imagin{\"a}re Argumenttransformation, reziproke
                 Modultransformation und imagin{\"a}re
                 Modultransformation \\
                 115. Ableitungen \\
                 116. Gausssche und Landensche Transformation.
                 Substitutionen f{\"u}r $ \zeta \pm \frac{1}{4}$ und
                 $\zeta \pm \frac{ix}{4} $ \\
                 117. Additionstheoreme. Transformationsgleichungen
                 f{\"u}r doppeltes und halbes Argument. Weitere
                 Substitutionen f{\"u}r $ \zeta \pm \frac{1}{4}$ und
                 $\zeta \pm \frac{ix}{4}$ sowie f{\"u}r $\zeta \pm
                 \frac{1}{4} \pm \frac{ix}{4} $ \\
                 118. Die Logarithmen der logarithmischen Ableitungen
                 der Jacobischen elliptischen Funktionen \\
                 119. {\"U}berg{\"a}nge vom (?,?)-System auf das $(z,
                 k)$-System \\
                 120. Funktionsverlauf der Jacobischen elliptischen
                 Funktionen und der zugeh{\"o}rigen Ableitungen und
                 logarithmischen Ableitungen im Reellen. Ausartungen \\
                 121. Differentialgleichungen erster und zweiter Ordnung
                 \\
                 122. Die Integrale der Jacobischen elliptischen
                 Funktionen \\
                 123. Die Integrale der logarithmischen Ableitungen der
                 Jacobischen elliptischen Funktionen \\
                 6 Umkehrfunktionen der Jacobischen elliptischen
                 Funktionen und elliptische Normalintegrale erster
                 Gattung. Elliptische Amplitudenfunktion sowie
                 Legendresche $F$- und $E$-Funktion. Elliptische
                 Normalintegrale zweiter Gattung. Jacobische Zeta- und
                 Heumansche Lambda-Funktion \\
                 124. Die 18 Umkehrfunktionen der Jacobischen
                 elliptischen Funktionen und ihrer logarithmischen
                 Ableitungen. (Elliptische Normalintegrale erster
                 Gattung.) Additionstheoreme der Umkehrfunktionen \\
                 125. Elliptische Normalintegrale erster Gattung in
                 hyperbolischer Form \\
                 126. Potenzreihen-Entwicklungen der Umkehrfunktionen
                 \\
                 127. Die elliptische Amplitudenfunktion $? = \am(z, k)$
                 und ihre Umkehrfunktion $z = F(?, k)$. Die vier
                 trigonometrischen Legendreschen Normalintegrale erster
                 Gattung \\
                 128. Darstellung der 18 Umkehrfunktionen und der
                 elliptischen Normalintegrale erster Gattung durch die
                 Funktion F. Die vier hyperbolischen Legendreschen
                 Normalintegrale erster Gattung und die Funktion $F$
                 f{\"u}r imagin{\"a}res Argument \\
                 129. Die Legendresche $E$-Funktion f{\"u}r reelles und
                 imagin{\"a}res Argument \\
                 130. Die 18 Integrale der Quadrate der Jacobischen
                 elliptischen Funktionen und ihrer logarithmischen
                 Ableitungen, die 12 durch Umformung der letzteren
                 entstehenden hyperbolischen Integrale, die 24
                 Normalintegrale zweiter Gattung und die acht
                 trigonometrischen und hyperbolischen Legendreschen
                 Normalintegrale zweiter Gattung \\
                 131. Die 46 Normalintegrale erster und zweiter Gattung
                 mit linearen trigonometrischen und hyperbolischen
                 Funktionen \\
                 132. Jacobische Zeta-Funktion und Heumansche
                 Lambda-Funktion \\
                 7 Normalintegrale dritter Gattung. Legendresche
                 $\Pi$-Funktion. Zur{\"u}ckf{\"u}hrung des allgemeinen
                 elliptischen Integrals auf Normalintegrale erster,
                 zweiter und dritter Gattung \\
                 133. Die 96 Normalintegrale dritter Gattung in
                 Jacobischer Form \\
                 134. Die acht zu den logarithmischen Ableitungen der
                 Jacobischen elliptischen Funktionen geh{\"o}rigen
                 Normalintegrale dritter Gattung \\
                 135. 48 Quotientenintegrale und 48 spezielle
                 Normalintegrale dritter Gattung in der Jacobischen Form
                 \\
                 136. Algebraische Form der elliptischen Normalintegrale
                 dritter Gattung \\
                 137. Darstellung der vollst{\"a}ndigen Normalintegrale
                 dritter Gattung durch Jacobische Zeta- und Heumansche
                 Lambda-Funktionen \\
                 138. Die $\Pi$-Funktion und die Integrale dritter
                 Gattung in trigonometrischer Form \\
                 139. Die 48 speziellen Normalintegrale dritter Gattung
                 in algebraischer Form \\
                 140. Weitere sechs spezielle Normalintegrale dritter
                 Gattung \\
                 141. Zur{\"u}ckf{\"u}hrung des allgemeinen elliptischen
                 Integrals in der Legendreschen Form auf Normalintegrale
                 erster, zweiter und dritter Gattung \\
                 8 Spezielle Weierstra{\ss}sche Zeta-Funktionen \\
                 142. Definitions- und Funktionalgleichungen \\
                 143. Substitutionen \\
                 144. Relatives Periodenverhalten. Spezielle
                 Funktionswerte. Funktionsverlauf \\
                 145. Lineare Beziehungen zu den logarithmischen
                 Ableitungen der Jacobischen elliptischen Funktionen und
                 deren Ableitungen \\
                 146. Integrale der $\Pi$-Funktionen als Weierstrasssche
                 Zeta-Funktionen und Ableitungen der Zeta-Funktionen \\
                 147. Differentialtransformationen f{\"u}r doppelte und
                 halbe Parameter \\
                 148. Gausssche und Landensche Transformation \\
                 149. Additionstheoreme und Transformationsgleichungen
                 f{\"u}r doppeltes und halbes Argument \\
                 150. Trigonometrische, hyperbolische und
                 Potenzreihen-Entwicklungen \\
                 151. Homogenit{\"a}tstransformation der Funktionen",
}

@Article{Verma:1967:NSG,
  author =       "Arun Verma",
  title =        "A Note on the Summation of the Generalised
                 Hypergeometric Functions (in {Technical Notes and Short
                 Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "98",
  pages =        "232--236",
  month =        apr,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Wigner:1967:BRW,
  author =       "Eugene P. Wigner",
  title =        "Book Review: {Wilhelm Magnus, Fritz Oberhettinger, and
                 R. P. Soni, \booktitle{Formulas and Theorems for the
                 Special Functions of Mathematical Physics}}",
  journal =      j-PHYS-TODAY,
  volume =       "20",
  number =       "12",
  pages =        "81--81",
  month =        dec,
  year =         "1967",
  CODEN =        "PHTOAD",
  DOI =          "https://doi.org/10.1063/1.3034082",
  ISSN =         "0031-9228 (print), 1945-0699 (electronic)",
  ISSN-L =       "0031-9228",
  bibdate =      "Sat Jul 28 07:53:52 MDT 2012",
  bibsource =    "http://www.physicstoday.org/search;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.aip.org/link/phtoad/v20/i12/p81/s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Today",
  journal-URL =  "http://www.physicstoday.org/",
}

@Article{Wood:1967:CEI,
  author =       "Van E. Wood",
  title =        "{Chebyshev} Expansions for Integrals of the Error
                 Function (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "99",
  pages =        "494--496",
  month =        jul,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 7-digit approximations for $ i^n \erfc (x),
                 n = 1, 2 $.",
}

@Article{Yarbrough:1967:PCC,
  author =       "Lynn Yarbrough",
  title =        "Precision calculations of $e$ and $ \pi $ constants",
  journal =      j-CACM,
  volume =       "10",
  number =       "9",
  pages =        "537--537",
  month =        sep,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363566.363578",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:15 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic; number base conversion",
  remark =       "Gives decimal, octal, and hexadecimal values of $e$
                 and $ \pi $ to 100 digits, and notes ``The difficulty
                 arises because assemblers and compilers are hardly ever
                 designed to convert decimal constants to a precision of
                 more than a dozen or so digits. Thus, if calculations
                 to greater precision are to be done, constants usually
                 must be input in octal or other binary-derived
                 representation.''. Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Anonymous:1968:ISA,
  author =       "Anonymous",
  title =        "Index by Subject to Algorithms, 1960--1968",
  journal =      j-CACM,
  volume =       "11",
  number =       "12",
  pages =        "827--830",
  month =        dec,
  year =         "1968",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Oct 30 09:29:34 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Book{Arsenin:1968:BES,
  author =       "V. Ja. (Vasilii Jakovlevich) Arsenin",
  title =        "Basic equations and special functions of mathematical
                 physics",
  publisher =    "Iliffe",
  address =      "London, UK",
  pages =        "7 + 361",
  year =         "1968",
  ISBN =         "0-592-05035-1",
  ISBN-13 =      "978-0-592-05035-5",
  LCCN =         "QC20 .A693",
  bibdate =      "Sat Oct 30 18:25:22 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Translation by S. Chomet, Kings College, London of
                 Matematicheska{\"e}i{\`\i}a fizika.",
  acknowledgement = ack-nhfb,
  subject =      "Mathematical physics",
}

@Article{Ascari:1968:LRG,
  author =       "A. Ascari and P. G. Novario",
  title =        "L'algoritmo {$ Q D $} di {Rutishauser} e la
                 generazione di funzioni speciali nel calcolo
                 automatico. ({Italian}) [{The} {$ Q D $} algorithm of
                 {Rutishauser} and the generation of special functions
                 in automatic calculation]",
  journal =      j-CALCOLO,
  volume =       "5",
  number =       "1",
  pages =        "162--173",
  month =        "????",
  year =         "1968",
  CODEN =        "CALOBK",
  DOI =          "https://doi.org/10.1007/BF02576063",
  ISSN =         "0008-0624 (print), 1126-5434 (electronic)",
  ISSN-L =       "0008-0624",
  bibdate =      "Mon Aug 24 21:37:24 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02576063",
  acknowledgement = ack-nhfb,
  fjournal =     "Calcolo: a quarterly on numerical analysis and theory
                 of computation",
  journal-URL =  "http://link.springer.com/journal/10092",
  language =     "Italian",
  subject-dates = "Heinz Rutishauser (30 January 1918--10 November
                 1970)",
}

@Book{Bell:1968:SFS,
  author =       "W. W. (William Wallace) Bell",
  title =        "Special functions for scientists and engineers",
  publisher =    "Van Nostrand",
  address =      "London, UK",
  pages =        "xiv + 247",
  year =         "1968",
  LCCN =         "QA351 .B4",
  bibdate =      "Fri Oct 29 21:30:38 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  remark =       "Fullerton: Gamma, Beta, Legendre, Bessel, and
                 Hypergeometric functions as well as orthogonal
                 polynomials. Reprinted in \cite{Bell:2004:SFS}.",
  subject =      "Functions, Special",
}

@Article{Bergson:1968:ACR,
  author =       "A. Bergson",
  title =        "Certification of and remark on {Algorithm 304}
                 [{S15}]: {Normal} curve integral",
  journal =      j-CACM,
  volume =       "11",
  number =       "4",
  pages =        "271--271",
  month =        apr,
  year =         "1968",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/362991.363048",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:19 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Hill:1967:ANCa,Hill:1967:RAS}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "probability functions",
  remark =       "Fullerton: 50-line Algol Program that is superceded by
                 numerous {\tt erf} routines.",
}

@Article{Bingulac:1968:RAA,
  author =       "S. P. Bingulac",
  title =        "{R68-38} Accurate Analog Computer Generation of
                 {Bessel} Functions for Large Ranges",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  number =       "8",
  pages =        "819--819",
  month =        aug,
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1968.229133",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 17:40:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687462",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Chiarella:1968:EIR,
  author =       "C. Chiarella and A. Reichel",
  title =        "On the Evaluation of Integrals Related to the Error
                 Function",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "101",
  pages =        "137--143",
  month =        jan,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Cody:1968:RCAa,
  author =       "W. J. Cody and H. C. {Thacher, Jr.}",
  title =        "Rational {Chebyshev} approximations for the
                 exponential integral {$ E_1 (x) $}",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "103",
  pages =        "641--649",
  month =        jul,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.25",
  MRnumber =     "38\#6745",
  bibdate =      "Wed Jan 17 08:57:34 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Relative errors down to $ 10^{-21} $.",
}

@Article{Dorrer:1968:ADS,
  author =       "Egon Dorrer",
  title =        "{Algorithm 322}: {$F$}-Distribution [{S14}]",
  journal =      j-CACM,
  volume =       "11",
  number =       "2",
  pages =        "116--117",
  month =        feb,
  year =         "1968",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:18 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: 50-line Algol Program.",
}

@Book{Fike:1968:CEM,
  author =       "C. T. Fike",
  title =        "Computer Evaluation of Mathematical Functions",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xii + 227",
  year =         "1968",
  LCCN =         "QA297 .F5",
  bibdate =      "Thu Sep 1 10:12:51 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}

@Article{Fleckner:1968:MCF,
  author =       "Oscar L. Fleckner",
  title =        "A Method for the Computation of the {Fresnel}
                 Integrals and Related Functions",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "103",
  pages =        "635--640",
  month =        jul,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Galant:1968:HAG,
  author =       "D. C. Galant and P. F. Byrd",
  title =        "High Accuracy Gamma Function Values for Some Rational
                 Arguments (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "104",
  pages =        "885--887",
  month =        oct,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Hart:1968:CAa,
  author =       "John F. Hart and E. W. Cheney and Charles L. Lawson
                 and Hans J. Maehly and Charles K. Mesztenyi and John R.
                 Rice and Henry G. {Thatcher, Jr.} and Christoph
                 Witzgall",
  title =        "Computer Approximations",
  publisher =    pub-R-E-KRIEGER,
  address =      pub-R-E-KRIEGER:adr,
  pages =        "x + 343",
  year =         "1968",
  ISBN =         "0-88275-642-7",
  ISBN-13 =      "978-0-88275-642-4",
  LCCN =         "QA 297 C64 1978",
  bibdate =      "Tue Dec 14 22:55:11 1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Reprinted 1978 with corrections.",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "1: The Design of a Function Subroutine / 1 \\
                 2: General Methods of Computing Functions / 10 \\
                 3: Least Maximum Approximations / 42 \\
                 4: The Choice and Application of Approximations / 58
                 \\
                 5: Description and Use of the Tables / 82 \\
                 6: Function Notes / 89 \\
                 7: Tables of Coefficients / 155 \\
                 Appendix A: Conversion Algorithms / 307 \\
                 Appendix B: Bibliography of Approximations / 313 \\
                 Appendix C: Decimal and Octal Constants / 333 \\
                 References / 336 \\
                 Index / 341",
  tableofcontents = "1: The Design of a Function Subroutine / 1 \\
                 1.1 Introduction / 1 \\
                 1.2 General Considerations in Writing a Function
                 Subroutine / 2 \\
                 1.3 Relation of the Function Subroutine to the Computer
                 System / 3 \\
                 1.4 The Three Main Types of Function Subroutine / 4 \\
                 1.5 Special Programming Techniques / 7 \\
                 1.6 Subroutine Errors / 7 \\
                 1.7 Final Steps / 9 \\
                 2: General Methods of Computing Functions / 10 \\
                 2.1 Introduction / 10 \\
                 2.2 Application of Infinite Expansions / 11 \\
                 2.3 Recurrence and Difference Relations / 23 \\
                 2.4 Iterative Techniques / 27 \\
                 2.5 Integral Representations / 28 \\
                 2.6 Differential Equations / 29 \\
                 2.7 Tabular Data / 32 \\
                 2.8 Convergence Acceleration / 33 \\
                 3: Least Maximum Approximations / 42 \\
                 3.1 Introduction / 42 \\
                 3.2 Properties of Least Maximum Approximations / 43 \\
                 3.3 Nearly Least Maximum Approximations / 46 \\
                 3.4 Rational Approximation / 51 \\
                 3.5 Segmented Approximation / 54 \\
                 3.6 Computation of the Tables / 55 \\
                 4: The Choice and Application of Approximations / 58
                 \\
                 4.1 Introduction / 5 8 \\
                 4.2 Domain Considerations / 58 \\
                 4.3 Machine Considerations / 62 \\
                 4.4 Conditioning of Approximations / 65 \\
                 4.5 Polynomial Forms / 67 \\
                 4.6 Rational Forms / 73 \\
                 4.7 Transformation Algorithms / 78 \\
                 5: Description and Use of the Tables / 82 \\
                 5.1 Introduction / 22 \\
                 5.2 Function Notes / 82 \\
                 5.3 Accuracy of the Coefficients / 83 \\
                 5.4 How to Use the Tables / 86 \\
                 5.5 Preparation of the Tables / 88 \\
                 6: Function Notes / 89 \\
                 6.1 Square Root, Cube Root / 89 \\
                 6.2 Exponential and Hyperbolic Functions / 96 \\
                 6.3 The Logarithm Function / 105 \\
                 6.4 Trigonometric Functions / 112 \\
                 6.5 The Inverse Trigonometric Functions / 120 \\
                 6.6 The Gamma Function and Its Logarithm / 130 \\
                 6.7 The Error Function / 136 \\
                 6.8 Bessel Functions / 141 \\
                 6.9 Complete Elliptic Integrals / 150 \\
                 7: Tables of Coefficients / 155 \\
                 Appendix A Conversion Algorithms / 307 \\
                 Appendix B Bibliography of Approximations / 313 \\
                 Appendix C Decimal and Octal Constants / 333 \\
                 References / 336 \\
                 Index / 341",
}

@Book{Hart:1968:CAb,
  author =       "John F. Hart and E. W. Cheney and Charles L. Lawson
                 and Hans J. Maehly and Charles K. Mesztenyi and John R.
                 Rice and Henry G. {Thatcher, Jr.} and Christoph
                 Witzgall",
  title =        "Computer Approximations",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "x + 343",
  year =         "1968",
  ISBN =         "0-471-35630-1",
  ISBN-13 =      "978-0-471-35630-1",
  LCCN =         "QA297 .C64",
  bibdate =      "Sat Jan 14 14:53:06 2006",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "The SIAM series in applied mathematics",
  acknowledgement = ack-nhfb,
}

@Article{Kolbig:1968:ADS,
  author =       "K. S. K{\"o}lbig",
  title =        "{Algorithm 327}: {Dilogarithm} [{S22}]",
  journal =      j-CACM,
  volume =       "11",
  number =       "4",
  pages =        "270--271",
  month =        apr,
  year =         "1968",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/362991.363043",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:19 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$d(x) = \int_0^x (\ln|1-y|/y)\,dy$; dilogarithm;
                 special functions",
}

@Article{Luke:1968:AEI,
  author =       "Yudell L. Luke",
  title =        "Approximations for Elliptic Integrals",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "103",
  pages =        "627--634",
  month =        jul,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{MacLaren:1968:RAP,
  author =       "M. D. MacLaren",
  title =        "Remark on {Algorithm 272}: {Procedure} for the normal
                 distribution functions",
  journal =      j-CACM,
  volume =       "11",
  number =       "7",
  pages =        "498--498",
  month =        jul,
  year =         "1968",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363397.363553",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:20 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{MacLaren:1965:APN}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "probability functions",
}

@Article{Mavromatis:1968:IFP,
  author =       "H. A. Mavromatis and K. Schilcher",
  title =        "Inverse Functions of the Products of Two {Bessel}
                 Functions and Applications to Potential Scattering",
  journal =      j-J-MATH-PHYS,
  volume =       "9",
  number =       "10",
  pages =        "1627--1632",
  month =        oct,
  year =         "1968",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.1664492",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Oct 28 11:55:17 MDT 2011",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1965.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v9/i10/p1627_s1",
  acknowledgement = ack-nhfb,
  classification = "A0380 (General theory of scattering)",
  corpsource =   "Dept. Physics, American Univ. Beirut, Lebanon",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "functions; mathematics; scattering",
  onlinedate =   "28 October 2003",
  pagecount =    "6",
}

@Article{Mechel:1968:IRT,
  author =       "Fr. Mechel",
  title =        "Improvement in Recurrence Techniques for the
                 Computation of {Bessel} Functions of Integral Order (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "101",
  pages =        "202--205",
  month =        jan,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Miller:1968:LTS,
  author =       "Willard Miller",
  title =        "{Lie} theory and special functions",
  volume =       "43",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xv + 338",
  year =         "1968",
  ISBN =         "0-12-497450-3",
  ISBN-13 =      "978-0-12-497450-0",
  LCCN =         "QA387 .M55 1968eb",
  bibdate =      "Sat Oct 30 19:07:04 MDT 2010",
  bibsource =    "catalog.library.cornell.edu:7090/voyager;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Mathematics in science and engineering",
  acknowledgement = ack-nhfb,
  remark =       "Reprinted 1979 with same ISBN.",
  subject =      "Lie groups; Functions, Special",
}

@Article{Nagashima:1968:EFN,
  author =       "Takashi Nagashima",
  title =        "On elementary functions of natural numbers",
  journal =      "Hitotsubashi J. Arts Sci.",
  volume =       "9",
  pages =        "50--58",
  year =         "1968",
  ISSN =         "0073-2788",
  MRclass =      "02.72",
  MRnumber =     "MR0232678 (38 \#1001)",
  MRreviewer =   "R. L. Goodstein",
  bibdate =      "Mon Oct 24 11:33:08 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Hitotsubashi Journal of Arts \&amp; Sciences",
}

@Article{Ng:1968:DSS,
  author =       "Edward W. Ng",
  title =        "On the direct summation of series involving higher
                 transcendental functions",
  journal =      j-J-COMPUT-PHYS,
  volume =       "3",
  number =       "2",
  pages =        "334--338",
  month =        oct,
  year =         "1968",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(68)90029-6",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 08:28:02 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999168900296",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{OBrien:1968:CAC,
  author =       "William M. O'Brien and Joan Wood",
  title =        "Certification of {Algorithm 299} [{S15}]:
                 {Chi-squared} integral",
  journal =      j-CACM,
  volume =       "11",
  number =       "4",
  pages =        "271--271",
  month =        apr,
  year =         "1968",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:19 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "chi-squared; probability functions",
  remark =       "Fullerton: Corrections to an Algol procedure.",
}

@Article{Osborn:1968:IBF,
  author =       "David Osborn and Richard Madey",
  title =        "The Incomplete Beta Function and its Ratio to the
                 Complete Beta Function",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "101",
  pages =        "159--162",
  month =        jan,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Richardson:1968:SUP,
  author =       "Daniel Richardson",
  title =        "Some Undecidable Problems Involving Elementary
                 Functions of a Real Variable",
  journal =      j-J-SYMBOLIC-LOGIC,
  volume =       "33",
  number =       "4",
  pages =        "514--520",
  month =        dec,
  year =         "1968",
  CODEN =        "JSYLA6",
  ISSN =         "0022-4812 (print), 1943-5886 (electronic)",
  ISSN-L =       "0022-4812",
  MRclass =      "02.75",
  MRnumber =     "39 #1330",
  bibdate =      "Mon May 19 13:04:20 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Logic",
  journal-URL =  "http://projecteuclid.org/euclid.jsl;
                 http://www.jstor.org/journal/jsymboliclogic",
}

@Article{Schmidt:1968:AEK,
  author =       "Jochen W. Schmidt",
  title =        "{Asymptotische Einschlie{\ss}ung bei
                 konvergenzbeschleunigenden Verfahren. II}. ({German})
                 [{Asymptotic enclosure with convergence acceleration
                 method. II}]",
  journal =      j-NUM-MATH,
  volume =       "11",
  number =       "1",
  pages =        "53--56",
  month =        jan,
  year =         "1968",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 16:12:48 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "convergence acceleration",
  language =     "German",
}

@Article{Strecok:1968:CIE,
  author =       "Anthony J. Strecok",
  title =        "On the Calculation of the Inverse of the Error
                 Function",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "101",
  pages =        "144--158",
  month =        jan,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2004772",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 18-digit approximations.",
}

@Book{Talman:1968:SFG,
  author =       "James D. Talman",
  title =        "Special Functions: a Group Theoretic Approach Based on
                 Lectures by {Eugene P. Wigner}",
  publisher =    pub-BENJAMIN,
  address =      pub-BENJAMIN:adr,
  pages =        "xii + 260",
  year =         "1968",
  LCCN =         "????",
  bibdate =      "Sat Oct 30 16:57:02 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "With an introduction by Eugene P. Wigner.",
  series =       "The mathematical physics monograph series",
  acknowledgement = ack-nhfb,
  keywords =     "group theory; mathematical function; special
                 functions",
}

@Book{Tolke:1968:PFA,
  author =       "Friedrich T{\"o}lke",
  title =        "{Praktische Funktionenlehre. 5. Allgemeine
                 Weierstrasssche Funktionen und Ableitungen nach dem
                 Parameter: Integrale der Theta-Funktionen und
                 Bilinear-Entwicklungen}. ({German}) [{Practical}
                 functional theory. 5. {General} information on
                 {Weierstrass} functions and derivatives according to
                 the parameters: integrals of theta functions and
                 bilinear developments]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 158",
  year =         "1968",
  ISBN =         "3-662-11121-7, 3-662-11120-9",
  ISBN-13 =      "978-3-662-11121-5, 978-3-662-11120-8",
  LCCN =         "????",
  bibdate =      "Mon Feb 13 19:01:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
  tableofcontents = "12 Allgemeine Weierstra{\ss}sche Funktionen.
                 Doppelreihen-Entwicklungen \\
                 13 Die Ableitungen nach dem Parameter und dem Modul \\
                 14 Integrale von Theta-Funktionen (D-Funktionen) \\
                 15 Mehrdimensionale Theta- und D-Funktionen \\
                 16 Theta- und D-Funktionen mit imagin{\"a}ren
                 Parametern \\
                 17 Greensche Funktionen und Bilinear-Entwicklungen",
  xxISBN =       "3-662-11031-8",
  xxisbn-13 =    "978-3-662-11031-7",
}

@Article{Tooper:1968:SCP,
  author =       "Robert F. Tooper and John Mark",
  title =        "Simplified Calculation of {$ \operatorname {Ei}(x) $}
                 for Positive Arguments, and a Short Table of $
                 \operatorname {Shi}(x) $ (in {Technical Notes and Short
                 Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "102",
  pages =        "448--449",
  month =        apr,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "exponential integral ($\operatorname{Ei}(x)$);
                 hyperbolic sine integral ($\operatorname{Shi}(x)$)",
}

@Article{Wilcox:1968:ZTN,
  author =       "Peter H. Wilcox",
  title =        "The Zeros of $ {P}^1_\nu (\cos \theta) $ and $ \frac
                 {\partial }{\partial \theta } {P}^1_\mu (\cos \theta) $
                 (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "101",
  pages =        "205--208",
  month =        jan,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2004783",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: $ P_\nu^1 $ are Legendre functions.",
}

@Article{Wimp:1968:RFH,
  author =       "Jet Wimp",
  title =        "Recursion Formulae of Hypergeometric Functions",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "102",
  pages =        "363--373",
  month =        apr,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Witte:1968:AAJ,
  author =       "B. F. W. Witte",
  title =        "{ACM Algorithm 332}: {Jacobi} Polynomials",
  journal =      j-CACM,
  volume =       "11",
  number =       "6",
  pages =        "436--437",
  month =        jun,
  year =         "1968",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:33:08 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Skovgaard:1975:RAJ}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Wrench:1968:CTS,
  author =       "John W. {Wrench, Jr.}",
  title =        "Concerning Two Series for the Gamma Function",
  journal =      j-MATH-COMPUT,
  volume =       "22",
  number =       "103",
  pages =        "617--626",
  month =        jul,
  year =         "1968",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRnumber =     "MR 0237078 (38:5371)",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Aharoni:1969:C,
  author =       "Amikam Aharoni",
  title =        "Computation of {$ K_p(x) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "4",
  number =       "2",
  pages =        "270--271",
  month =        aug,
  year =         "1969",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(69)90072-2",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 08:28:03 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999169900722",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Boersma:1969:ECW,
  author =       "J. Boersma",
  title =        "Expansions for {Coulomb} Wave Functions",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "105",
  pages =        "51--59",
  month =        jan,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Buchholz:1969:CHF,
  author =       "Herbert Buchholz",
  title =        "The confluent hypergeometric function with special
                 emphasis on its applications",
  volume =       "15",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xviii + 238",
  year =         "1969",
  LCCN =         "QA351 .B813",
  bibdate =      "Sat Oct 30 21:06:31 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Translation by H. Lichtblau and K. Wetzel to English
                 from German ``Die konfluente hypergeometrische
                 Funktion.''",
  series =       "Springer tracts in natural philosophy",
  acknowledgement = ack-nhfb,
  subject =      "Hypergeometric functions",
}

@Article{Bulirsch:1969:EBT,
  author =       "R. Bulirsch",
  title =        "An extension of the {Bartky}-transformation to
                 incomplete elliptic integrals of the third kind",
  journal =      j-NUM-MATH,
  volume =       "13",
  number =       "3",
  pages =        "266--284",
  month =        jul,
  year =         "1969",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 19:01:15 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Bulirsch:1969:NCE,
  author =       "R. Bulirsch",
  title =        "Numerical calculation of elliptic integrals and
                 elliptic functions. {III}",
  journal =      j-NUM-MATH,
  volume =       "13",
  number =       "4",
  pages =        "305--315",
  month =        aug,
  year =         "1969",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 19:01:15 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Carlson:1969:CBE,
  author =       "B. C. Carlson",
  title =        "A connection between elementary functions and higher
                 transcendental functions",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "17",
  pages =        "116--148",
  year =         "1969",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  MRclass =      "33.20 (30.00)",
  MRnumber =     "40 \#408",
  MRreviewer =   "S. K. Bose",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
}

@InProceedings{Clark:1969:SCE,
  author =       "N. W. Clark and W. J. Cody",
  title =        "Self-contained exponentiation",
  crossref =     "AFIPS:1969:ACPb",
  pages =        "701--706",
  year =         "1969",
  bibdate =      "Wed Sep 07 10:49:33 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}

@Article{Clemm:1969:ACV,
  author =       "Donald S. Clemm",
  title =        "{Algorithm 352}: {Characteristic} Values and
                 Associated Solutions of {Mathieu}'s Differential
                 Equation [{S22}]",
  journal =      j-CACM,
  volume =       "12",
  number =       "7",
  pages =        "399--407",
  month =        jul,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:27 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Frisch:1972:RAR}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4170 (Differential equations); C7300 (Natural
                 sciences computing)",
  corpsource =   "Wright-Patterson Air Force Base, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "differential equations; function evaluation;
                 subroutines",
  remark =       "Fullerton: Long set of FORTRAN routines to evaluate
                 Mathieu functions as well as several Bessel
                 functions.",
}

@Article{Cobb:1969:CAS,
  author =       "S. M. Cobb",
  title =        "Certification of {Algorithm 47} [{S16}]: {Associated}
                 {Legendre} functions of the first kind for real or
                 imaginary arguments",
  journal =      j-CACM,
  volume =       "12",
  number =       "11",
  pages =        "635--636",
  month =        nov,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:28 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "associated Legendre functions of the first kind;
                 special functions",
  remark =       "Fullerton: Numerous additional corrections and changes
                 to an Algol procedure.",
}

@Article{Cody:1969:CAE,
  author =       "W. J. Cody and Henry C. {Thacher, Jr.}",
  title =        "{Chebyshev} Approximations for the Exponential
                 Integral {$ \hbox {Ei}(x) $}",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "106",
  pages =        "289--303",
  month =        apr,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.25",
  MRnumber =     "39\#3680",
  bibdate =      "Wed Jan 17 08:57:33 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Cody:1969:CRA,
  author =       "W. J. Cody and G. Meinardus and R. S. Varga",
  title =        "{Chebyshev} rational approximations to $ e^{-x} $ on $
                 [0, \infty) $ and applications to heat conduction
                 problems",
  journal =      j-J-APPROX-THEORY,
  volume =       "2",
  number =       "??",
  pages =        "50--65",
  month =        "??",
  year =         "1969",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  MRclass =      "65.67 (41.00)",
  MRnumber =     "40\#999",
  bibdate =      "Wed Jan 17 08:57:33 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-wjc,
  fjournal =     "Journal of Approximation Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
}

@Article{Cody:1969:RCA,
  author =       "W. J. Cody",
  title =        "Rational {Chebyshev} Approximations for the Error
                 Function",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "107",
  pages =        "631--637",
  month =        jul,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Farkas:1969:CAS,
  author =       "I. Farkas",
  title =        "Certification of {Algorithm 165} [{S21}]: {Complete}
                 elliptic integrals",
  journal =      j-CACM,
  volume =       "12",
  number =       "1",
  pages =        "38--38",
  month =        jan,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:24 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}

@Article{Gautschi:1969:ACE,
  author =       "Walter Gautschi",
  title =        "{Algorithm 363}: {Complex} Error Function [{S15}]",
  journal =      j-CACM,
  volume =       "12",
  number =       "11",
  pages =        "635--635",
  month =        nov,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:28 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See certification \cite{Kolbig:1972:CAC}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\erf(z)$; special functions",
  remark =       "Fullerton: 50-line Algol procedure with accuracy to 10
                 decimal places.",
}

@Article{Gautschi:1969:RAS,
  author =       "Walter Gautschi",
  title =        "Remark on {Algorithm 292} [{S22}]: {Regular} {Coulomb}
                 wave functions",
  journal =      j-CACM,
  volume =       "12",
  number =       "5",
  pages =        "280--280",
  month =        may,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:26 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Coulomb wave functions; special functions",
  remark =       "Fullerton: The first of many remarks.",
}

@Article{Herman:1969:NHE,
  author =       "G. T. Herman",
  title =        "A new hierarchy of elementary functions",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "20",
  pages =        "557--562",
  year =         "1969",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "02.77",
  MRnumber =     "40 \#4110",
  MRreviewer =   "G. E. Sacks",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}

@Article{Holzwarth:1969:VBB,
  author =       "A. Holzwarth",
  title =        "{Ein Verfahren zur Bestimmung bester
                 Tscheb\-y\-scheff-Ap\-prox\-i\-ma\-tion\-en der
                 Quadratwurzelfunktion}. ({German}) {A Method for
                 Determination of Best Chebyshev Approximations to the
                 Square Root Function}",
  journal =      j-COMPUTING,
  volume =       "4",
  number =       "2",
  pages =        "168--177",
  month =        jun,
  year =         "1969",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:51 MST 2001",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "T{\"u}bingen, West Germany",
  classification = "C4130",
  description =  "Chebyshev approximation; numerical analysis",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  language =     "German",
}

@Article{King:1969:LEN,
  author =       "Richard F. King and David L. Phillips",
  title =        "The Logarithmic Error and {Newton}'s Method for the
                 Square Root",
  journal =      j-CACM,
  volume =       "12",
  number =       "2",
  pages =        "87--88",
  month =        feb,
  year =         "1969",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/362848.362861",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.50",
  MRnumber =     "44\#2333",
  bibdate =      "Fri Nov 25 18:20:24 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The problem of obtaining optimal starting values for
                 the calculation of the square root using Newton's
                 method is considered. It has been pointed out elsewhere
                 that if relative error is used as the measure of
                 goodness of fit, optimal results are not obtained when
                 the initial approximation is a best fit. It is shown
                 here that if, instead, the so-called logarithmic error
                 is used, then a best initial fit is optimal for both
                 types of error. Moreover, use of the logarithmic error
                 appears to simplify the problem of determining the
                 optimal initial approximation.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C4120 (Functional analysis)",
  corpsource =   "Argonne Nat. Lab., Argonne, IL, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions; function evaluation;
                 iterative methods",
}

@Article{Kolbig:1969:CASa,
  author =       "K. S. K{\"o}lbig",
  title =        "Certification of {Algorithm 292} [{S22}]: {Regular}
                 {Coulomb} wave functions and of remark on {Algorithm
                 292} [{S22}]: {Regular} {Coulomb} wave functions",
  journal =      j-CACM,
  volume =       "12",
  number =       "5",
  pages =        "278--279",
  month =        may,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:26 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Coulomb wave functions; special functions",
  remark =       "Fullerton: Tests of an Algol procedure.",
}

@Article{Kolbig:1969:CASb,
  author =       "K. S. K{\"o}lbig",
  title =        "Certification of {Algorithm 300} [{S22}]: {Coulomb}
                 wave functions",
  journal =      j-CACM,
  volume =       "12",
  number =       "5",
  pages =        "279--280",
  month =        may,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:26 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Coulomb wave functions; special functions",
  remark =       "Fullerton: The first of many remarks.",
}

@Article{Kolbig:1969:RAS,
  author =       "K. S. K{\"o}lbig",
  title =        "Remark on {Algorithm 300} [{S22}]: {Coulomb} wave
                 functions",
  journal =      j-CACM,
  volume =       "12",
  number =       "12",
  pages =        "692--692",
  month =        dec,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:29 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Coulomb wave functions; special functions",
  remark =       "Fullerton: One of many remarks.",
}

@Article{Lardner:1969:RBB,
  author =       "Thomas J. Lardner",
  title =        "Relations Between {${}_0 F_3 $} and {Bessel}
                 Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "11",
  number =       "1",
  pages =        "69--72",
  month =        "????",
  year =         "1969",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1011007",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:06:04 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/11/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "January 1969",
}

@Article{Lewis:1969:FII,
  author =       "Richard L. Lewis",
  title =        "On Finite Integrals Involving Trigonometric, {Bessel},
                 and {Legendre} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "106",
  pages =        "259--273",
  month =        apr,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Luke:1969:SFTa,
  author =       "Yudell L. Luke",
  title =        "The Special Functions and Their Approximations",
  volume =       "I",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xx + 349",
  year =         "1969",
  ISBN =         "0-12-459901-X",
  ISBN-13 =      "978-0-12-459901-7",
  LCCN =         "QA351 .L94 1969",
  bibdate =      "Wed Dec 15 17:55:35 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Mathematics in Science and Engineering, Volume 53-I,
                 Editor: Richard Bellman",
  acknowledgement = ack-nhfb,
}

@Book{Luke:1969:SFTb,
  author =       "Yudell L. Luke",
  title =        "The Special Functions and Their Approximations",
  volume =       "II",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xx + 485",
  year =         "1969",
  ISBN =         "0-12-459902-8",
  ISBN-13 =      "978-0-12-459902-4",
  LCCN =         "QA351 .L797",
  bibdate =      "Wed Dec 15 17:55:38 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  series =       "Mathematics in Science and Engineering, Volume 53-II,
                 Editor: Richard Bellman",
  URL =          "http://www.sciencedirect.com/science/book/9780124599024",
  acknowledgement = ack-nhfb,
  tableofcontents = "Dedication / v \\
                 Preface / vii--ix \\
                 Contents of Volume I / xv \\
                 Introduction / xvii--xx \\
                 IX: Expansions of Generalized Hypergeometric Functions
                 in Series of Functions of the Same Kind / 1--65 \\
                 X: The $\tau$-Method / 66--91 \\
                 XI: Polynomial and Rational Approximations to
                 Generalized Hypergeometric Functions / 92--132 \\
                 XII: Recursion Formulas for Polynomials and Functions
                 which Occur in Infinite Series and Rational
                 Approximations to Generalized Hypergeometric Functions
                 / 133--166 \\
                 XIII: Polynomial and Rational Approximations for $E(z)
                 = _2F_1(1, \sigma; \rho + 1; 1/z)$ / 167--185 \\
                 XIV: Polynomial and Rational Approximations for the
                 Incomplete Gamma Function / 186--213 \\
                 XV: Trapezoidal Rule Integration Formulas / 214--226
                 \\
                 XVI: Applications / 227--281 \\
                 XVII: Tables of Coefficients / 282--452 \\
                 Bibliography / 453--461 \\
                 Notation Index / 463--467 \\
                 Subject Index to Volumes I and II / 468--485",
}

@TechReport{Moses:1969:ICS,
  author =       "Joel Moses",
  title =        "The integration of a class of special functions with
                 the {Risch} algorithm",
  type =         "{AI} Memo (180)",
  number =       "MAC-M-421",
  institution =  "Artificial Intelligence Laboratory, Massachusetts
                 Institute of Technology",
  address =      "Cambridge, MA, USA",
  pages =        "13 + 1",
  year =         "1969",
  LCCN =         "Q334 M533 no. 180",
  bibdate =      "Sat Oct 30 18:37:28 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Ng:1969:CPE,
  author =       "Edward W. Ng and C. J. Devine and R. F. Tooper",
  title =        "{Chebyshev} Polynomial Expansion of {Bose--Einstein}
                 Functions of Orders $1$ to $ 10$",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "107",
  pages =        "639--643",
  month =        jul,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: $ B_p(\eta) = \frac {1}{\Gamma (p - 1)}
                 \int_0^\infty \frac {x^p}{e^{x - \eta } - 1} \, d t $.
                 Relative errors down to $ 3 \times 10^{-19} $.",
}

@Article{Reichel:1969:IPV,
  author =       "Alex Reichel",
  title =        "The Integral of the $n$ th Power of the {Voigt}
                 Function",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "107",
  pages =        "645--649",
  month =        jul,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: The function $ \chi_n(t) = \int_{- \infty
                 }^\infty \{ U_0 (x, t) \}^n \, d x $, where $ U_0 (x,
                 t) = \frac {1}{\sqrt {4 \pi t}} \frac {\exp [ - (x -
                 y)^2 / 4 t]}{1 + y^2} \, d y $ is considered.",
}

@Article{Robertson:1969:CNC,
  author =       "G. H. Robertson",
  title =        "Computation of the Noncentral Chi-Square
                 Distribution",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "48",
  number =       "1",
  pages =        "201--207",
  month =        jan,
  year =         "1969",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1969/BSTJ.1969.4801.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol48/bstj48-1-201.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}

@Article{Sollfrey:1969:IFP,
  author =       "William Sollfrey",
  title =        "Inverse Functions of the Products of Two {Bessel}
                 Functions",
  journal =      j-J-MATH-PHYS,
  volume =       "10",
  number =       "8",
  pages =        "1429--1430",
  month =        aug,
  year =         "1969",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.1664985",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Oct 28 11:55:26 MDT 2011",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1965.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v10/i8/p1429_s1",
  acknowledgement = ack-nhfb,
  classification = "A0200 (Mathematical methods in physics)",
  corpsource =   "RAND Corp., Santa Monica, CA, USA",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "functions",
  onlinedate =   "4 November 2003",
  pagecount =    "2",
}

@Article{TadeudeMedeiros:1969:APF,
  author =       "Adilson {Tadeu de Medeiros} and Georges Schwachheim",
  title =        "{Algorithm 349}: {Polygamma} Functions with Arbitrary
                 Precision [{S14}]",
  journal =      j-CACM,
  volume =       "12",
  number =       "4",
  pages =        "213--214",
  month =        apr,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:25 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See certification \cite{Lewis:1975:CPF}.",
  abstract =     "This procedure assigns to polygam the value of the
                 polygamma function of order n for any real argument
                 $z$. For $ n = 0$, we have the psi or digamma function,
                 for $ n = 1$ the trigamma function, for $ n = 2$ the
                 tetragamma function, and so on.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C7300 (Natural sciences computing)",
  corpsource =   "Centro Brasileiro de Pesquisas Fisicas, Rio de
                 Janeiro, Brazil",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "digamma function; mathematics; polygamma function; psi
                 function; special functions; subroutines; tetragamma
                 function; trigamma function",
  remark =       "Fullerton: 150-line Algol procedure.",
}

@InProceedings{Tesler:1969:AEF,
  author =       "G. S. Tesler",
  booktitle =    "Mathematical provisioning of electronic digital
                 computers and effective organization of the computing
                 process (Proc. Sem., Kiev, 1969) ({Russian}), No. 2",
  title =        "The approximation of elementary functions by means of
                 polynomials of degree zero and one. ({Russian})",
  publisher =    "Akad. Nauk Ukrain. SSR",
  address =      "Kiev, USSR",
  pages =        "75--88",
  year =         "1969",
  MRclass =      "65D15",
  MRnumber =     "45 \#4600",
  MRreviewer =   "I. Selihova",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Book{Tolke:1969:PFT,
  author =       "Friedrich T{\"o}lke",
  title =        "{Praktische Funktionenlehre. 6. Tafeln aus dem Gebiet
                 der Theta-Funktionen und der elliptischen Funtionen}.
                 ({German}) [{Practical} functional theory. 6. {Tables}
                 from the field of theta functions and elliptic
                 functions]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "lxxxii + 449 (vol. 1)",
  year =         "1969",
  ISBN =         "",
  ISBN-13 =      "",
  LCCN =         "????",
  bibdate =      "Mon Feb 13 19:01:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Two volumes",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Turner:1969:DSC,
  author =       "L. R. Turner",
  title =        "Difficulty in {$ \sin $ \slash$ \cos $} Routine",
  journal =      j-SIGNUM,
  volume =       "4",
  number =       "3",
  pages =        "13--13",
  year =         "1969",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Feb 15 15:23:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@Article{VandeVel:1969:SEM,
  author =       "H. {Van de Vel}",
  title =        "On the Series Expansion Method for Computing
                 Incomplete Elliptic Integrals of the First and Second
                 Kinds",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "105",
  pages =        "61--69",
  month =        jan,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Zaker:1969:CCE,
  author =       "T. A. Zaker",
  title =        "Calculation of the complementary error function of
                 complex argument",
  journal =      j-J-COMPUT-PHYS,
  volume =       "4",
  number =       "3",
  pages =        "427--430",
  month =        oct,
  year =         "1969",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(69)90011-4",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Thu Dec 04 16:20:39 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1960.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Bray:1970:CAR,
  author =       "T. Bray",
  title =        "Certification of {Algorithm 22, Ricatti--Bessel
                 Functions of First and Second Kind}",
  journal =      j-CACM,
  volume =       "13",
  number =       "7",
  pages =        "448--448",
  month =        jul,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Oct 29 21:49:15 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: An error in an Algol procedure is
                 reported.",
}

@Article{Carlitz:1970:SRF,
  author =       "L. Carlitz",
  title =        "Some Reduction Formulas for Generalized Hypergeometric
                 Functions",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "1",
  number =       "2",
  pages =        "243--245",
  month =        may,
  year =         "1970",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  bibdate =      "Sun Nov 28 19:21:58 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/1/2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@Article{Carlson:1970:HSS,
  author =       "B. C. Carlson",
  title =        "Hidden Symmetries of Special Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "12",
  number =       "3",
  pages =        "332--345",
  month =        jul,
  year =         "1970",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1012078",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:06:20 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/12/3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://www.jstor.org/stable/2028552",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "July 1970",
}

@Article{Chen:1970:CGI,
  author =       "Reuven Chen",
  title =        "On the Computation of the Generalized Integral in Glow
                 Curve Theory",
  journal =      j-J-COMPUT-PHYS,
  volume =       "6",
  number =       "2",
  pages =        "314--316",
  month =        oct,
  year =         "1970",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(70)90027-6",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Fri Oct 29 22:09:19 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Cochran:1970:NTF,
  author =       "James Alan Cochran and Judith N. Hoffspiegel",
  title =        "Numerical Techniques for Finding $ \nu $-Zeros of
                 {Hankel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "110",
  pages =        "413--422",
  month =        apr,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Cody:1970:CAC,
  author =       "W. J. Cody and K. E. Hillstrom",
  title =        "{Chebyshev} Approximations for the {Coulomb} Phase
                 Shift",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "111",
  pages =        "671--677",
  month =        jul,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.25",
  MRnumber =     "42\#8661",
  bibdate =      "Wed Jan 17 08:57:04 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-wjc,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Relative errors down to $ 4 \times 10^{-19}
                 $.",
}

@Article{Cody:1970:CAD,
  author =       "W. J. Cody and Kathleen A. Paciorek and Henry C.
                 {Thacher, Jr.}",
  title =        "{Chebyshev} approximations for {Dawson}'s integral",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "109",
  pages =        "171--178",
  month =        jan,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.20",
  MRnumber =     "41\#2883",
  bibdate =      "Wed Jan 17 08:57:30 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Cody:1970:RAC,
  author =       "W. J. Cody and Kathleen A. Paciorek",
  title =        "Remark on {Algorithm} 292 [{S22}]: Regular {Coulomb}
                 Wave Functions",
  journal =      j-CACM,
  volume =       "13",
  number =       "9",
  pages =        "573",
  month =        sep,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Nov 16 23:58:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-wjc,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: More modifications to an Algol procedure.",
}

@Article{Darlington:1970:AAA,
  author =       "Sidney Darlington",
  title =        "Analytical Approximations to Approximations in the
                 {Chebyshev} Sense",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "49",
  number =       "1",
  pages =        "1--32",
  month =        jan,
  year =         "1970",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4901.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-1-1.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}

@TechReport{DeLugish:1970:CAA,
  author =       "Bruce Gene DeLugish",
  title =        "A Class of Algorithms for Automatic Evaluation of
                 Certain Elementary Functions in a Binary Computer",
  number =       "399",
  institution =  "Department of Computer Science, University of Illinois
                 at Urbana-Champaign",
  address =      "Urbana, Illinois",
  pages =        "191",
  year =         "1970",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Gautschi:1970:RAD,
  author =       "Walter Gautschi and Bruce J. Klein",
  title =        "Remark on {Algorithm 282, Derivatives of $ e^x / x $,
                 $ \cos (x) / x $, and $ \sin (x) / x $}",
  journal =      j-CACM,
  volume =       "13",
  number =       "1",
  pages =        "53--54",
  month =        jan,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Oct 30 07:27:17 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Gautschi:1966:AD}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: Corrections are given for several Algol
                 procedures.",
}

@Article{Gautschi:1970:RCC,
  author =       "Walter Gautschi and Bruce J. Klein",
  title =        "Recursive computation of certain derivatives --- a
                 study of error propagation",
  journal =      j-CACM,
  volume =       "13",
  number =       "1",
  pages =        "7--9",
  month =        jan,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65Q05",
  MRnumber =     "46 1115",
  MRreviewer =   "D. F. Mayers",
  bibdate =      "Tue Mar 25 13:26:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "A brief study is made of the propagation of errors in
                 linear first-order difference equations. The recursive
                 computation of successive derivatives of $ (e^x) / x $
                 and $ (\cos x) / x $ is considered as an
                 illustration.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4110 (Error analysis in numerical methods)",
  corpsource =   "Purdue Univ., Lafayette, IN, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "difference equations; error analysis; error
                 propagation; recursive computation; successive
                 derivatives",
  remark =       "Fullerton: Recursive calculation of derivatives of $
                 e^x / x $ and $ \cos (x) / x $ is considered.",
}

@Article{Hill:1970:AASa,
  author =       "G. W. Hill",
  title =        "{ACM Algorithm 395}: {Student}'s $t$-Distribution",
  journal =      j-CACM,
  volume =       "13",
  number =       "10",
  pages =        "617--619",
  month =        oct,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Mar 25 13:26:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{elLozy:1979:RAS,Hill:1981:RSD}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C7310 (Mathematics computing)",
  corpsource =   "CSIRO, Glen Osmond, Australia",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "statistics; subroutines",
  remark =       "Fullerton: Description of a 50-line Algol procedure.",
}

@Article{Hill:1970:AASb,
  author =       "G. W. Hill",
  title =        "{ACM Algorithm 396}: {Student}'s $t$-Quantiles",
  journal =      j-CACM,
  volume =       "13",
  number =       "10",
  pages =        "619--620",
  month =        oct,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Mar 25 13:26:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also
                 \cite{Hill:1981:RSD,Hill:1981:RSQ,elLozy:1979:RAS}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4120 (Functional analysis); C7310 (Mathematics
                 computing)",
  corpsource =   "CSIRO, Glen Osmond, Australia",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "function evaluation; statistics; subroutines",
  remark =       "Fullerton: Description of a 50-line Algol procedure.",
}

@Article{Holmgren:1970:RAN,
  author =       "Bo Holmgren",
  title =        "Remark on {Algorithm 304, Normal Curve Integral}",
  journal =      j-CACM,
  volume =       "13",
  number =       "10",
  pages =        "624--624",
  month =        oct,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Oct 30 08:18:38 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Jones:1970:GHF,
  author =       "Alan L. Jones",
  title =        "The generalized hypergeometric function",
  journal =      j-SIGPLAN,
  volume =       "5",
  number =       "3",
  pages =        "26--27",
  month =        mar,
  year =         "1970",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Thu May 25 06:40:57 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@Article{Kolbig:1970:CZI,
  author =       "K. S. Kolbig",
  title =        "Complex Zeros of an Incomplete {Riemann} Zeta Function
                 and of the Incomplete Gamma Function",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "111",
  pages =        "679--696",
  month =        jul,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Lehman:1970:DZR,
  author =       "R. S. Lehman",
  title =        "On the distribution of zeros of the {Riemann}
                 zeta-function",
  journal =      j-PROC-LONDON-MATH-SOC-1,
  volume =       "3",
  number =       "20",
  pages =        "303--320",
  month =        "????",
  year =         "1970",
  ISSN =         "0024-6115 (print), 1460-244X (electronic)",
  ISSN-L =       "0024-6115",
  MRnumber =     "MR0258768 (41:3414)",
  bibdate =      "Mon Oct 24 12:42:07 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "This paper corrects several errors in
                 \cite{Turing:1953:SCR}. See also
                 \cite{Trudgian:2011:ITM}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the London Mathematical Society. First
                 Series",
  journal-URL =  "http://plms.oxfordjournals.org/content/by/year",
}

@TechReport{Lugish:1970:CAA,
  author =       "B. G. de Lugish",
  title =        "A Class of Algorithms for Automatic Evaluation of
                 Certain Elementary Function in a Binary Computer",
  type =         "Report",
  number =       "399",
  institution =  "Department of Computer Science, University of
                 Illinois",
  pages =        "????",
  month =        jun,
  year =         "1970",
  bibdate =      "Fri Sep 02 22:49:20 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}

@Article{Luke:1970:FAE,
  author =       "Yudell L. Luke",
  title =        "Further Approximations for Elliptic Integrals",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "109",
  pages =        "191--198",
  month =        jan,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Minton:1970:GHF,
  author =       "Barry M. Minton",
  title =        "Generalized Hypergeometric Function of Unit Argument",
  journal =      j-J-MATH-PHYS,
  volume =       "11",
  number =       "4",
  pages =        "1375--1376",
  month =        apr,
  year =         "1970",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.1665270",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Oct 28 16:39:25 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1970.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v11/i4/p1375_s1",
  acknowledgement = ack-nhfb,
  classification = "A0200 (Mathematical methods in physics)",
  corpsource =   "Univ. Calgary, Alta., Canada",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "functions",
  onlinedate =   "28 October 2003",
  pagecount =    "2",
}

@Article{Ng:1970:CAE,
  author =       "E. N. Ng",
  title =        "Certification of {Algorithm 385, Exponential Integral
                 $ \operatorname {Ei}(x) $}",
  journal =      j-CACM,
  volume =       "13",
  number =       "7",
  pages =        "448--449",
  month =        jul,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Oct 30 09:18:14 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: Comments on a FORTRAN routine.",
}

@Article{Ng:1970:CDF,
  author =       "E. W. Ng and C. J. Devine",
  title =        "On the Computation of {Debye} Functions of Integer
                 Orders",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "110",
  pages =        "405--407",
  month =        apr,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Debye functions are incomplete Riemann zeta
                 functions. $ \overbar {D}_p(x) = \frac {1}{\Gamma (p -
                 1)} \int_0^x \frac {t^p}{e^t - 1} \, d t $ and the
                 complementary integral are calculated to 20 digits.",
}

@Article{Ninomiya:1970:BRS,
  author =       "Ichizo Ninomiya",
  title =        "Best Rational Starting Approximations and Improved
                 {Newton} Iteration for the Square Root",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "110",
  pages =        "391--404",
  month =        apr,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Nagoya Univ., Chikua ku, Japan",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computing procedure; function approximation; iterative
                 methods; Newton iteration; rational approximation;
                 square root",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Paciorek:1970:AEI,
  author =       "K. A. Paciorek",
  title =        "{Algorithm 385}: {Exponential} Integral {$
                 \operatorname {Ei}(x) $}",
  journal =      j-CACM,
  volume =       "13",
  number =       "7",
  pages =        "446--447",
  month =        jul,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Mar 25 13:26:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Redish:1970:RAE,Frisch:1972:RAR}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4160 (Numerical integration and differentiation);
                 C7300 (Natural sciences computing)",
  corpsource =   "Argonne Nat. Lab., IL, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "integration; subroutines",
  remark =       "Fullerton: A 100-line FORTRAN routine for both $
                 \operatorname {E1}(x) $ and $ \operatorname {Ei}(x)
                 $.",
}

@Article{Raff:1970:CGF,
  author =       "Morton S. Raff",
  title =        "On Calculating the Gamma Function of Non-Integral
                 Arguments",
  journal =      j-AMER-STAT,
  volume =       "24",
  number =       "2",
  pages =        "22--24",
  month =        apr,
  year =         "1970",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Jan 27 10:52:18 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326364;
                 https://www.math.utah.edu/pub/tex/bib/amstat1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2681926",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Redish:1970:RAE,
  author =       "K. A. Redish",
  title =        "Remark on {Algorithm 385, Exponential Integral $
                 \operatorname {Ei}(x) $}",
  journal =      j-CACM,
  volume =       "13",
  number =       "12",
  pages =        "750--750",
  month =        dec,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Oct 30 09:56:59 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Paciorek:1970:AEI}",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: Minor corrections to a FORTRAN routine.",
}

@TechReport{Rothmaier:1970:BQN,
  author =       "B. Rothmaier",
  title =        "{Die Berechnung der Quadratwurzel nebst Schranken auf
                 Dualmaschinen} \toenglish {The Computation of the
                 Square Root together with [Interval] Bounds on Binary
                 Machines} \endtoenglish",
  type =         "{Interner Bericht}",
  number =       "Nr. 70/17",
  institution =  "Institut f{\"u}r Informatik, Universit{\"a}t
                 Karlsruhe",
  pages =        "??",
  year =         "1970",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@TechReport{Rothmaier:1970:DSB,
  author =       "B. Rothmaier",
  title =        "{Dokumentation der Standardfunktionen des
                 Betriebssystems Hydra X8} \toenglish {Documentation} of
                 the Elementary Functions of the Operating System {Hydra
                 X8} \endtoenglish",
  type =         "Interner {Bericht}",
  number =       "Nr. 70/8",
  institution =  "Institut f{\"u}r Informatik, Universit{\"a}t
                 Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  year =         "1970",
  bibdate =      "Fri Jun 11 12:37:53 1999",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}

@Article{Smith:1970:ASH,
  author =       "Robert R. Smith and Dennis McCall",
  title =        "{Algorithm 392}: {Systems} of Hyperbolic {P.D.E.}",
  journal =      j-CACM,
  volume =       "13",
  number =       "9",
  pages =        "567--570",
  month =        sep,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Mar 25 13:26:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Frisch:1972:RAR}.",
  acknowledgement = ack-nhfb,
  classcodes =   "C4170 (Differential equations); C7310 (Mathematics
                 computing)",
  corpsource =   "US Naval Electronics Lab. Center, San Diego, CA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "boundary-value problems; partial differential
                 equations",
}

@Book{Spain:1970:FMP,
  author =       "Barry Spain and M. G. (Michael Gambier) Smith",
  title =        "Functions of Mathematical Physics",
  publisher =    pub-VAN-NOSTRAND-REINHOLD,
  address =      pub-VAN-NOSTRAND-REINHOLD:adr,
  pages =        "xi + 208",
  year =         "1970",
  ISBN =         "0-442-07871-4, 0-442-07876-5 (hardcover)",
  ISBN-13 =      "978-0-442-07871-3, 978-0-442-07876-8 (hardcover)",
  LCCN =         "QA351 .S69",
  bibdate =      "Tue Dec 5 10:54:45 MST 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "The New university mathematics series",
  URL =          "http://books.google.com/books?id=kYgZAQAAIAAJ",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Mathematical physics; Fonctions
                 sp{\'e}ciales; Physique math{\'e}matique; Functions,
                 Special; Mathematical physics; Functions, Special;
                 Fonctions",
  tableofcontents = "1: Series solution of second-order linear
                 homogeneous equations \\
                 2: Contour integral solutions of an ordinary linear
                 differential equation \\
                 3: Oscillation Theorems and Sturm--Liouville Theory \\
                 4: Asymptotics \\
                 5: The Gamma function \\
                 6: The Hypergeometric Equation \\
                 7: The confluent hypergeometric function \\
                 8: The Legendre Functions \\
                 9: Bessel Functions \\
                 10: Laguerre Polynomials \\
                 11: Hermite Polynomials \\
                 Appendix 1: The Laplace and Helmholtz Equations \\
                 Appendix 2: The Schr{\"o}dinger Equation \\
                 References \\
                 Index",
}

@Article{Squire:1970:RAI,
  author =       "William Squire",
  title =        "A Rational Approximation to an Integral Appearing in
                 Glow Curve Theory",
  journal =      j-J-COMPUT-PHYS,
  volume =       "6",
  number =       "1",
  pages =        "152--253",
  month =        aug,
  year =         "1970",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(70)90016-1",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sat Oct 30 10:57:00 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Srivastava:1970:CRI,
  author =       "H. M. Srivastava",
  title =        "Certain Results Involving Generalized Hypergeometric
                 Functions",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "1",
  number =       "1",
  pages =        "75--81",
  month =        feb,
  year =         "1970",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  bibdate =      "Sun Nov 28 19:21:56 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/1/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@Article{Stegun:1970:ACM,
  author =       "I. A. Stegun and R. Zucker",
  title =        "Automatic Computing Methods for Special Functions.
                 Part 1. {Error}, Probability, and Related Functions",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "74B",
  number =       "3",
  pages =        "211--224",
  month =        jul,
  year =         "1970",
  ISSN =         "0091-0635",
  bibdate =      "Sat Oct 30 10:58:39 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards (1934)",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Fullerton: Adjustable double precision FORTRAN
                 routines for $ \erf $ and $ \erfc $.",
}

@Book{Tolke:1970:PFT,
  author =       "Friedrich T{\"o}lke",
  title =        "{Praktische Funktionenlehre. 6. Tafeln aus dem Gebiet
                 der Theta-Funktionen und der elliptischen Funtionen}.
                 ({German}) [{Practical} functional theory. 6. {Tables}
                 from the field of theta functions and elliptic
                 functions]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "452--1047 (vol. 2)",
  year =         "1970",
  ISBN =         "3-662-13079-3 (print), 3-662-13078-5",
  ISBN-13 =      "978-3-662-13079-7 (print), 978-3-662-13078-0",
  LCCN =         "????",
  bibdate =      "Mon Feb 13 19:01:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Two volumes",
  acknowledgement = ack-nhfb,
  language =     "German",
  tableofcontents = "Sechsstellige Tafel III der Theta-Funktionen und
                 ihrer logarithmischen Ableitungen, der Jacobischen
                 elliptischen Funktionen und ihrer logarithmischen
                 Ableitungen sowie der Weierstrassschen $z$, $?$, und
                 $?$-Funktionen einschlie{\ss}lich einiger
                 Parameterfunktionen f{\"u}r $? = z/2K$ als Argument und
                 bzw. $1/?$ als Parameter $2$ H{\"a}lfte,
                 Parameterbereich $1 ? 1 / ? 0$ \\
                 Neunstellige Tafel IV der Legendreschen Normalintegrale
                 erster und zweiter Gattung sowie der Jacobischen
                 Zeta-Funktion und der abgewandelten Heumanschen
                 Lambda-Funktion \\
                 Sechsstellige Tafel V der $D$-Funktionen erster bis
                 vierter Ordnung f{\"u}r die Charakteristiken 1 bis 4
                 \\
                 Sechsstellige Tafel VI der Legendreschen
                 Normalintegrale erster und zweiter Gattung sowie der
                 Funktion \\
                 \ldots{}",
}

@Article{Wilson:1970:OSA,
  author =       "M. Wayne Wilson",
  title =        "Optimal Starting Approximations for Generating Square
                 Root for Slow or No Divide",
  journal =      j-CACM,
  volume =       "13",
  number =       "9",
  pages =        "559--560",
  month =        sep,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.50",
  MRnumber =     "44\#2338",
  MRreviewer =   "J. E. {Dennis, Jr.}",
  bibdate =      "Tue Apr 08 20:38:30 1997",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "On computing machines with slow or no division, it is
                 preferable to use an iterative scheme for the square
                 root different from the classical Heron scheme. The
                 problem of optimal initial approximants is considered,
                 and some optimal polynomial initial approximations are
                 tabulated.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "IBM, Houston, TX, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "CACMA; digital arithmetic; ele; iterative methods;
                 mathematics; numerical methods; optimisation",
}

@Article{Winograd:1970:NMN,
  author =       "Shmuel Winograd",
  title =        "On the number of multiplications necessary to compute
                 certain functions",
  journal =      j-COMM-PURE-APPL-MATH,
  volume =       "23",
  number =       "2",
  pages =        "165--179",
  month =        mar,
  year =         "1970",
  CODEN =        "CPAMAT, CPMAMV",
  DOI =          "https://doi.org/10.1002/cpa.3160230204",
  ISSN =         "0010-3640 (print), 1097-0312 (electronic)",
  ISSN-L =       "0010-3640",
  bibdate =      "Sat Oct 21 12:05:50 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://doi.org/10.1002/cpa.3160230204",
  acknowledgement = ack-nhfb,
  ajournal =     "Comm. Pure Appl. Math.",
  fjournal =     "Communications on Pure and Applied Mathematics (New
                 York)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
  keywords =     "number of multiplications to evaluate a polynomial",
  remark =       "From the second paragraph: ``Motzkin [3] introduced
                 the notion of preconditioning of the coefficients.
                 Motzkin showed that if, in the course of computing $
                 P_n(x) = \sum_{i = 0}^n a_i x^i $, operations which
                 depend only the $ a_i $ are not counted, then only
                 about $ n / 2 $ multiplications are necessary to
                 evaluate $ P_n(x) $. The obvious application of this
                 result is when the same polynomial $ P_n(x) $ has to be
                 evaluated at many different points.''.",
}

@TechReport{Yohe:1970:RBC,
  author =       "J. M. Yohe",
  title =        "Rigorous Bounds on Computed Approximations to Square
                 Roots and Cube Roots",
  type =         "MRC Technical Summary",
  number =       "1088",
  institution =  "University of Wisconsin, Madison",
  year =         "1970",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-jr,
}

@Article{Yong:1970:GBA,
  author =       "Lam Lay Yong",
  title =        "The Geometrical Basis of the {Ancient Chinese}
                 Square-Root Method",
  journal =      j-ISIS,
  volume =       "61",
  number =       "1",
  pages =        "92--102",
  month =        "Spring",
  year =         "1970",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:28:39 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i302287;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1970.bib",
  URL =          "http://www.jstor.org/stable/229151",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/page/journal/isis/about.html",
}

@Article{Zill:1970:SEI,
  author =       "D. G. Zill and B. C. Carlson",
  title =        "Symmetric Elliptic Integrals of the Third Kind",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "109",
  pages =        "199--214",
  month =        jan,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Bohan:1971:ADC,
  author =       "K. A. Bohan and K. V. La{\v{s}}{\v{c}}enov",
  title =        "The analytic definition of certain elementary
                 functions. ({Russian}) Questions of modern mathematics
                 and methods of teaching it at institutions of higher
                 learning",
  journal =      "Leningrad. Gos. Ped. Inst. U{\v{c}}en. Zap.",
  volume =       "404",
  pages =        "59--78",
  year =         "1971",
  MRclass =      "26A09",
  MRnumber =     "55 \#10612",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Book{Byrd:1971:HEI,
  author =       "Paul F. Byrd and Morris D. Friedman",
  title =        "Handbook of Elliptic Integrals for Engineers and
                 Scientists",
  volume =       "67",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xvi + 358",
  year =         "1971",
  DOI =          "https://doi.org/10.1007/978-3-642-65138-0",
  ISBN =         "0-387-05318-2 (New York)",
  ISBN-13 =      "978-0-387-05318-9 (New York)",
  LCCN =         "QA343 .B95 1971",
  bibdate =      "Mon Oct 15 16:40:14 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Die Grundlehren der mathematischen Wissenschaften in
                 Einzeldarstellungen",
  acknowledgement = ack-nhfb,
  subject =      "Elliptic functions",
  tableofcontents = "Introduction / 1--7 \\
                 Definitions and Fundamental Relations / 8--41 \\
                 Reduction of Algebraic Integrands to Jacobian Elliptic
                 Functions / 42--161 \\
                 Reduction of Trigonometric Integrands to Jacobian
                 Elliptic Functions / 162--181 \\
                 Reduction of Hyperbolic Integrands to Jacobian Elliptic
                 Functions / 182--190 \\
                 Table of Integrals of Jacobian Elliptic Functions /
                 191--222 \\
                 Elliptic Integrals of the Third Kind / 223--239 \\
                 Miscellaneous Elliptic Integrals Involving
                 Trigonometric and Hyperbolic Integrands / 240--248 \\
                 Elliptic Integrals Resulting from Laplace
                 Transformations / 249--251 \\
                 Hyperelliptic Integrals / 252--271 \\
                 Integrals of the Elliptic Integrals / 272--281 \\
                 Derivatives / 282--287 \\
                 Miscellaneous Integrals and Formulas / 288--297 \\
                 Expansions in Series / 298--307 \\
                 Appendix / 308 \\
                 Bibliography / 351 \\
                 Supplemental Bibliography / 353 \\
                 Index / 355",
}

@Misc{Chen:1971:BAU,
  author =       "Tien Chi Chen",
  title =        "Binary arithmetic unit implementing a multiplicative
                 iteration for the exponential, logarithm, quotient and
                 square root functions",
  howpublished = "United States Patent 3,631,230",
  day =          "28",
  month =        dec,
  year =         "1971",
  bibdate =      "Tue Jan 08 21:54:11 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.freepatentsonline.com/3631230.html",
  abstract =     "Apparatus and a method is described for efficiently
                 achieving arithmetic evaluations for functions such as
                 exponential, logarithm, quotient, and square root with
                 a minimum use of multiplications or divisions.
                 Basically, use is made of the fact that $ x(1 \pm
                 2^{-m}) $ can be evaluated by a shift followed by an
                 add. A pair of numbers $ (x_k, y_k) $ can represent a
                 function $ x : f(x) = g(x_k, y_k) $, such that $ g(l,
                 y_n) = y_n $ for logarithm, quotient and square root.
                 Then, multiplication by shifting is applied to $ x_k $
                 with suitable adjustments on $ y_k $, until $ x_k $ is
                 close to unity, at which time $ y_k $ represents the
                 desired answer. The exponential is computed by
                 essentially reversing the logarithm procedure. A
                 termination algorithm further improves accuracy. The
                 apparatus involves two registers for $ x_k $ and $ y_k
                 $, a local memory, an adder and a shift register.",
  acknowledgement = ack-nhfb,
}

@Article{Choong:1971:RA,
  author =       "K. Y. Choong and D. E. Daykin and C. R. Rathbone",
  title =        "Rational Approximations to $ \pi $",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "114",
  pages =        "387--392",
  month =        apr,
  year =         "1971",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1971-0300981-0",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib; JSTOR
                 database",
  note =         "See errata \cite{Shanks:1976:TER}.",
  URL =          "http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0300981-0",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Cody:1971:CAR,
  author =       "W. J. Cody and K. E. Hillstrom and Henry C. {Thatcher,
                 Jr.}",
  title =        "{Chebyshev} approximations for the {Riemann} zeta
                 function",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "115",
  pages =        "537--547",
  month =        jul,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20",
  MRnumber =     "47 2785",
  bibdate =      "Wed Jan 17 08:57:00 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-wjc,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 20-digit approximations for either $ \zeta
                 (s) $ or $ \zeta (s) - 1 $.",
}

@InCollection{Cody:1971:SEF,
  author =       "W. J. Cody",
  title =        "Software for the Elementary Functions",
  crossref =     "Rice:1971:MS",
  pages =        "171--186",
  year =         "1971",
  bibdate =      "Thu Sep 15 18:56:47 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}

@Article{Glasser:1971:CFE,
  author =       "M. L. Glasser and V. E. Wood",
  title =        "A Closed Form Evaluation of the Elliptic Integral",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "115",
  pages =        "535--536",
  month =        jul,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Glasser:1971:EII,
  author =       "M. L. Glasser",
  title =        "An Elliptic Integral Identity",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "115",
  pages =        "533--534",
  month =        jul,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Herman:1971:EDH,
  author =       "G. T. Herman",
  title =        "The equivalence of different hierarchies of elementary
                 functions",
  journal =      "Z. Math. Logik Grundlagen Math.",
  volume =       "17",
  pages =        "219--224",
  year =         "1971",
  MRclass =      "02.77 (68.00)",
  MRnumber =     "44 \#6494",
  MRreviewer =   "D. A. Clarke",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Book{Hochstadt:1971:FMP,
  author =       "Harry Hochstadt",
  title =        "The Functions of Mathematical Physics",
  volume =       "XXIII",
  publisher =    pub-WI,
  address =      pub-WI:adr,
  pages =        "xi + 322",
  year =         "1971",
  ISBN =         "0-471-40170-6 (hardcover)",
  ISBN-13 =      "978-0-471-40170-4 (hardcover)",
  LCCN =         "QA351 .H68",
  bibdate =      "Tue Dec 5 10:48:41 MST 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Pure and applied mathematics: a series of texts and
                 monographs",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Fonctions sp{\'e}ciales;
                 Fonctions (math{\'e}matiques)",
  tableofcontents = "1: Orthogonal Polynomials \\
                 1 Linear Spaces / 1 \\
                 2 Orthogonal Polynomials / 6 \\
                 3 The Recurrence Formula / 8 \\
                 4 The Christoffel--Darboux Formula / 9 \\
                 5 The Weierstrass Approximation Theorem / 11 \\
                 6 The Zeros of the Orthogonal Polynomials / 14 \\
                 7 Approximation Theory / 16 \\
                 8 More about the Zeros of the Orthonormal Polynomials /
                 23 \\
                 9 The completeness of the Orthonormal Polynomials in
                 the Space of Square-Integrable Functions / 27 \\
                 10 Generalizations and an Application to Conformal
                 Mappings / 32 \\
                 \\
                 2: The Classical Orthogonal Polynomials 1 Rodrigues'
                 Formula and the Classical Orthogonal Polynomials / 39
                 \\
                 2 The Differential Equations Satisfied by the Classical
                 Orthogonal Polynomials / 43 \\
                 3 On the Zeros of the Jacobi Polynomials / 45 \\
                 4 An Alternative Approach to the Tchebicheff
                 Polynomials / 46 \\
                 5 An Application of the Hermite Polynomials to Quantum
                 Mechanics / 49 \\
                 6 The Completeness of the Hermite and Laguerre
                 Polynomials / 53 \\
                 7 Generating Functions / 57 \\
                 \\
                 3: The Gamma Function 1 Definitions and Basic
                 Properties / 61 \\
                 2 Analytic Continuation and Integral Representations /
                 65 \\
                 3 Asymptotic Expansions / 69 \\
                 4 Beta Functions / 75 \\
                 5 The Logarithmic Derivative of the Gamma Function / 77
                 \\
                 6 Mellin--Barnes Integrals / 78 \\
                 7 Mellin Transforms / 80 \\
                 8 Applications to Algebraic Equations / 81 \\
                 \\
                 4: Hypergeometric Functions 1 Review of Linear
                 Differential Equations with Regular Singular Points /
                 88 \\
                 2 The Hypergeometric Differential Equation / 90 \\
                 3 The Hypergeometric Function / 93 \\
                 4 A General Method for Finding Integral Representations
                 / 100 \\
                 5 Integral Representations for the Hypergeometric
                 Function / 105 \\
                 6 The Twenty-four Solutions of the Hypergeometric /
                 Equation106 \\
                 7 The Schwarz--Christoffel Transformation / 112 \\
                 8 Mappings of Curvilinear Triangles / 119 \\
                 9 Group Theoretic Discussion of the Case $ \pi(\alpha_1
                 + \alpha_2 + \alpha_3) > \pi$ / 130 \\
                 10 Nonlinear Transformations of Hypergeometric
                 Functions / 132 \\
                 \\
                 5: The Legendre Functions 1 Laplace's Differential
                 Equation / 138 \\
                 2 Maxwell's Theory of Poles / 140 \\
                 3 Relationship to the Hypergeometric Functions / 141
                 \\
                 4 Expansion Formulas / 147 \\
                 5 The Addition Theorem / 149 \\
                 6 Green's Functions / 153 \\
                 7 The Complete Solution of Legendre's Differential
                 Equation / 156 \\
                 8 Asymptotic Formulas / 161 \\
                 \\
                 6: Spherical Harmonics in $p$ Dimensions 1 Homogeneous
                 Polynomials / 168 \\
                 2 Orthogonality of Spherical Harmonics / 171 \\
                 3 Legendre Polynomials / 175 \\
                 4 Applications to Boundary Value Problems / 183 \\
                 \\
                 7: Confluent Hypergeometric Functions 1 Relationship to
                 the Hypergeometric Functions / 189 \\
                 2 Applications of These Functions in Mathematical
                 Physics / 191 \\
                 3 Integral Representations / 195 \\
                 4 Asymptotic Representations / 198 \\
                 \\
                 8: Bessel Functions 1 Basic Definitions / 200 \\
                 2 Integral Representations / 203 \\
                 3 Relationship to the Legendre Functions / 205 \\
                 4 The Generating Function of the Bessel Function / 207
                 \\
                 5 More Integral Representations / 210 \\
                 6 Addition Theorems / 216 \\
                 7 The Complete Solution of Bessel's Equation / 223 \\
                 8 Asymptotic Expansions for Large Argument / 225 \\
                 9 Airy Functions / 230 \\
                 10 Asymptotic Expansions for Large Indices and Large
                 Arguments / 235 \\
                 11 Some Applications of Bessel Functions in Physical
                 Optics / 241 \\
                 12 The Zeros of Bessel Functions / 249 \\
                 13 Fourier--Bessel Expansions / 257 \\
                 14 Applications in Mathematical Physics / 266 \\
                 15 Discontinuous Integrals / 269 \\
                 \\
                 9: Hill's Equation 1 Mathieu's Equation / 281 \\
                 2 Hill's Equation / 282 \\
                 3 The Discriminant / 287 \\
                 4 Expansion Theorems / 299 \\
                 5 Inverse Problems / 305 \\
                 6 Hill's Equations with Even Coefficients / 309 \\
                 7 Mathieu's Equation Revisited / 310 \\
                 8 Energy Bands in Crystals / 313 \\
                 Appendix / 314 \\
                 \\
                 Bibliography / 318 \\
                 \\
                 Index / 321",
}

@Article{Honey:1971:CCD,
  author =       "D. W. Honey",
  title =        "Correspondence: Calculation of a double-length square
                 root from a double length number using single precision
                 techniques",
  journal =      j-COMP-J,
  volume =       "14",
  number =       "4",
  pages =        "443--443",
  month =        nov,
  year =         "1971",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:51:58 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/140443.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/tiff/443.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Kuki:1971:FEP,
  author =       "H. Kuki and J. Ascoly",
  title =        "{FORTRAN} extended-precision library",
  journal =      j-IBM-SYS-J,
  volume =       "10",
  number =       "1",
  pages =        "39--61",
  year =         "1971",
  CODEN =        "IBMSA7",
  ISSN =         "0018-8670",
  bibdate =      "Thu Sep 15 18:51:32 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmsysj.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Systems Journal",
  xxmonth =      "(none)",
}

@InCollection{Kuki:1971:MFS,
  author =       "H. Kuki",
  title =        "Mathematical Function Subprograms for Basic System
                 Libraries{}\emdash Objectives, Constraints, and
                 Trade-Off",
  crossref =     "Rice:1971:MS",
  pages =        "187--199",
  year =         "1971",
  bibdate =      "Fri Sep 16 16:27:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}

@Article{Lehmer:1971:CCM,
  author =       "D. H. Lehmer",
  title =        "On the compounding of certain means",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "36",
  number =       "1",
  pages =        "183--200",
  month =        oct,
  year =         "1971",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1016/0022-247x(71)90029-1",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  bibdate =      "Tue Mar 14 18:52:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "arithmetic--geometric mean (AGM) iteration; complete
                 elliptic integrals of the first and second kinds.
                 Landen s transformation",
}

@Article{Liron:1971:ISR,
  author =       "N. Liron",
  title =        "Infinite Sums of Roots for a Class of Transcendental
                 Equations and {Bessel} Functions of Order One-Half",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "116",
  pages =        "769--781",
  month =        oct,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Lucas:1971:AAC,
  author =       "C. W. {Lucas, Jr.} and C. W. Terrill",
  title =        "{ACM Algorithm 404}: Complex Gamma Function [{S14}]",
  journal =      j-CACM,
  volume =       "14",
  number =       "1",
  pages =        "48--49",
  month =        jan,
  year =         "1971",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:00:03 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#LucasT71;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4120 (Functional analysis); C7310 (Mathematics
                 computing)",
  corpsource =   "Coll. William and Mary, Williamsburg, VA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "algorithm; CGAMMA; complex gamma function evaluation;
                 formula; function evaluation; poles of gamma function;
                 recursion formula; reflection; Stirling's asymptotic
                 series; subroutine in ALGOL; subroutines",
  oldlabel =     "LucasT71",
  remark =       "Fullerton: Fortran routine with machine-dependent
                 constants.",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/LucasT71",
}

@Article{Luke:1971:MTBa,
  author =       "Yudell L. Luke",
  title =        "Miniaturized Tables of {Bessel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "114",
  pages =        "323--330",
  month =        apr,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Luke:1971:MTBb,
  author =       "Yudell L. Luke",
  title =        "Miniaturized Tables of {Bessel} Functions, {II}",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "116",
  pages =        "789--795",
  month =        oct,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Majithia:1971:CAN,
  author =       "J. C. Majithia and R. Kitai",
  title =        "A Cellular Array for the Nonrestoring Extraction of
                 Square Roots",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "12",
  pages =        "1617--1618",
  month =        dec,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223191",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671784",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Matta:1971:UCE,
  author =       "F. Matta and A. Reichel",
  title =        "Uniform Computation of the Error Function and Other
                 Related Functions",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "114",
  pages =        "339--344",
  month =        apr,
  year =         "1971",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1971-0295538-4",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  URL =          "http://www.ams.org/journals/mcom/1971-25-114/S0025-5718-1971-0295538-4",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@PhdThesis{Rothmaier:1971:BEF,
  author =       "B. Rothmaier",
  title =        "{Die Berechnung der elementaren Funktionen mit
                 beliebiger Genauigkeit} \toenglish {The Computation of
                 Elementary Functions with Arbitrary Accuracy}
                 \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  year =         "1971",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}

@Article{Sarkar:1971:EPP,
  author =       "B. P. Sarkar and E. V. Krishnamurthy",
  title =        "Economic Pseudodivision Processes for Obtaining Square
                 Root, Logarithm, and Arctan",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "12",
  pages =        "1589--1593",
  month =        dec,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223178",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 01 10:32:36 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Scarton:1971:DPF,
  author =       "Henry A. Scarton",
  title =        "Double precision {FORTRAN} subroutines to compute both
                 ordinary and modified {Bessel} functions of the first
                 kind and of integer order with arbitrary complex
                 argument: {$ J_n(x + j y) $} and {$ I_n(x + j y) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "8",
  number =       "2",
  pages =        "295--299",
  month =        oct,
  year =         "1971",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(71)90010-6",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:04 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999171900106",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Shenton:1971:CFP,
  author =       "L. R. Shenton and K. O. Bowman",
  title =        "Continued Fractions for the Psi Function and its
                 Derivatives",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "20",
  number =       "4",
  pages =        "547--554",
  month =        jun,
  year =         "1971",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2099856",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
}

@Article{Shipman:1971:HSE,
  author =       "L. L. Shipman and R. E. Christoffersen",
  title =        "High Speed Evaluation of {$ F_0 (x) $}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "2",
  number =       "4",
  pages =        "201--206",
  month =        may # "\slash " # jun,
  year =         "1971",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(71)90053-1",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Oct 30 10:40:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465571900531",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  remark =       "Fullerton: $ F_0 (x) = \int_0^1 \exp ( - x u^2) \, d u
                 $, which is simply related to $ \erf $ for $ x > 0 $
                 and to Dawson's function for $ x < 0 $.",
}

@Article{Spellucci:1971:DPA,
  author =       "P. Spellucci",
  title =        "Double precision approximations to the elementary
                 functions using {Jacobi-fractions}",
  journal =      j-NUM-MATH,
  volume =       "18",
  pages =        "127--143",
  year =         "1971/1972",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65D20",
  MRnumber =     "45 \#7938",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Spira:1971:CGF,
  author =       "Robert Spira",
  title =        "Calculation of the Gamma Function by {Stirling}'s
                 Formula",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "114",
  pages =        "317--322",
  month =        apr,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Sundblad:1971:AFT,
  author =       "Y. Sundblad",
  title =        "The {Ackermann} Function. {A} Theoretical,
                 Computational, and Formula Manipulative Study",
  journal =      j-BIT,
  volume =       "11",
  number =       "1",
  pages =        "107--119",
  month =        mar,
  year =         "1971",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01935330",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:11 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=11&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=1&spage=107",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  remark =       "Fullerton: Ackermann's function is a recursively
                 defined function of importance to computer science
                 theorists.",
}

@InProceedings{Walther:1971:UAE,
  author =       "J. S. Walther",
  title =        "A unified algorithm for elementary functions",
  crossref =     "AFIPS:1971:ACP",
  volume =       "38",
  pages =        "379--385",
  year =         "1971",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}

@Article{Wills:1971:URR,
  author =       "John G. Wills",
  title =        "On the use of recursion relations in the numerical
                 evaluation of spherical {Bessel} functions and
                 {Coulomb} functions",
  journal =      j-J-COMPUT-PHYS,
  volume =       "8",
  number =       "1",
  pages =        "162--166",
  month =        aug,
  year =         "1971",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(71)90043-X",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:04 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/002199917190043X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Wong:1971:SEI,
  author =       "R. Wong and E. Rosenbloom",
  title =        "Series Expansions of $ {W}_{k, m}(z) $ Involving
                 Parabolic Cylinder Functions",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "116",
  pages =        "783--787",
  month =        oct,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Bardin:1972:CFE,
  author =       "C. Bardin and Y. Dandeu and L. Gauthier and J.
                 Guillermin. T. Lena. J.-M. Pernet and H. H. Wolter and
                 T. Tamura",
  title =        "{Coulomb} Functions in Entire $ (\eta, \rho) $ Plane",
  journal =      j-COMP-PHYS-COMM,
  volume =       "3",
  number =       "2",
  pages =        "73--87",
  month =        mar,
  year =         "1972",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(72)90057-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Oct 29 21:09:33 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Book{Bark:1972:MTF,
  author =       "L. S. Bark",
  title =        "{{\cyr Mnogoznachnye tablitsy {\`e}lementarnykh
                 funktsi{\u\i}}} ($ \operatorname {sin} x $, $
                 \operatorname {cos} x $, $ e^x $ {\cyr i} $ e^{-x} $).
                 ({Russian}) [Multiplace tables of the elementary
                 functions ($ \operatorname {sin} \ x $, $ \operatorname
                 {cos} \ x $, $ e^x $ and $ e^{-x} $ )]",
  publisher =    "Vy{\v{c}}isl. Centr Akad. Nauk SSSR",
  address =      "Moscow, USSR",
  edition =      "Second, unrevised",
  pages =        "134",
  year =         "1972",
  MRclass =      "65A05",
  MRnumber =     "50 \#6100",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Tables processed and text translated from the English
                 by L. S. Bark. Library of Mathematical Tables, No. 9.
                 1972",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Carlson:1972:ACL,
  author =       "B. C. Carlson",
  title =        "An algorithm for computing logarithms and
                 arctangents",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "118",
  pages =        "543--549",
  month =        apr,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Iowa State Univ., Ames, IA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "acceleration; arctangents; auxiliary; Borchardt's
                 algorithm; convergence; fast; function approximation;
                 functions; inverse circular functions; inverse
                 hyperbolic; iterative algorithm; logarithms; numerical
                 methods; rational operations; recurrence relation;
                 square roots",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Chen:1972:ACE,
  author =       "Tien Chi Chen",
  title =        "Automatic Computation of Exponentials, Logarithms,
                 Ratios and Square Roots",
  journal =      j-IBM-JRD,
  volume =       "16",
  number =       "4",
  pages =        "380--388",
  month =        jul,
  year =         "1972",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "65D20",
  MRnumber =     "49 \#1738",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.research.ibm.com/journal/rd/164/chen.pdf",
  abstract =     "It is shown how a relatively simple device can
                 evaluate exponentials, logarithms, ratios and square
                 roots for fraction arguments, employing only shifts,
                 adds, high-speed table lookups, and bit counting. The
                 scheme is based on the cotransformation of a number
                 pair $ (x, y) $ such that the $ F(x, y) = f(x_0) $ is
                 invariant; when $x$ is driven towards a known value $
                 x_w $, $y$ is driven towards the result. For an $N$-bit
                 fraction about $ N / 4 $ iterations are required, each
                 involving two or three adds; then a termination
                 algorithm, based on an add and an abbreviated multiply,
                 completes the process, for a total cost of about one
                 conventional multiply time. Convergence, errors and
                 simulation using APL are discussed.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "IBM, San Jose, CA, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "adds; APL; bit counting; convergence;
                 cotransformation; digital arithmetic; errors;
                 exponentials; high speed table; iteration; logarithms;
                 lookups; ratios; shifts; simulation; square roots;
                 termination algorithm",
  reviewer =     "F. Gotze",
  treatment =    "P Practical",
}

@TechReport{Ercegovac:1972:RES,
  author =       "Milos D. Ercegovac",
  title =        "Radix 16 Evaluation of Some Elementary Functions",
  number =       "540",
  institution =  "Department of Computer Science, University of Illinois
                 at Urbana-Champaign",
  address =      "Urbana, Illinois",
  pages =        "30",
  year =         "1972",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/Uiuc.Tr.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Frisch:1972:RAR,
  author =       "Michael J. Frisch",
  title =        "Remark on ``{Algorithms 352, 385, 392}: Remarks on
                 Characteristic Values and Associated Solutions of
                 {Mathieu}'s Differential Equation, Exponential
                 Integral, and Systems of Hyperbolic {P.D.E.}''",
  journal =      j-CACM,
  volume =       "15",
  number =       "12",
  pages =        "1074--??",
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:42:24 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Frisch72;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See
                 \cite{Clemm:1969:ACV,Paciorek:1970:AEI,Smith:1970:ASH}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Frisch72",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Frisch72",
}

@Article{Fullerton:1972:MIG,
  author =       "W. Fullerton",
  title =        "{ACM Algorithm 435}: Modified Incomplete Gamma
                 Function",
  journal =      j-CACM,
  volume =       "15",
  number =       "11",
  pages =        "993--995",
  month =        nov,
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Schoene:1978:RMI}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: Fortran subprogram for evaluating $ e^{x_1}
                 \int_{x_1}^{x_2} |y|^{a - 1} e^{-y} \, d y $ for $a$
                 roughly between $1$ and $2$.",
}

@Article{Hunter:1972:NEC,
  author =       "D. B. Hunter and T. Regan",
  title =        "A note on the evaluation of the complementary error
                 function",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "118",
  pages =        "539--541",
  month =        apr,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4160 (Numerical integration and differentiation)",
  corpsource =   "Univ. Bradford, UK",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "complementary error function; complex variable;
                 evaluation; integration; method of Matta and Reichel;
                 modification; numerical; stability",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Kim:1972:AEH,
  author =       "Shoon K. Kim",
  title =        "The Asymptotic Expansion of a Hypergeometric Function
                 $_2 {F}_2 (1, \alpha; \rho_1, \rho_2; z)$",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "120",
  pages =        "963--963",
  month =        oct,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Kolbig:1972:CAC,
  author =       "K. S. K{\"o}lbig",
  title =        "Certification of ``{Algorithm 363}: {Complex} error
                 function''",
  journal =      j-CACM,
  volume =       "15",
  number =       "6",
  pages =        "465--466",
  month =        jun,
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:55:38 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kolbig72;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Gautschi:1969:ACE}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4120 (Functional analysis); C7310 (Mathematics
                 computing)",
  corpsource =   "CERN, Geneva, Switzerland",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\erf(z)$; complex error function; function
                 evaluation; special functions; subroutines; Voigt
                 function",
  oldlabel =     "Kolbig72",
  remark =       "Fullerton: Corrections and tests of an Algol
                 procedure.",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kolbig72",
}

@Article{Kolbig:1972:PCL,
  author =       "K. S. K{\"o}lbig",
  title =        "Programs for Computing the Logarithm of the Gamma
                 Function, and the Digamma Function, for Complex
                 Argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "4",
  number =       "2",
  pages =        "221--226",
  month =        nov,
  year =         "1972",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(72)90012-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Oct 30 08:33:42 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Kolbig:1972:RCC,
  author =       "K. S. K{\"o}lbig",
  title =        "Remarks on the Computation of {Coulomb}
                 Wavefunctions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "4",
  number =       "2",
  pages =        "214--220",
  month =        nov,
  year =         "1972",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(72)90011-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Oct 30 08:35:38 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Kolbig:1972:ZIG,
  author =       "K. S. Kolbig",
  title =        "On the Zeros of the Incomplete Gamma Function",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "119",
  pages =        "751--755",
  month =        jul,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "CERN, Geneva, Switzerland",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "asymptotic formulae; complex w plane; function
                 approximation; incomplete gamma function; poles and
                 zeros; zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Kuki:1972:AAC,
  author =       "Hirondo Kuki",
  title =        "{ACM Algorithm 421}: Complex Gamma Function with Error
                 Control [{S14}]",
  journal =      j-CACM,
  volume =       "15",
  number =       "4",
  pages =        "271--272",
  month =        apr,
  year =         "1972",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/361284.361296",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65D20",
  MRnumber =     "47 1249",
  MRreviewer =   "L. Fox",
  bibdate =      "Mon Jan 22 06:56:30 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kuki72a;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4130 (Interpolation and function approximation);
                 C7310 (Mathematics computing)",
  corpsource =   "Univ. Chicago, IL, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "algorithm; complex; complex gamma function; complex
                 loggamma; error control; FORTRAN; function; function
                 approximation; loggamma function; programme;
                 subroutines",
  oldlabel =     "Kuki72a",
  remark =       "Fullerton: 100-line FORTRAN routine with double
                 complex accuracy to $ 10^{-14} $.",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kuki72a",
}

@Article{Kuki:1972:CGF,
  author =       "Hirondo Kuki",
  title =        "Complex Gamma Function with Error Control [{S14}]",
  journal =      j-CACM,
  volume =       "15",
  number =       "4",
  pages =        "262--267",
  month =        apr,
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65D20",
  MRnumber =     "47 1249",
  MRreviewer =   "L. Fox",
  bibdate =      "Mon Jan 22 06:56:30 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kuki72a;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4130 (Interpolation and function approximation);
                 C7310 (Mathematics computing)",
  corpsource =   "Univ. Chicago, IL, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "algorithm; complex; complex gamma function; complex
                 loggamma; error control; FORTRAN; function; function
                 approximation; loggamma function; programme;
                 subroutines",
  oldlabel =     "Kuki72a",
  remark =       "Fullerton: Description of a FORTRAN routine with some
                 math details.",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kuki72a",
}

@Book{Lebedev:1972:SFT,
  author =       "N. N. (Nikolai Nikolaevich) Lebedev",
  title =        "Special functions and their applications",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xii + 308",
  year =         "1972",
  ISBN =         "0-486-60624-4 (paperback)",
  ISBN-13 =      "978-0-486-60624-8 (paperback)",
  LCCN =         "QA351 .L3613 1972",
  bibdate =      "Sat Oct 30 16:25:05 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Translated to English and edited by Richard A.
                 Silverman.",
  URL =          "http://www.loc.gov/catdir/description/dover031/72086228.html",
  acknowledgement = ack-nhfb,
  remark =       "Translation of Spe{\"e}t{\`\i}sial\S{}nye
                 funk{\"e}t{\`\i}sii i ikh prilozheni{\"e}i{\`\i}a.",
  subject =      "Functions, Special; Mathematical physics",
  tableofcontents = "1 The Gamma Function \\
                 \\
                 1.1. Definition of the Gamma Function \\
                 1.2. Some Relations Satisfied by the Gamma Function \\
                 1.3. The Logarithmic Derivative of the Gamma Function
                 \\
                 1.4. Asymptotic Representation of the Gamma Function
                 for Large $|z|$ \\
                 1.5. Definite Integrals Related to the Gamma Function
                 \\
                 Problems \\
                 \\
                 2 The Probability Integral and Related Functions \\
                 \\
                 2.1. The Probability Integral and Its Basic Properties
                 \\
                 2.2. Asymptotic Representation of the Probability
                 Integral for Large $|z|$ \\
                 2.3. The Probability Integral of Imaginary Argument.
                 The Function $F(z)$ \\
                 2.4. The Probability Integral of Argument $\sqrt{i} x$.
                 The Fresnel Integrals, 21. \\
                 2.5. Application to Probability Theory \\
                 2.6. Application to the Theory of Heat Conduction.
                 Cooling of the Surface of a Heated Object \\
                 2.7. Application to the Theory of Vibrations.
                 Transverse Vibrations of an Infinite Rod under the
                 Action of a Suddenly Applied Concentrated Force \\
                 Problems \\
                 \\
                 3 The Exponential Integral and Related Functions \\
                 \\
                 3.1. The Exponential Integral and its Basic Properties
                 \\
                 3.2. Asymptotic Representation of the Exponential
                 Integral for Large $|z|$ \\
                 3.3. The Exponential Integral of Imaginary Argument.
                 The Sine and Cosine Integrals \\
                 3.4. The Logarithmic Integral \\
                 3.5. Application to Electromagnetic Theory, Radiation
                 of a Linear Half-Wave Oscillator Problems \\
                 \\
                 4 Orthogonal Polynomials \\
                 \\
                 4.1. Introductory Remarks \\
                 4.2. Definition and Generating Function of the Legendre
                 Polynomials \\
                 4.3. Recurrence Relations and Differential Equation for
                 the Legendre Polynomials \\
                 4.4. Integral Representations of the Legendre
                 Polynomials \\
                 4.5. Orthogonality of the Legendre Polynomials \\
                 4.6. Asymptotic Representation of the Legendre
                 Polynomials for Large $n$ \\
                 4.7. Expansion of Functions in Series of Legendre
                 Polynomials \\
                 4.8. Examples of Expansions in Series of Legendre
                 Polynomials \\
                 4.9. Definition and Generating Function of the Hermite
                 Polynomials \\
                 4.10. Recurrence Relations and Differential Equation
                 for the Hermite Polynomials \\
                 4.11. Integral Representations of the Hermite
                 Polynomials \\
                 4.12. Integral Equations Satisfied by the Hermite
                 Polynomials \\
                 4.13. Orthogonality of the Hermite Polynomials \\
                 4.14. Asymptotic Representation of the Hermite
                 Polynomials for Large n \\
                 4.15. Expansion of Functions in Series of Hermite
                 Polynomials \\
                 4.16. Examples of Expansions in Series of Hermite
                 Polynomials \\
                 4.17. Definition and Generating Function of the
                 Laguerre Polynomials \\
                 4.18. Recurrence Relations and Differential Equation
                 for the Laguerre Polynomials \\
                 4.19. An Integral Representation of the Laguerre
                 Polynomials. Relation between the Laguerre and Hermite
                 Polynomials \\
                 4.20. An Integral Equation Satisfied by the Laguerre
                 Polynomials \\
                 4.21. Orthogonality of the Laguerre Polynomials \\
                 4.22. Asymptotic Representation of the Laguerre
                 Polynomials for Large $n$ \\
                 4.23. Expansion of Functions in Series of Laguerre
                 Polynomials \\
                 4.24. Examples of Expansions in Series of Laguerre
                 Polynomials \\
                 4.25. Application to the Theory of Propagation of
                 Electromagnetic Waves. Reflection from the End of a
                 Long Transmission Line Terminated by a Lumped
                 Inductance \\
                 Problems \\
                 \\
                 5 Cylinder Functions: Theory \\
                 \\
                 5.1. Introductory Remarks \\
                 5.2. Bessel Functions of Nonnegative Integral Order \\
                 5.3. Bessel Functions of Arbitrary Order \\
                 5.4. General Cylinder Functions. Bessel Functions of
                 the Second Kind \\
                 5.5. Series Expansion of the Function $Y_n(z)$ \\
                 5.6. Bessel Functions of the Third Kind \\
                 5.7. Bessel Functions of Imaginary Argument \\
                 5.8. Cylinder Functions of Half-Integral Order \\
                 5.9. Wronskians of Pairs of Solutions of Bessel s
                 Equation \\
                 5.10. Integral Representations of the Cylinder
                 Functions \\
                 5.11. Asymptotic Representations of the Cylinder
                 Functions for Large $|z|$ \\
                 5.12. Addition Theorems for the Cylinder Functions,
                 124.Zeros of the Cylinder Functions \\
                 5.13. Expansions in Series and Integrals Involving
                 Cylinder Functions \\
                 5.14. Definite Integrals Involving Cylinder Functions
                 \\
                 5.15. Cylinder Functions of Nonnegative Argument and
                 Order \\
                 5.16. Airy Functions \\
                 Problems \\
                 \\
                 6 Cylinder Functions: Applications \\
                 \\
                 6.1. Introductory Remarks \\
                 6.2. Separation of Variables in Cylindrical Coordinates
                 \\
                 6.3. The Boundary Value Problems of Potential Theory.
                 The Dirichlet Problem for a Cylinder \\
                 6.4. The Dirichlet Problem for a Domain Bounded by Two
                 Parallel Planes \\
                 6.5. The Dirichlet Problem for a Wedge \\
                 6.6. The Field of a Point Charge near the Edge of a
                 Conducting Sheet \\
                 6.7. Cooling of a Heated Cylinder \\
                 6.8. Diffraction by a Cylinder \\
                 Problems \\
                 \\
                 7 Spherical Harmonics: Theory \\
                 \\
                 7.1. Introductory Remarks \\
                 7.2. The Hypergeometric Equation and Its Series
                 Solution \\
                 7.3. Legendre Functions \\
                 7.4. Integral Representations of the Legendre Functions
                 \\
                 7.5. Some Relations Satisfied by the Legendre Functions
                 \\
                 7.6. Series Representations of the Legendre Functions
                 \\
                 7.7. Wronskians of Pairs of Solutions of Legend-re s
                 Equation \\
                 7.8. Recurrence Relations for the Legendre Functions
                 \\
                 7.9. Legendre Functions of Nonnegative Integral Degree
                 and Their Relation to Legendre Polynomials \\
                 7.10. Legendre Functions of Half-Integral Degree \\
                 7.11. Asymptotic Representations of the Legendre
                 Functions for Large $|v|$ \\
                 7.12. Associated Legendre Functions \\
                 Problems \\
                 \\
                 8 Spherical Harmonics: Applications \\
                 \\
                 8.1. Introductory Remarks \\
                 8.2. Solution of Laplace s Equation in Spherical
                 Coordinates \\
                 8.3. The Dirichlet Problem for a Sphere \\
                 8.4. The Field of a Point Charge Inside a Hollow
                 Conducting Sphere \\
                 8.5. The Dirichlet Problem for a Cone \\
                 8.6. Solution of Laplace s Equation in Spheroidal
                 Coordinates \\
                 8.7. The Dirichlet Problem for a Spheroid \\
                 8.8. The Gravitational Attraction of a Homogeneous
                 Solid Spheroid \\
                 8.9. The Dirichlet Problem for a Hyperboloid of
                 Revolution \\
                 8.10. Solution of Laplace s Equation in Toroidal
                 Coordinates \\
                 8.11. The Dirichlet Problem for a Torus \\
                 8.12. The Dirichlet Problem for a Domain Bounded by Two
                 Intersecting Spheres \\
                 8.13. Solution of Laplace s Equation in Bipolar
                 Coordinates \\
                 8.14. Solution of Helmholtz s Equation in Spherical
                 Coordinates \\
                 Problems \\
                 \\
                 9 Hypergeometric Functions \\
                 \\
                 9.1. The Hypergeometric Series and Its Analytic
                 Continuation \\
                 9.2. Elementary Properties of the Hypergeometric
                 Function \\
                 9.3. Evaluation of $F(\alpha, \beta; \gamma; z)$ for
                 $\Re(\gamma \alpha \beta) > 0$, 243. \\
                 9.4. $F(\alpha, \beta; \gamma; z)$ as a Function of its
                 Parameters \\
                 9.5. Linear Transformations of the Hypergeometric
                 Function \\
                 9.6. Quadratic Transformations of the Hypergeometric
                 Function \\
                 9.7. Formulas for Analytic Continuation of $F(\alpha,
                 \beta; \gamma; z)$ in Exceptional Cases \\
                 9.8. Representation of Various Functions in Terms of
                 the Hypergeometric Function \\
                 9.9. The Confluent Hypergeometric Function \\
                 9.10. The Differential Equation for the Confluent
                 Hypergeometric Function and Its Solution. The Confluent
                 Hypergeometric Function of the Second Kind \\
                 9.11. Integral Representations of the Confluent
                 Hypergeometric Functions \\
                 9.12. Asymptotic Representations of the Confluent
                 Hypergeometric Functions for Large $|z|$ \\
                 9.13. Representation of Various Functions in Terms of
                 the Confluent Hypergeometric Functions \\
                 9.14. Generalized Hypergeometric Functions \\
                 Problems \\
                 \\
                 10 Parabolic Cylinder Functions \\
                 \\
                 10.1. Separation of Variables in Laplace s Equation in
                 Parabolic Coordinates \\
                 10.2. Hermite Functions \\
                 10.3. Some Relations Satisfied by the Hermite Functions
                 \\
                 10.4. Recurrence Relations for the Hermite Functions
                 \\
                 10.5. Integral Representations of the Hermite Functions
                 \\
                 10.6. Asymptotic Representations of the Hermite
                 Functions for Large $|z|$ \\
                 10.7. The Dirichlet Problem for a Parabolic Cylinder
                 \\
                 10.8. Application to Quantum Mechanics \\
                 Problems \\
                 \\
                 Bibliography \\
                 \\
                 Index",
}

@Article{Ling:1972:EM,
  author =       "Chih-Bing Ling and Jung Lin",
  title =        "On Evaluation of Moments of $ {K}_\nu (t) / {I}_\nu
                 (t) $",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "118",
  pages =        "529--537",
  month =        apr,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4190 (Other numerical methods)",
  corpsource =   "Virginia Politech. Inst., Blacksburg, VA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "evaluation; K/sub nu/(t)/I/sub; moments; nu/(t);
                 numerical methods; Watson's method",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Linz:1972:MCB,
  author =       "Peter Linz",
  title =        "A Method for Computing {Bessel} Function Integrals",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "118",
  pages =        "509--513",
  month =        apr,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4160 (Numerical integration and differentiation)",
  corpsource =   "Univ. California, Davis, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Abel; Bessel function integrals; Fourier integrals;
                 infinite integrals; integration; numerical computation;
                 transform",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Luke:1972:MTB,
  author =       "Yudell L. Luke",
  title =        "Miniaturized Tables of {Bessel} Functions. {III}",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "117",
  pages =        "237--240",
  month =        jan,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4190 (Other numerical methods)",
  corpsource =   "Univ. Missouri, Kansas City, KS, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; miniaturized tables; numerical
                 methods",
  treatment =    "T Theoretical or Mathematical",
}

@Article{MacKinnon:1972:AEH,
  author =       "Robert F. MacKinnon",
  title =        "The asymptotic expansions of {Hankel} transforms and
                 related integrals",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "118",
  pages =        "515--527",
  month =        apr,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0230 (Integral transforms); C1130 (Integral
                 transforms)",
  corpsource =   "Defence Res. Establ., Pacific, Victoria, BC, Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "asymptotic expansions; Bessel; functions; Hankel
                 transforms; integrals; transforms",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Majithia:1972:CAE,
  author =       "J. C. Majithia",
  title =        "Cellular Array for Extraction of Squares and Square
                 Roots of Binary Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "9",
  pages =        "1023--1024",
  month =        sep,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009084",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009084",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Manos:1972:CCA,
  author =       "Paul Manos and L. Richard Turner",
  title =        "Constrained {Chebyshev} approximations to some
                 elementary functions suitable for evaluation with
                 floating-point arithmetic",
  type =         "{NASA} Technical Note",
  number =       "TN D-6698",
  institution =  pub-NASA,
  address =      pub-NASA:adr,
  pages =        "iii + 68",
  month =        mar,
  year =         "1972",
  bibdate =      "Mon May 22 11:27:24 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720010958_1972010958.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Marino:1972:NAA,
  author =       "D. Marino",
  title =        "New Algorithms for the Approximate Evaluation in
                 Hardware of Binary Logarithms and Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "12",
  pages =        "1416--1421",
  month =        dec,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1972.223516",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 08 08:05:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Morita:1972:CAG,
  author =       "Tohru Morita and Tsuyoshi Horiguchi",
  title =        "Convergence of the arithmetic-geometric mean procedure
                 for the complex variables and the calculation of the
                 complete elliptic integrals with complex modulus",
  journal =      j-NUM-MATH,
  volume =       "20",
  number =       "5",
  pages =        "425--430",
  month =        oct,
  year =         "1972",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01402565",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Thu Jan 13 10:01:46 MST 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=20&issue=5;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=20&issue=5&spage=425",
  abstract =     "The convergence of the arithmetic-geometric mean
                 procedure is checked for complex variables. The
                 procedure is shown to be useful for the evaluation of
                 the complete elliptic integrals of the first and second
                 kinds with complex modulus. It is suggested that the
                 procedure will be useful also for the numerical
                 calculation of the elliptic integrals and the Jacobian
                 elliptic functions with complex modulus in general.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Moses:1972:TGT,
  author =       "Joel Moses",
  title =        "Toward a General Theory of Special Functions",
  journal =      j-CACM,
  volume =       "15",
  number =       "7",
  pages =        "550--554",
  month =        jul,
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "34-02 12H05",
  MRnumber =     "53 3384",
  MRreviewer =   "K. Okugawa",
  bibdate =      "Mon Jan 22 07:06:21 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Moses72;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/macsyma.bib",
  note =         "Twenty-fifth anniversary of the Association for
                 Computing Machinery.",
  acknowledgement = ack-nhfb,
  classcodes =   "C1100 (Mathematical techniques)",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "general theory; mathematics; special functions",
  oldlabel =     "Moses72",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Moses72",
}

@Article{Olver:1972:NBR,
  author =       "F. W. J. Olver and D. J. Sookne",
  title =        "Note on Backward Recurrence Algorithms",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "120",
  pages =        "941--947",
  month =        oct,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290Z (Other numerical methods); C4190 (Other
                 numerical methods)",
  corpsource =   "Univ. Maryland, College Park, MD, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "backward recurrence algorithms; Bessel; Bessel
                 functions; difference equations; functions; recessive
                 solution; second order linear difference equation",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Parnes:1972:CZM,
  author =       "R. Parnes",
  title =        "Complex zeros of the modified {Bessel} function {$
                 K_n(Z) $}",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "120",
  pages =        "949--953",
  month =        oct,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "City Univ., New York, NY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "and zeros; Bessel functions; complex zeros;
                 interpolation; interpolation scheme; iterative;
                 iterative methods; modified Bessel function; poles",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Rabin:1972:FEP,
  author =       "Michael O. Rabin and Shmuel Winograd",
  title =        "Fast evaluation of polynomials by rational
                 preparation",
  journal =      j-COMM-PURE-APPL-MATH,
  volume =       "25",
  number =       "4",
  pages =        "433--458",
  month =        jul,
  year =         "1972",
  CODEN =        "CPAMAT, CPMAMV",
  DOI =          "https://doi.org/10.1002/cpa.3160250405",
  ISSN =         "0010-3640 (print), 1097-0312 (electronic)",
  ISSN-L =       "0010-3640",
  bibdate =      "Fri Oct 20 09:03:28 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://doi.org/10.1002/cpa.3160250405",
  acknowledgement = ack-nhfb,
  ajournal =     "Comm. Pure Appl. Math.",
  fjournal =     "Communications on Pure and Applied Mathematics (New York)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
  keywords =     "number of multiplications to evaluate a polynomial",
}

@Article{Ramamoorthy:1972:SPI,
  author =       "C. V. Ramamoorthy and James R. Goodman and K. H. Kim",
  title =        "Some Properties of Iterative Square-Rooting Methods
                 Using High-Speed Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "8",
  pages =        "837--847",
  month =        aug,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009039",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:45 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009039",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Samet:1972:CDL,
  author =       "P. A. Samet and D. W. Honey",
  title =        "Calculation of a Double-Length Square Root from
                 Double-Length Number using Single Precision
                 Techniques",
  journal =      j-COMP-J,
  volume =       "15",
  number =       "2",
  pages =        "116--116",
  month =        may,
  year =         "1972",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/15.2.116",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:49 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/15/2.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/15/2/116.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/tiff/116.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Univ. Coll., London, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "digital arithmetic; double length; precision
                 techniques; single; square root",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Strecok:1972:HPE,
  author =       "A. J. Strecok and J. A. Gregory",
  title =        "High Precision Evaluation of the Irregular {Coulomb}
                 Wave Functions",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "120",
  pages =        "955--961 + s1--s10",
  month =        oct,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "A0365G (Solutions of wave equations: bound state in
                 quantum theory); B0290F (Interpolation and function
                 approximation); C4130 (Interpolation and function
                 approximation)",
  corpsource =   "Argonne Nat. Lab., IL, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "function approximation; high precision evaluation;
                 irregular Coulomb wave functions; numerical methods;
                 wave functions",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Turunov:1972:EFD,
  author =       "M. Turunov",
  title =        "Elementary functions of a discrete real and complex
                 argument. ({Russian})",
  journal =      "Ta{\v{s}}kent. Gos. Univ. Nau{\v{c}}n. Trudy",
  volume =       "418 Voprosy Mat.",
  pages =        "263--271, 386",
  year =         "1972",
  MRclass =      "30A95",
  MRnumber =     "50 \#13556",
  MRreviewer =   "G. Berzsenyi",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Wimp:1972:CPE,
  author =       "Jet Wimp",
  title =        "Corrigendum: {{\booktitle{Polynomial expansions of
                 Bessel functions and some associated functions}} (Math.
                 Comp. {\bf 16} (1962), 446--458)}",
  journal =      j-MATH-COMPUT,
  volume =       "26",
  number =       "117",
  pages =        "309--309",
  month =        jan,
  year =         "1972",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Sat Dec 22 06:54:10 MST 2018",
  bibsource =    "http://www.ams.org/mcom/1972-26-117;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib",
  note =         "See \cite{Wimp:1962:PEB}.",
  URL =          "http://www.ams.org/journals/mcom/1972-26-117/S0025-5718-1972-0400659-X;
                 http://www.ams.org/journals/mcom/1972-26-117/S0025-5718-1972-0400659-X/S0025-5718-1972-0400659-X.pdf;
                 https://www.ams.org/mathscinet-getitem?mr=400659;
                 https://www.ams.org/mathscinet/search/authors.html?authorName=Wimp%2C%20Jet",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Wynn:1972:CAM,
  author =       "Peter Wynn",
  title =        "Convergence Acceleration by a Method of
                 Intercalation",
  journal =      j-COMPUTING,
  volume =       "9",
  number =       "4",
  pages =        "267--273",
  year =         "1972",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:51 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-ec # " and " # ack-nhfb,
  affiliation =  "Louisiana State Univ., New Orleans, LA, USA",
  classification = "B0290Z; C4190",
  description =  "convergence; series (mathematics)",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "convergence acceleration; method of intercalation;
                 series of real terms",
}

@Article{Amos:1973:BIC,
  author =       "D. E. Amos",
  title =        "Bounds on Iterated Coerror Functions and Their
                 Ratios",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "122",
  pages =        "413--427",
  month =        apr,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Baker:1973:PAS,
  author =       "P. W. Baker",
  title =        "Predictive algorithms for some elementary functions in
                 radix $2$",
  journal =      j-ELECT-LETTERS,
  volume =       "9",
  pages =        "493--494",
  year =         "1973",
  CODEN =        "ELLEAK",
  ISBN =         "0013-5194",
  ISBN-13 =      "0013-5194",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  MRclass =      "68A10",
  MRnumber =     "57 \#18203",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}

@Article{Besslich:1973:MDS,
  author =       "P. W. Besslich and S. Raman",
  title =        "Multiplication, Division and Square Root Extraction
                 Methods for Electronic Desk Calculators",
  journal =      "Journal of the Institution of Telecommunication
                 Engineers (India)",
  volume =       "19",
  number =       "4",
  month =        apr,
  year =         "1973",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Braithwaite:1973:ALP,
  author =       "W. J. Braithwaite",
  title =        "Associated {Legendre} Polynomials, Ordinary and
                 Modified Spherical Harmonics",
  journal =      j-COMP-PHYS-COMM,
  volume =       "5",
  number =       "5",
  pages =        "390--394",
  month =        may,
  year =         "1973",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(73)90065-9",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Oct 29 21:45:41 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Cody:1973:CAP,
  author =       "W. J. Cody and Anthony J. Strecok and Henry C.
                 {Thacher, Jr.}",
  title =        "{Chebyshev} Approximations for the Psi Function",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "121",
  pages =        "123--127",
  month =        jan,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65-06 (68-06)",
  MRnumber =     "50 6095",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Argonne Nat. Lab., IL, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Chebyshev approximation; Chebyshev approximations;
                 digamma function; psi function",
  remark =       "Fullerton: Relative errors down to $ 10^{-20} $",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Dingle:1973:AET,
  author =       "Robert B. Dingle",
  title =        "Asymptotic expansions: their derivation and
                 interpretation",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xv + 521",
  year =         "1973",
  ISBN =         "0-12-216550-0",
  ISBN-13 =      "978-0-12-216550-4",
  LCCN =         "QA295 .D45",
  bibdate =      "Sat Feb 18 14:52:17 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Asymptotic expansions; Power series",
}

@Article{Ercegovac:1973:REC,
  author =       "M. D. Ercegovac",
  title =        "Radix-16 Evaluation of Certain Elementary Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "561--566",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009107",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:39 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Fettis:1973:CZE,
  author =       "Henry E. Fettis and James C. Caslin and Kenneth R.
                 Cramer",
  title =        "Complex zeros of the error function and of the
                 complementary error function",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "122",
  pages =        "401--407",
  month =        apr,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Wright-Patterson Air Force Base, OH, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "asymptotic formula; complementary error function;
                 complex zeros; error function; errors; first one
                 hundred zeros; function evaluation; poles and zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Fettis:1973:SPC,
  author =       "Henry E. Fettis and James C. Caslin and Kenneth R.
                 Cramer",
  title =        "Saddle Points of the Complementary Error Function",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "122",
  pages =        "409--412",
  month =        apr,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Sandia Labs., Albuquerque, NM, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "asymptotic; complementary error function; errors;
                 formula; function evaluation; poles and zeros; saddle
                 points",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Fisher:1973:NEI,
  author =       "N. I. Fisher",
  title =        "A note on the evaluation of the incomplete gamma
                 function",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "2",
  number =       "4",
  pages =        "325--332",
  year =         "1973",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949657308810058",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Tue Apr 22 09:10:34 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
}

@Article{Gautschi:1973:AAE,
  author =       "Walter Gautschi",
  title =        "{ACM Algorithm 471}: Exponential Integrals [{S13}]",
  journal =      j-CACM,
  volume =       "16",
  number =       "12",
  pages =        "761--763",
  month =        dec,
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:43:23 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Gautschi73;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation);
                 C7310 (Mathematics computing)",
  corpsource =   "Purdue Univ., Lafayette, IN, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "ALGOL; computation; continued fractions; exponential
                 integrals; integration; recurrence relations;
                 recursive; subroutine; subroutines",
  oldlabel =     "Gautschi73",
  remark =       "Fullerton: Algol-language routine for $ E_n(x) =
                 \int_1^\infty e^{-x t} t^n \, d t, x > 0 $.",
  treatment =    "A Application; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Gautschi73",
}

@TechReport{Hemker:1973:SDL,
  author =       "P. W. Hemker and W. Hoffmann and S. P. N. {van Kampen}
                 and H. L. Oudshoorn and D. T. Winter",
  title =        "Single- and double-length computation of elementary
                 functions",
  number =       "NW 7",
  institution =  "Mathematical Centre",
  address =      "Amsterdam",
  year =         "1973",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hemker-pieter-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hill:1973:AAN,
  author =       "G. W. Hill and A. W. Davis",
  title =        "{ACM Algorithm 442}: Normal Deviate [{S14}]",
  journal =      j-CACM,
  volume =       "16",
  number =       "1",
  pages =        "51--52",
  month =        jan,
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:49:54 MST 2001",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1973.bib;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#HillD73;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C7310 (Mathematics computing)",
  corpsource =   "CSIRO, Glen Osmond, Australia",
  country =      "USA",
  descriptors =  "RVG",
  enum =         "7393",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "ALGOL; normal deviate; normal distribution inverse;
                 probit; statistics; subroutines; Taylor series
                 approximation; transform",
  oldlabel =     "HillD73",
  references =   "0",
  remark =       "Fullerton: Short Algol-language procedure with
                 accuracy to 24 digits.",
  treatment =    "P Practical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/HillD73",
}

@Article{Hill:1973:AAS,
  author =       "G. W. Hill",
  title =        "{ACM Algorithm 465}: {Student}'s $t$ Frequency
                 [{S14}]",
  journal =      j-CACM,
  volume =       "16",
  number =       "11",
  pages =        "690--690",
  month =        nov,
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:49:52 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Hill73a;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C7310 (Mathematics computing)",
  corpsource =   "CSIRO, Glen Osmond, SA, Australia",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "ALGOL; approximation; density function; series;
                 statistics; student's t statistic; subroutine;
                 subroutines",
  oldlabel =     "Hill73a",
  remark =       "Fullerton: Algol-language routine for $ f(t | n) =
                 \frac {\Gamma (n / 2 + 1 / 2)}{(\pi n)^{1 / 2} \Gamma
                 (n / 2)} (1 + t^2 / n)^{n / 2 + 1 / 2} $.",
  treatment =    "P Practical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Hill73a",
}

@Article{Hill:1973:SAA,
  author =       "I. D. Hill",
  title =        "Statistical Algorithms: {Algorithm AS 66}: The Normal
                 Integral",
  journal =      j-APPL-STAT,
  volume =       "22",
  number =       "3",
  pages =        "424--427",
  month =        sep,
  year =         "1973",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  bibdate =      "Sat Apr 21 10:20:49 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/as1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://lib.stat.cmu.edu/apstat/66",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}

@Article{Hwang:1973:RRS,
  author =       "W. G. Hwang and John Todd",
  title =        "A recurrence relation for the square root",
  journal =      j-J-APPROX-THEORY,
  volume =       "9",
  pages =        "299--306",
  year =         "1973",
  CODEN =        "JAXTAZ",
  DOI =          "https://doi.org/10.1016/0021-9045(73)90075-0",
  ISSN =         "0021-9045,1096-0430",
  ISSN-L =       "0021-9045",
  MRclass =      "65H05",
  MRnumber =     "373270",
  MRreviewer =   "L. Fox",
  bibdate =      "Sat Oct 21 14:25:01 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0271.65032",
  acknowledgement = ack-nhfb,
  author-dates = "John Todd (16 May 1911--21 June 2007)",
  fjournal =     "Journal of Approximation Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  received =     "19 April 1971",
  ZBmath =       "3426800",
}

@Article{Laurenzi:1973:DWF,
  author =       "Bernard J. Laurenzi",
  title =        "Derivatives of {Whittaker} Functions $ {W}_{k, 1 / 2}
                 $ and $ {M}_{k, 1 / 2} $ with Respect to Order $ {K}
                 $",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "121",
  pages =        "129--132",
  month =        jan,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Levin:1973:DNL,
  author =       "D. Levin",
  title =        "Development of non-linear transformations for
                 improving convergence of sequences",
  journal =      j-INT-J-COMPUT-MATH,
  volume =       "3",
  number =       "1--4",
  pages =        "371--388",
  month =        "????",
  year =         "1973",
  CODEN =        "IJCMAT",
  DOI =          "https://doi.org/10.1080/00207167308803075",
  ISSN =         "0020-7160",
  ISSN-L =       "0020-7160",
  bibdate =      "Thu Dec 01 10:27:34 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "0274.65004",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Computer Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/gcom20",
  keywords =     "convergence acceleration",
}

@Article{Linz:1973:NCI,
  author =       "Peter Linz and T. E. Kropp",
  title =        "A note on the computation of integrals involving
                 products of trigonometric and {Bessel} functions",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "124",
  pages =        "871--872",
  month =        oct,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation)",
  corpsource =   "Univ. California, Davies, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; computation; integration; numerical;
                 numerical methods; products; trigonometric",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Lozier:1973:BCP,
  author =       "D. W. Lozier and L. C. Maximon and W. L. Sadowski",
  title =        "A bit comparison program for algorithm testing",
  journal =      j-COMP-J,
  volume =       "16",
  number =       "2",
  pages =        "111--117",
  month =        may,
  year =         "1973",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:52:11 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/160111.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/111.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/112.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/113.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/114.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/115.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/116.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_02/tiff/117.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C6150G (Diagnostic, testing, debugging and evaluating
                 systems)",
  corpsource =   "Nat. Bur. Stand., Washington, DC, USA",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "accuracy; algorithm testing; bit comparison program;
                 computer algorithms; program debugging",
  treatment =    "P Practical",
}

@Article{McNolty:1973:SPD,
  author =       "Frank McNolty",
  title =        "Some probability density functions and their
                 characteristic functions",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "123",
  pages =        "495--504",
  month =        jul,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0240 (Probability and statistics); C1140 (Probability
                 and statistics)",
  corpsource =   "Lockheed Palo Alto Res. Lab., CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel function; characteristic functions; functions;
                 hypergeometric function; probability; probability
                 density functions",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Rice:1973:EEI,
  author =       "S. O. Rice",
  title =        "Efficient Evaluation of Integrals of Analytic
                 Functions by the Trapezoidal Rule",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "52",
  number =       "5",
  pages =        "707--722",
  month =        may # "--" # jun,
  year =         "1973",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1973/BSTJ.1973.5205.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol52/bstj52-5-707.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}

@Article{Schmid:1973:BLVa,
  author =       "H. Schmid",
  title =        "{BCD} logic {V}: {BCD} square root",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "21",
  number =       "17",
  pages =        "62--69",
  month =        aug,
  year =         "1973",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
  keywords =     "decimal fixed-point arithmetic",
}

@Article{Sookne:1973:BFC,
  author =       "D. J. Sookne",
  title =        "{Bessel} Functions {$I$} and {$J$} of Complex Argument
                 and Integer Order",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "77B",
  number =       "3--4",
  pages =        "111--114",
  month =        jul,
  year =         "1973",
  ISSN =         "0091-0635",
  bibdate =      "Sat Oct 30 10:49:13 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards (1934)",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Fullerton: A program is described but not published.",
}

@Article{Sookne:1973:BFR,
  author =       "D. J. Sookne",
  title =        "{Bessel} Functions of Real Argument and Integer
                 Order",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "77A",
  number =       "3--4",
  pages =        "125--132",
  month =        jul,
  year =         "1973",
  ISSN =         "0091-0635",
  bibdate =      "Sat Oct 30 10:51:18 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards (1934)",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Fullerton: Sequences of $ I_n(x) $ and $ J_n(x) $ are
                 computed with a FORTRAN routine.",
}

@Article{Sookne:1973:CABa,
  author =       "D. J. Sookne",
  title =        "Certification of an Algorithm for {Bessel} Functions
                 of Real Argument",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "77B",
  number =       "3--4",
  pages =        "115--124",
  month =        jul,
  year =         "1973",
  ISSN =         "0091-0635",
  bibdate =      "Sat Oct 30 10:55:03 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards (1934)",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Fullerton: An algorithm is shown to lose at most about
                 3 bits of precision.",
}

@Article{Sookne:1973:CABb,
  author =       "D. J. Sookne",
  title =        "Certification of an Algorithm for {Bessel} Functions
                 of Complex Argument",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "77B",
  number =       "3",
  pages =        "133--136",
  month =        jul,
  year =         "1973",
  ISSN =         "0091-0635",
  bibdate =      "Sat Oct 30 10:53:39 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards (1934)",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Fullerton: The algorithm is shown to lose at most
                 about 3 bits of precision.",
}

@Article{Vos:1973:RAC,
  author =       "H. Vos",
  title =        "Remark on ``{Algorithm 300}: {Coulomb} Wave
                 Functions''",
  journal =      j-CACM,
  volume =       "16",
  number =       "5",
  pages =        "308--309",
  month =        may,
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:27:34 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Vos73;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Gunn:1967:ACW}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis); C7310 (Mathematics computing)",
  corpsource =   "Vrije Univ., Amsterdam, Netherlands",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Coulomb wave functions; function evaluation;
                 mathematics; wave functions",
  oldlabel =     "Vos73",
  remark =       "Fullerton: Algol-language accuracy monitor for
                 Algorithm 300, which is generally accurate only to 3
                 digits.",
  treatment =    "A Application; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Vos73",
}

@Article{Wong:1973:AEL,
  author =       "R. Wong",
  title =        "An Asymptotic Expansion of {$ W_{k, m}(z) $} with
                 Large Variable and Parameters",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "122",
  pages =        "429--436",
  month =        apr,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Wong:1973:UAE,
  author =       "R. Wong",
  title =        "On uniform asymptotic expansion of definite
                 integrals",
  journal =      j-J-APPROX-THEORY,
  volume =       "7",
  number =       "1",
  pages =        "76--86",
  month =        jan,
  year =         "1973",
  CODEN =        "JAXTAZ",
  DOI =          "https://doi.org/10.1016/0021-9045(73)90055-5",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  MRclass =      "41A60",
  MRnumber =     "0340910",
  MRreviewer =   "L. Berg",
  bibdate =      "Sat Feb 18 15:20:40 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021904573900555",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Approximation Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  keywords =     "incomplete gamma functions",
}

@Article{Wrench:1973:ECT,
  author =       "John W. Wrench",
  title =        "Erratum: {Concerning Two Series for the Gamma
                 Function}",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "123",
  pages =        "681--682",
  month =        jul,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Minor last-digit rounding errors are
                 reported.",
}

@Article{Wrigge:1973:EII,
  author =       "H. S. Wrigge",
  title =        "An Elliptic Integral Identity",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "124",
  pages =        "839--840",
  month =        oct,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Yohe:1973:IBS,
  author =       "J. M. Yohe",
  title =        "Interval Bounds for Square Roots and Cube Roots",
  journal =      j-COMPUTING,
  volume =       "11",
  number =       "1",
  pages =        "51--57",
  month =        mar,
  year =         "1973",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:51 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  affiliation =  "Univ. Wisconsin, Madison, WI, USA",
  classification = "C5230",
  description =  "digital arithmetic; error analysis",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "binary computers; cube roots; error analysis; interval
                 bounds; machine representable number; optimal upward
                 directed rounding; smallest machine representable
                 interval; square roots",
}

@Article{Acton:1974:RRF,
  author =       "Forman S. Acton",
  title =        "Recurrence relations for the {Fresnel} integral $
                 \int_0^{\infty } \exp ( - c t) \, d t / \sqrt {t (1 +
                 t^2)} $ and similar integrals",
  journal =      j-CACM,
  volume =       "17",
  number =       "8",
  pages =        "480--481",
  month =        aug,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65D20 (33A70)",
  MRnumber =     "49 6554",
  bibdate =      "Mon Jan 22 06:20:27 MST 2001",
  bibsource =    "Compendex database;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Acton74;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The class of functions defined by $ \int_0^\infty
                 [\exp ( - c X)d t / (1 + Y)(t^{1 / 2})^k] $ where $X$
                 and $Y$ are either $t$ or $ t^2 $ and $k$ is $ - 1 $,
                 $0$, or $1$ can be evaluated by recurrences for all but
                 small values of the parameter $c$. These recurrences,
                 given here, are more efficient than the usual
                 asymptotic series.",
  acknowledgement = ack-nhfb,
  classification = "921",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "exponential integral; Fresnel integral; mathematical
                 techniques; recurrence relations",
  oldlabel =     "Acton74",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Acton74",
}

@Article{Amos:1974:CMB,
  author =       "D. E. Amos",
  title =        "Computation of modified {Bessel} functions and their
                 ratios",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "125",
  pages =        "239--251",
  month =        jan,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Sandia Labs., Albuquerque, NM, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; computation; low order Bessel
                 functions; modified Bessel functions; monotonicity;
                 properties; ratios; recursion; relation",
  remark =       "Fullerton: Ratios $ I_{\nu + 1}(x) / I_\nu (x) $ are
                 considered.",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Anonymous:1974:TCH,
  editor =       "Anonymous",
  title =        "Tables of Complex Hyperbolic and Circular Functions",
  volume =       "23",
  publisher =    "Corona Pub. Co.",
  address =      "Tokyo, Japan",
  pages =        "621",
  year =         "1974",
  LCCN =         "QA55 .T172",
  bibdate =      "Sat Apr 1 14:49:41 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Advanced series of mathematical and engineering
                 tables",
  acknowledgement = ack-nhfb,
  remark =       "Title and introduction also in Japanese: Fukuso
                 s{\aa}okyokusen kans{\aa}u hy{\aa}o.",
  subject =      "Mathematics; Tables; Exponential functions;
                 Trigonometrical functions",
}

@Article{Barlow:1974:CCF,
  author =       "R. H. Barlow",
  title =        "Convergent Continued Fraction Approximants to
                 Generalised Polylogarithms",
  journal =      j-BIT,
  volume =       "14",
  number =       "1",
  pages =        "112--116",
  month =        mar,
  year =         "1974",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01933124",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:13 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=14&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=14&issue=1&spage=112",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  remark =       "Fullerton: Nielsen's generalization $ S_{n, p}(z) =
                 \frac {( - 1)^{n + p - 1}(n - 1)! p!} \int_0^1 \ln^{n -
                 1}(t) \ln^p(1 - z t) / t \, d t $ is evaluated in the
                 complex plane.",
}

@Article{Barnett:1974:CWF,
  author =       "A. R. Barnett and D. H. Feng and J. W. Steed and L. J.
                 B. Goldfarb",
  title =        "{Coulomb} wave functions for all real $ \eta $ and $
                 \rho $",
  journal =      j-COMP-PHYS-COMM,
  volume =       "8",
  number =       "5",
  pages =        "377--395",
  month =        dec,
  year =         "1974",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(74)90013-7",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Jul 14 09:47:42 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  remark =       "This paper may contain the first presentation of
                 Steed's algorithm for computing continued fractions.",
}

@Article{Blair:1974:RCA,
  author =       "J. M. Blair",
  title =        "Rational {Chebyshev} approximations for the modified
                 {Bessel} functions {$ I_0 (x) $} and {$ I_1 (x) $}",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "126",
  pages =        "581--583",
  month =        apr,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Atomic Energy Canada Ltd., Chalk River, Ont., Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Chebyshev approximation; functions; modified Bessel;
                 nearly best rational approximations; rational Chebyshev
                 approximations; series (mathematics)",
  remark =       "Fullerton: With microfiche supplement. Relative errors
                 down to $ 10^{-23} $.",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Bosten:1974:RAI,
  author =       "Nancy E. Bosten and E. L. Battiste",
  title =        "Remark on ``{Algorithm 179}: {Incomplete} Beta
                 Ratio''",
  journal =      j-CACM,
  volume =       "17",
  number =       "3",
  pages =        "156--157",
  month =        mar,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:27:36 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#BostenB74;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Ludwig:1963:AIB,Pike:1976:RIB}.",
  acknowledgement = ack-nhfb,
  bdate =        "Mon Jan 22 06:27:36 MST 2001",
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation); C7310
                 (Mathematics computing)",
  corpsource =   "IMSL, Houston, TX, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Algorithm 179; computer aided analysis; function
                 approximation; incomplete beta ratio; subroutines",
  oldlabel =     "BostenB74",
  remark =       "Fullerton: FORTRAN routine with accuracy about $
                 10^{-6} $. See M. C. Pike (1976) for a Remark.",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/BostenB74",
}

@Article{Brent:1974:AAG,
  author =       "Richard P. Brent",
  title =        "{ACM Algorithm 488}: a {Gaussian} pseudo-random number
                 generator [{G5}]",
  journal =      j-CACM,
  volume =       "17",
  number =       "12",
  pages =        "704--706",
  month =        dec,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:28:05 MST 2001",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Brent74;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C7890 (Other special applications of computing)",
  corpsource =   "Australian Nat. Univ., Canberra, Australia",
  country =      "USA",
  descriptors =  "RVG",
  enum =         "7061",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "distribution; FORTRAN; Gaussian; generator; GRAND;
                 normal distribution; pseudo random numbers; random
                 number generation; random numbers; subroutines",
  location =     "SEL: Wi",
  oldlabel =     "Brent74",
  references =   "0",
  remark =       "Fullerton: A FORTRAN routine that returns normally
                 distributed numbers with zero mean and unit standard
                 deviation.",
  revision =     "16/01/94",
  treatment =    "A Application; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Brent74",
}

@Article{Burrell:1974:AAE,
  author =       "Keith H. Burrell",
  title =        "{ACM Algorithm 484}: Evaluation of the Modified
                 {Bessel} Functions {$ K_0 (z) $} and {$ K_1 (z) $} for
                 Complex Arguments [{S17}]",
  journal =      j-CACM,
  volume =       "17",
  number =       "9",
  pages =        "524--526",
  month =        sep,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:28:58 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Burrell74;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis); C7310 (Mathematics computing)",
  corpsource =   "California Inst. Technol., Pasadena, CA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "algorithm; applications of computers; Bessel
                 functions; complex arguments; function evaluation;
                 Gauss-Hermite quadrature; Hankel functions; modified
                 Bessel functions; natural sciences; subroutines",
  oldlabel =     "Burrell74",
  remark =       "Fullerton: 10-digit accuracy FORTRAN program.",
  treatment =    "A Application; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Burrell74",
}

@Article{Buschman:1974:FSR,
  author =       "R. G. Buschman",
  title =        "Finite sum representations for partial derivatives of
                 special functions with respect to parameters",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "127",
  pages =        "817--824",
  month =        jul,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation)",
  corpsource =   "Univ. Wyoming, Laramie, WY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; differentiation; finite sum
                 representations; finite sums; functions; G function;
                 Gegenbauer functions; hypergeometric; Legendre; Mellin
                 transformation; partial derivatives; special functions;
                 Whittaker functions",
  remark =       "Fullerton: Whittaker and Bessel functions are
                 considered.",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Carta:1974:HLR,
  author =       "David G. Carta",
  title =        "Help!!: {The} Lost Reference: ({A} Modified {Newton}
                 Method for Square Roots)",
  journal =      j-SIGNUM,
  volume =       "9",
  number =       "4",
  pages =        "9--9",
  month =        oct,
  year =         "1974",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1206085.1206086",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Jun 17 18:47:00 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/signum.bib",
  abstract =     "Around 1970 I saw a journal article describing a
                 modified Newton iteration for square roots. It involved
                 changing the usual factor of 0.5 in $ x_{n + 1} = 0.5
                 (x_n + a / x_n) $ to $ c_n $ where $ c_n \rightarrow
                 0.5 $, thereby increasing the asymptotic rate of
                 convergence from $ e_{n + 1} = 0.5 e_n^2 $ to $ e_{n +
                 1} = 0.25 e_n^2 $.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@Article{Fettis:1974:SAC,
  author =       "Henry E. Fettis",
  title =        "A stable algorithm for computing the inverse error
                 function in the `tail-end' region",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "126",
  pages =        "585--587",
  month =        apr,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Wright-Patterson Air Force Base, OH, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "function evaluation; inverse error function; iterative
                 algorithm; stability; stable algorithm; tail end
                 region",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Glasser:1974:SDI,
  author =       "M. L. Glasser",
  title =        "Some definite integrals of the product of two {Bessel}
                 functions of the second kind: (order zero)",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "126",
  pages =        "613--615",
  month =        apr,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Battelle Memorial Inst., Columbus, OH, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; definite integrals; evaluate;
                 function evaluation; integral representation; order;
                 second kind; zero",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Hitotumatu:1974:NMC,
  author =       "Sin Hitotumatu",
  title =        "A new method for the computation of square root,
                 exponential and logarithmic functions through
                 hyperbolic {CORDIC}",
  journal =      "Revue d'Analyse Num{\'e}rique et de la Th{\'e}orie de
                 l'Approximation",
  volume =       "3",
  number =       "2",
  pages =        "173--180",
  year =         "1974",
  ISSN =         "1010-3376 (print), 2457-8118 (electronic)",
  ISSN-L =       "1010-3376",
  MRclass =      "65D20",
  MRnumber =     "381249",
  MRreviewer =   "L. Fox",
  bibdate =      "Tue Nov 14 17:19:58 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://ictp.acad.ro/jnaat/journal/article/view/1974-vol3-no2-art7",
  acknowledgement = ack-nhfb,
  ajournal =     "Rev. Anal. Num{\'e}r. Th{\'e}orie Approximation",
  fjournal =     "Revue d'Analyse Num{\'e}rique et de la Th{\'e}orie de
                 l'Approximation",
  journal-URL =  "https://ictp.acad.ro/jnaat/journal",
  reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}

@Article{Koppelaar:1974:CRA,
  author =       "Henk Koppelaar",
  title =        "Certification and Remark on ``{Algorithm 191}:
                 Hypergeometric''",
  journal =      j-CACM,
  volume =       "17",
  number =       "10",
  pages =        "589--590",
  month =        oct,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:55:45 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Kopelaar74;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Relph:1963:AH}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C7310 (Mathematics computing)",
  corpsource =   "Utrecht State Univ., Netherlands",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "algorithm; hypergeometric; improvements; inefficiency;
                 natural sciences applications of computers;
                 subroutines",
  oldlabel =     "Kopelaar74",
  remark =       "Fullerton: Algol-language modifications for Algorithm
                 191, which does not appear to be accurate far from the
                 origin.",
  treatment =    "G General Review; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kopelaar74",
}

@Article{Kyriakopoulos:1974:GFH,
  author =       "E. Kyriakopoulos",
  title =        "Generating functions of the hypergeometric functions",
  journal =      j-J-MATH-PHYS,
  volume =       "15",
  number =       "6",
  pages =        "753--759",
  month =        jun,
  year =         "1974",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.1666724",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Oct 28 16:40:13 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1970.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v15/i6/p753_s1",
  acknowledgement = ack-nhfb,
  classification = "A0210 (Algebra, set theory, and graph theory); A0220
                 (Group theory); A0230 (Function theory, analysis)",
  corpsource =   "Nuclear Res. Center 'Democritos', Athens, Greece",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "functions; generating functions; hypergeometric
                 functions; Lie groups; Lie theory; multiplier
                 representation theory; Weisner's technique",
  onlinedate =   "4 November 2003",
  pagecount =    "7",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Latham:1974:CPC,
  author =       "W. P. Latham and Rogers W. Redding",
  title =        "On the calculation of the parabolic cylinder
                 functions",
  journal =      j-J-COMPUT-PHYS,
  volume =       "16",
  number =       "1",
  pages =        "66--75",
  month =        sep,
  year =         "1974",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(74)90104-1",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:15 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999174901041",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{McCabe:1974:CFE,
  author =       "J. H. McCabe",
  title =        "A continued fraction expansion, with a truncation
                 error estimate, for {Dawson}'s integral",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "127",
  pages =        "811--816",
  month =        jul,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290B (Error analysis in numerical methods); B0290F
                 (Interpolation and function approximation); C4110
                 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation)",
  corpsource =   "Univ. St. Andrews, Fife, UK",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "continued fraction expansion; convergents; Dawson's
                 integral; error analysis; function approximation;
                 rational approximations; truncation error estimate",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Nasell:1974:IMB,
  author =       "Ingemar Nasell",
  title =        "Inequalities for Modified {Bessel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "125",
  pages =        "253--256",
  month =        jan,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Bell Labs., Holmdel, NJ, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; inequalities; modified Bessel
                 functions; sharp versions",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Olver:1974:ASF,
  author =       "F. W. J. Olver",
  title =        "Asymptotics and Special Functions",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xvi + 572",
  year =         "1974",
  ISBN =         "0-12-525850-X",
  ISBN-13 =      "978-0-12-525850-0",
  LCCN =         "QA351 .O481 1974",
  bibdate =      "Wed Dec 15 10:40:06 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Pisarskii:1974:QCD,
  author =       "A. V. Pisarski{\u\i} and A. F. Kurgaev and A. V.
                 Palagin",
  title =        "On the question of the convergence of the {``digit by
                 digit''} methods of computing the elementary
                 functions",
  journal =      "Kibernetika (Kiev)",
  volume =       "4",
  pages =        "147--149",
  year =         "1974",
  CODEN =        "KBRNA5",
  ISSN =         "0023-1274",
  MRclass =      "65D20",
  MRnumber =     "53 \#1915",
  MRreviewer =   "V. V. Ivanov",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Pomeranz:1974:AAE,
  author =       "John Pomeranz",
  title =        "{ACM Algorithm 487}: Exact Cumulative Distribution of
                 the {Kolmogorov--Smirnov} Statistic for Small Samples",
  journal =      j-CACM,
  volume =       "17",
  number =       "12",
  pages =        "703--704",
  month =        dec,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:12:56 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Pomeranz74;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Pomeranz:1976:REC}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C7310 (Mathematics computing)",
  corpsource =   "Purdue Univ., West Lafayette, IN, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "algorithm; exact cumulative distribution; FORTRAN;
                 Kolmogorov Smirnov test; natural sciences applications
                 of computers; small samples; statistic; statistics;
                 subroutines",
  oldlabel =     "Pomeranz74",
  remark =       "Fullerton: FORTRAN routine accurate apparently to 5
                 digits.",
  treatment =    "A Application; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Pomeranz74",
}

@Article{Shaw:1974:NME,
  author =       "Mary Shaw and J. F. Traub",
  title =        "On the Number of Multiplications for the Evaluation of
                 a Polynomial and Some of Its Derivatives",
  journal =      j-J-ACM,
  volume =       "21",
  number =       "1",
  pages =        "161--167",
  month =        jan,
  year =         "1974",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321796.321810",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  abstract =     "A family of new algorithms is given for evaluating the
                 first $m$ derivatives of a polynomial. In particular,
                 it is shown that all derivatives may be evaluated in $
                 3 n - 2 $ multiplications. The best previous result
                 required $ (1 / 2) n (n + 1) $ multiplications. Some
                 optimality results are presented.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  classification = "921",
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "https://dl.acm.org/loi/jacm",
  keywords =     "mathematical techniques; number of multiplications to
                 evaluate a polynomial",
}

@Article{Sheorey:1974:CEW,
  author =       "V. B. Sheorey",
  title =        "{Chebyshev} Expansions for Wavefunctions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "7",
  number =       "1",
  pages =        "1--12",
  month =        jan,
  year =         "1974",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(74)90053-8",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Oct 30 10:36:29 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Stegun:1974:ACM,
  author =       "I. A. Stegun and R. Zucker",
  title =        "Automatic Computing Methods for Special Functions.
                 {Part II}. {The} Exponential Integral {$ E_n(x) $}",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "78B",
  number =       "4",
  pages =        "199--216",
  month =        oct,
  year =         "1974",
  ISSN =         "0091-0635",
  bibdate =      "Sat Oct 30 11:00:40 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards (1934)",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Fullerton: Adjustable double precision FORTRAN
                 routines for $ E_n(x) $ and $ e^x E_n(x) $.",
}

@Article{Wang:1974:UEZ,
  author =       "Paul S. Wang",
  title =        "The Undecidability of the Existence of Zeros of Real
                 Elementary Functions",
  journal =      j-J-ACM,
  volume =       "21",
  number =       "4",
  pages =        "586--589",
  month =        oct,
  year =         "1974",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 ftp://ftp.ira.uka.de/pub/bibliography/Math/hilbert10.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "From Richardson's undecidability results, it is shown
                 that the predicate ``there exists a real number such
                 that G(r) equals 0'' is recursively undecidable for
                 G(x) in a class of functions which involves polynomials
                 and the sine function. The deduction follows that the
                 convergence of a class of improper integrals is
                 recursively undecidable.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  classification = "921",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
  keywords =     "mathematical techniques",
}

@Article{Wimp:1974:CTP,
  author =       "J. Wimp",
  title =        "On the computation of {Tricomi}'s {Psi} function",
  journal =      j-COMPUTING,
  volume =       "13",
  number =       "3--4",
  pages =        "195--203",
  year =         "1974",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:52 MST 2001",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-nhfb,
  affiliation =  "Drexel Univ., Philadelphia, PA, USA",
  citedby =      "Fullerton:1980:BEM",
  classification = "723; 921; B0290D; C4120",
  description =  "convergence of numerical methods; function
                 evaluation",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput (Vienna/NY)",
  keywords =     "computation; computer programming --- Subroutines;
                 confluent hypergeometric function; convergence;
                 mathematical techniques; recurrence relations;
                 Tricomi's",
  remark =       "Fullerton: Backward recursion methods are discussed.",
}

@Article{Baker:1975:MER,
  author =       "P. W. Baker",
  title =        "More efficient radix-$2$ algorithms for some
                 elementary functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "11",
  pages =        "1049--1054",
  month =        nov,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224132",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "68A10",
  MRnumber =     "52 \#7193",
  MRreviewer =   "I. Kaufmann",
  bibdate =      "Tue Jul 12 07:57:58 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672725",
  acknowledgement = ack-nhfb # "\slash " # ack-nj,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Baker:1975:PMA,
  author =       "P. W. Baker",
  title =        "Parallel Multiplicative Algorithms for Some Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "3",
  pages =        "322--325",
  month =        mar,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224215",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672808",
  abstract =     "This correspondence presents generalized higher radix
                 algorithms for some elementary functions which use fast
                 parallel $m$-bit multipliers where $ \mathrm {radix} =
                 2^m $. These algorithms are extensions of those
                 iterative schemes which are based on multiplications by
                 $ (1 + 2^{-i}) $ and the use of prestored values of $
                 \ln (1 + 2^{-i}) $ and $ \tan^{-1}(2^{-i}) $. The
                 particular functions under consideration are $ y / x $,
                 $ y / x^{1 / 2} $, $ y \exp (x) $, $ y + \ln (x) $, $
                 \sin (x) $ and $ \cos (x) $ [and hence $ \tan (x) $ ].
                 The extended algorithms rely on multiplication by $ (1
                 + \mathrm {dir}^{-k}) $ where $ \mathrm {dir} $, $ 0
                 \leq \mathrm {dir} $, is an $m$-bit integer. Using a
                 simple selection procedure for $ \mathrm {dir} $,
                 simulations show that $p$ (radix $r$ ) digits of a
                 function may be generated, on the average, in less than
                 $ p + 1 $ iterations.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Boris:1975:NEO,
  author =       "Jay P. Boris and Elaine S. Oran",
  title =        "Numerical evaluation of oscillatory integrals such as
                 the modified {Bessel} function {$ K_{i \zeta }(x) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "17",
  number =       "4",
  pages =        "425--433",
  month =        apr,
  year =         "1975",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(75)90045-5",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:17 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999175900455",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@TechReport{Brent:1975:FMP,
  author =       "R. P. Brent",
  title =        "Fast Multiple-precision Evaluation of Elementary
                 Functions",
  type =         "Technical Report",
  number =       "STAN-CS-75-515",
  institution =  inst-STAN-CS,
  address =      inst-STAN-CS:adr,
  pages =        "i + 22",
  month =        aug,
  year =         "1975",
  bibdate =      "Thu Jan 11 16:47:21 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://bitsavers.org/pdf/stanford/cs_techReports/STAN-CS-75_515_Brent_Fast_Multiple-Precision_Evaluation_Of_Elementary_Functions_Aug75.pdf",
  abstract =     "Let $ f(x) $ be one of the usual elementary functions
                 ($ \exp $, $ \log $, $ \arctan $, $ \sin $, $ \cosh $,
                 etc.), and let $ M(n) $ be the number of
                 single-precision operations required to multiply n-bit
                 integers. We show that f(x) can be evaluated, with
                 relative error $ O(2^{-n}) $, in $ O(M(n) \log (n)) $
                 operations as $ n \to \infty $, for any floating-point
                 number $x$ (with an $n$-bit fraction) in a suitable
                 finite interval. From the Sch{\"o}nhage--Strassen bound
                 on $ M(n)$, it follows that an $n$-bit approximation to
                 $ f(x)$ may be evaluated in $ O(n \log^2 (n) \log \log
                 (n))$ operations. Special cases include the evaluation
                 of constants such as $ \pi $, $e$, and $ e^p i$. The
                 algorithms depend on the theory of elliptic integrals,
                 using the arithmetic--geometric mean iteration and
                 ascending Landen transformations.",
  acknowledgement = ack-nhfb,
}

@TechReport{Brent:1975:MZM,
  author =       "R. P. (Richard P.) Brent",
  title =        "Multiple-precision zero-finding methods and the
                 complexity of elementary function evaluation",
  institution =  "Department of Computer Science, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  pages =        "26",
  year =         "1975",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Iterative methods (Mathematics)",
  searchkey =    "ti:elementary n1 function",
}

@Article{Bujnowski:1975:EFC,
  author =       "G. Rudnicki Bujnowski",
  title =        "Explicit Formulas for {Clebsch--Gordan} Coefficients",
  journal =      j-COMP-PHYS-COMM,
  volume =       "10",
  number =       "4",
  pages =        "245--250",
  month =        oct,
  year =         "1975",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(75)90069-7",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Oct 30 10:13:20 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465575900697",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  remark =       "Fullerton: A PL/I-FORMAC procedure is discussed.",
}

@Article{Carta:1975:LOA,
  author =       "David G. Carta",
  title =        "Low-Order Approximations for the Normal Probability
                 Integral and the Error Function",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "131",
  pages =        "856--862",
  month =        jul,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0260 (Optimisation techniques); B0290R (Integral
                 equations); C1180 (Optimisation techniques); C4180
                 (Integral equations)",
  corpsource =   "Jet Propulsion Lab., California Inst. of Technol.,
                 Pasadena, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "error function; fraction; integral equations; linear
                 minimax problems; linear programming; low; normal
                 probability integral; order approximations;
                 polynomials; rational",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Cody:1975:FPS,
  author =       "W. J. Cody",
  title =        "The {FUNPACK} Package of Special Function
                 Subroutines",
  journal =      j-TOMS,
  volume =       "1",
  number =       "1",
  pages =        "13--25",
  month =        mar,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355626.355631",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@PhdThesis{Epstein:1975:AET,
  author =       "Harvey Irwin Epstein",
  title =        "Algorithms for elementary transcendental function
                 arithmetic",
  school =       "University of Wisconsin",
  address =      "Madison, WI, USA",
  pages =        "409",
  year =         "1975",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  annote =       "Typescript. Vita. Thesis (Ph. D.)--University of
                 Wisconsin--Madison, 1975.",
  keywords =     "Algorithms.; Functions -- Data processing.; Functions,
                 Transcendental.",
  searchkey =    "ti:elementary n1 function",
}

@PhdThesis{Ercegovac:1975:GMEa,
  author =       "Milo{\v{s}} Dragutin Ercegovac",
  title =        "A General Method for Evaluation of Functions and
                 Computations in a Digital Computer",
  type =         "{Ph.D.} Thesis",
  school =       "Department of Computer Science, University of Illinois
                 at Urbana-Champaign",
  address =      "Urbana-Champaign, IL, USA",
  pages =        "viii + 109",
  month =        jul,
  year =         "1975",
  bibdate =      "Mon Feb 10 07:18:12 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://search.proquest.com/pqdtglobal/docview/302756306",
  acknowledgement = ack-nhfb,
  advisor =      "James E. Robertson",
}

@Article{Ferguson:1975:PFI,
  author =       "Helaman Rolfe Pratt Ferguson and Dale E. Nielsen and
                 Grant Cook",
  title =        "A partition formula for the integer coefficients of
                 the theta function nome",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "131",
  pages =        "851--855",
  month =        jul,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290R (Integral equations); C4180 (Integral
                 equations)",
  corpsource =   "Dept. of Math., Brigham Young Univ., Provo, UT, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "coefficients; complete elliptic integrals; elliptic
                 function theory; elliptic integrals; incomplete;
                 integral equations; partition formula; theta function
                 nome integer",
  remark =       "Fullerton: Incomplete elliptic integrals can be
                 expressed as a series of theta functions.",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Fornberg:1975:CZJ,
  author =       "B. Fornberg and K. S. Kolbig",
  title =        "Complex zeros of the {Jonquiere} or polylogarithm
                 function",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "130",
  pages =        "582--599",
  month =        apr,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "CERN, Geneva, Switzerland",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "asymptotic; behaviour; complex zero trajectories;
                 Jonquiere function; poles and zeros; polylogarithm
                 function; polynomials; Riemann zeta function",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Gargantini:1975:PSR,
  author =       "I. Gargantini",
  editor =       "K. Nickel",
  booktitle =    "Interval Mathematics",
  title =        "Parallel Square Root Iterations",
  volume =       "29",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "196--204",
  year =         "1975",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Lecture Notes In Computer Science",
  acknowledgement = ack-jr,
}

@InProceedings{Gautschi:1975:CMS,
  author =       "W. Gautschi",
  title =        "Computational Methods in Special Functions --- a
                 Survey",
  crossref =     "Askey:1975:TAS",
  pages =        "1--98",
  year =         "1975",
  bibdate =      "Sat Oct 30 07:42:41 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  remark =       "Fullerton: Extensive list of references.",
}

@Article{Ginsberg:1975:AAD,
  author =       "E. S. Ginsberg and Dorothy Zaborowski",
  title =        "{ACM Algorithm 490}: The Dilogarithm Function of a
                 Real Argument [{S22}]",
  journal =      j-CACM,
  volume =       "18",
  number =       "4",
  pages =        "200--202",
  month =        apr,
  year =         "1975",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/360715.360722",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:44:28 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#GinsbergZ75;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Morris:1976:RDF}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis); C7310 (Mathematics computing)",
  corpsource =   "Dept. of Phys., Univ. of Massachusetts, Boston, MA,
                 USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "dilogarithm function; electrodynamics; ferromagnets;
                 function evaluation; function subroutine; ideal;
                 library; network analysis; polymers; quantum; real
                 argument; subprograms; subroutines; thermodynamics",
  oldlabel =     "GinsbergZ75",
  remark =       "Fullerton: FORTRAN routine accurate to 15 digits for
                 evaluating $ \operatorname {Li}_2 (x) = - \int_0^\infty
                 \frac {\ln (1 z)z} \, d z $.",
  treatment =    "A Application; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/GinsbergZ75",
}

@Article{Headley:1975:DZG,
  author =       "V. B. Headley and V. K. Barwell",
  title =        "On the distribution of the zeros of generalized {Airy}
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "131",
  pages =        "863--877",
  month =        jul,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290P (Differential equations); C4170 (Differential
                 equations)",
  corpsource =   "Dept. of Math., Brock Univ., St. Catherines, Ont.,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; boundary rays; differential
                 equations; generalized Airy functions; nonreal zeros;
                 zeros distribution",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Hitotumatu:1975:SRU,
  author =       "Sin Hitotumatu",
  title =        "Some remarks on the unified treatment of elementary
                 functions by microprogramming",
  crossref =     "Miller:1975:TNA",
  pages =        "51--56 (vol. 2)",
  year =         "1975",
  MRclass =      "65D15",
  MRnumber =     "54 \#11733",
  MRreviewer =   "Luciano Biasini",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Ikebe:1975:ZRC,
  author =       "Yasuhiko Ikebe",
  title =        "The Zeros of Regular {Coulomb} Wave Functions and of
                 Their Derivatives",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "131",
  pages =        "878--887",
  month =        jul,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290H (Linear algebra); C4140 (Linear algebra)",
  corpsource =   "Centre Numerical Analysis, Univ. of Texas, Austin, TX,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel function; compact matrix; eigenvalues;
                 eigenvalues and eigenfunctions; function zeros
                 characterisation; matrix algebra; methods; numerical;
                 operators; regular Coulomb wave functions; wave
                 functions; zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Kioustelidis:1975:PLA,
  author =       "J. B. Kioustelidis and J. K. Petrou",
  title =        "A Piecewise Linear Approximation of $ \log_2 x $ with
                 Equal Maximum Errors in All Intervals",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "9",
  pages =        "858--861",
  month =        sep,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224330",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672923",
  abstract =     "In this paper it is shown how to divide the interval $
                 [1, 2] $ into $n$ parts so that the uniform linear
                 approximation of $ \log_2 x $ in each subinterval has
                 the same maximum error. This error is, in the case $ n
                 = 4 $, smaller by a factor of $ 2.3 $ than the error of
                 the linear mean-square approximation given by Hall et
                 al. [1]. The final products of the mathematical
                 analysis are explicit formulas which allow the direct
                 determination of all parameters and the maximum error
                 for any desired number $n$ of subdivisions of $ [1, 2]
                 $.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "$\log_2(x)$; elementary function",
}

@Article{Lewis:1975:CPF,
  author =       "John Gregg Lewis",
  title =        "Certification of ``{Algorithm} 349: Polygamma
                 Functions with Arbitrary Precision''",
  journal =      j-TOMS,
  volume =       "1",
  number =       "4",
  pages =        "380--382",
  month =        dec,
  year =         "1975",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 16 10:31:40 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{TadeudeMedeiros:1969:APF}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "polygamma functions; special functions",
}

@Book{Luke:1975:MFT,
  author =       "Yudell L. Luke",
  title =        "Mathematical Functions and Their Approximations",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xvii + 568",
  year =         "1975",
  ISBN =         "0-12-459950-8, 1-4832-6245-6 (e-book)",
  ISBN-13 =      "978-0-12-459950-5, 978-1-4832-6245-1 (e-book)",
  LCCN =         "QA55 .L96 1975",
  bibdate =      "Fri Jun 30 05:58:16 MDT 2023",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  URL =          "https://shop.elsevier.com/books/mathematical-functions-and-their-approximations/luke/978-0-12-459950-5",
  acknowledgement = ack-nhfb,
  libnote =      "Not in my library.",
  remark =       "An updated version of part of Handbook of mathematical
                 functions with formulas, graphs, and mathematical
                 tables, edited by M. Abramowitz and I.A. Stegun.
                 Includes indexes.",
  subject =      "Mathematics; Tables; Fonctions (Math{\'e}ematiques);
                 Math{\'e}ematiques; Calculus; Mathematical Analysis;
                 Mathematics; Approximation; Funktion; Mathematik;
                 Spezielle Funktion",
  tableofcontents = "Preface / xv \\
                 \\
                 I. The Gamma Function and Related Functions \\
                 \\
                 1.1 Definitions and Elementary Properties / 1 \\
                 1.2 Power Series and Other Series Expansions / 1 \\
                 1.3 Asymptotic Expansions / 7 \\
                 1.4 Rational Approximations for y (z) / 13 \\
                 1.5 Inequalities / 17 \\
                 1.6 Bibliographic and Numerical Data / 20 \\
                 1.6.1 General References / 20 \\
                 1.6.2 Description of and References to Tables / 21 \\
                 1.6.3 Description of and References to Other
                 Approximations and Expansions / 22 \\
                 \\
                 II. The Binomial Function \\
                 \\
                 2.1 Power Series / 24 \\
                 2.2 Expansions in Series of Jacobi and Chebyshev
                 Polynomials / 24 \\
                 2.3 Expansions in Series of Bessel Functions / 26 \\
                 2.4 Pad{\'e} Approximations / 27 \\
                 24.1 $(1 + 1 / z)^{-c}$ / 27 \\
                 2.4.2 The Square Root / 28 \\
                 2.4.3 Pad{\'e} Coefficients / 30 \\
                 2.4.4 The Function $e^{-w}$ / 31 \\
                 2.5 Inequalities / 34 \\
                 \\
                 III. Elementary Functions \\
                 \\
                 3.1 Logarithmic Functions / 36 \\
                 3.1.1 Power Series / 36 \\
                 3.1.2 Expansion in Series of Chebyshev Polynomials / 38
                 \\
                 3.1.3 Pad{\'e} Approximations / 39 \\
                 3.1.4 Inequalities / 41 \\
                 3.2 Exponential Function / 42 \\
                 3.2.1 Series Expansions / 42 \\
                 3.2.2 Expansions in Series of Jacobi and Chebyshev
                 Polynomials and Bessel Functions / 42 \\
                 3.2.3 Pad{\'e} Approximations / 46 \\
                 3.2.4 Inequalities / 51 \\
                 3.3 Circular and Hyperbolic Functions / 52 \\
                 3.3.1 Power Series / 52 \\
                 3.3.2 Expansions in Series of Jacobi and Chebyshev
                 Polynomials and Bessel Functions / 52 \\
                 3.3.3 Rational and Pad{\'e} Approximations / 57 \\
                 3.3.4 Inequalities / 60 \\
                 3.4 Inverse Circular and Hyperbolic Functions / 61 \\
                 3.4.1 Power Series / 61 \\
                 3.4.2 Expansions in Series of Chebyshev Polynomials /
                 63 \\
                 3.4.3 Pad{\'e} Approximations / 68 \\
                 3.4.4 Inequalities / 72 \\
                 3.5 Bibliographic and Numerical Data / 74 \\
                 3.5.1 Description of and References to Tables / 74 \\
                 3.5.2 Description of and References to Other
                 Approximations and Expansions / 74 \\
                 \\
                 IV. Incomplete Gamma Functions \\
                 \\
                 4.1 Definitions and Series Expansions / 77 \\
                 4.2 Differential Equations and Difference Equations /
                 78 \\
                 4.3 Pad{\'e} Approximations / 79 \\
                 4.3.1 $_1F_1(1; \nu + 1; -z)$ / 79 \\
                 4.3.2 $z^{1 - \nu} e^z \Gamma(\nu, z)$ / 82 \\
                 4.3.3 The Error $T_n(\nu, z)$ for $|{\rm arg} z/k| \leq
                 \pi$ / 84 \\
                 4.3.4 The Negative Real Axis and the Zeros of $F_n(\nu,
                 z)$ / 89 \\
                 4.4 Inequalities / 95 \\
                 4.4.1 $H(\nu, z)$ / 95 \\
                 4.4.2 $\Gamma(\nu, z)$ / 96 \\
                 4.5 Notes on the Computation of the Incomplete Gamma
                 Function / 97 \\
                 4.6 Exponential Integrals / 103 \\
                 4.6.1 Relation to Incomplete Gamma Function and Other
                 Properties / 103 \\
                 4.6.2 Expansions in Series of Chebyshev Polynomials /
                 104 \\
                 4.6.3 Rational and Pad Approximations / 106 \\
                 4.7 Cosine and Sine Integrals / 115 \\
                 4.7.1 Relation to Exponential Integral and Other
                 Properties / 115 \\
                 4.7.2 Expansions in Series of Chebyshev Polynomials /
                 116 \\
                 4.8 Error Functions / 119 \\
                 4.8.1 Relation to Incomplete Gamma Function and Other
                 Properties / 119 \\
                 4.8.2 Expansions in Series of Chebyshev Polynomials and
                 Bessel Functions / 122 \\
                 4.8.3 Pad{\'e} Approximations / 124 \\
                 4.8.4 Trapezoidal Rule Approximations / 134 \\
                 4.8.5 Inequalities / 137 \\
                 4.9 Fresnel Integrals / 139 \\
                 4.9.1 Relation to Error Functions and Other Properties
                 / 139 \\
                 4.9.2 Expansions in Series of Chebyshev Polynomials /
                 140 \\
                 4.10 Bibliographic and Numerical Data / 143 \\
                 4.10.1 References / 143 \\
                 4.10.2 Description of and References to Tables / 143
                 \\
                 4.10.3 Description of and References to Other
                 Approximations and Expansions / 149 \\
                 \\
                 V. The Generalized Hypergeometric Function $_pF_g$ and
                 the $G$-Function \\
                 \\
                 5.1 Introduction / 154 \\
                 5.2 The $_pF_q$ / 155 \\
                 5.2.1 Power Series / 155 \\
                 5.2.2 Derivatives and Contiguous Relations / 159 \\
                 5.2.3 Integral Representations and Integrals Involving
                 the $_pF_q$ / 160 \\
                 5.2.4 Evaluation for Special Values of the Variable and
                 Parameters / 163 \\
                 5.3 The $G$-Function / 170 \\
                 5.3.1 Definition and Relation to the $_pF_q$ / 170 \\
                 5.3.2 Elementary Properties / 176 \\
                 5.3.3 Analytic Continuation of $G_{p, p}^{m, n}(z)$ /
                 178 \\
                 5.4 The Confluence Principle / 179 \\
                 5.5 Multiplication Theorems / 184 \\
                 5.6 Integrals Involving $G$-Functions / 186 \\
                 5.7 Differential Equations / 190 \\
                 5.7.1 The $_pF_q$ / 190 \\
                 5.7.2 The $G$-Function / 192 \\
                 5.8 Series of $G$-Functions / 194 \\
                 5.8.1 Introduction / 194 \\
                 5.8.2 Notation / 194 \\
                 5.8.3 Expansion Theorems / 197 \\
                 5.9 Asymptotic Expansions / 199 \\
                 5.9.1 $G_{p, q}^{q, n}(z)$, $n = 0, 1$ / 199 \\
                 5.9.2 $G_{p, q}^{m, n}(z)$ / 201 \\
                 5.9.3 $_pF_q(z)$ / 206 \\
                 5.10 Expansions in Series of Generalized Jacobi,
                 Generalized Laguerre and Chebyshev Polynomials / 213
                 \\
                 5.10.1 Expansions for $G$-Functions / 213 \\
                 5.10.2 Expansions for $_pF_q$ / 220 \\
                 5.11 Expansions in Series of Bessel Functions / 223 \\
                 5.12 Polynomial and Rational Approximations / 224 \\
                 5.13 Recurrence Formulas for Polynomials and Functions
                 Occurring in Approximations to Generalized
                 Hypergeometric Functions / 234 \\
                 5.13.1 Introduction / 234 \\
                 5.13.2 Recursion Formulas for Extended Jacobi and
                 Laguerre Functions / 235 \\
                 5.13.3 Recursion Formulas for the Numerator and
                 Denominator Polynomials in the Rational Approximations
                 for the Generalized Hypergeometric Function / 244 \\
                 5.13.4 Recursion Formula for Coefficients in the
                 Expansion of the $G$-Function in Series of Extended
                 Jacobi Polynomials / 247 \\
                 5.14 Inequalities / 252 \\
                 \\
                 VI. The Gaussian Hypergeometric Function $_2F_1$ \\
                 \\
                 6.1 Introduction / 257 \\
                 6.2 Elementary Properties / 257 \\
                 6.2.1 Derivatives / 257 \\
                 6.2.2 Contiguous Relations / 258 \\
                 6.2.3 Integral Representations / 259 \\
                 6.3 Differential Equations / 260 \\
                 6.4 Kummer Solutions and Transformation Formulae / 262
                 \\
                 6.5 Analytic Continuation / 263 \\
                 6.6 The Complete Solution and Wronskians / 265 \\
                 6.7 Quadratic Transformations / 270 \\
                 6.8 The $_2F_1$ for Special Values of the Argument /
                 271 \\
                 6.9 Expansion in Series of Chebyshev Polynomials / 274
                 \\
                 6.10 Pad{\'e} Approximations for $_2F_1(1, \sigma;\rho
                 + 1;-1/z)$ / 274 \\
                 6.11 Inequalities / 278 \\
                 6.12 Bibliographic and Numerical Data / 279 \\
                 6.12.1 References / 279 \\
                 6.12.2 Description of and References to Tables / 279
                 \\
                 \\
                 VII. The Confluent Hypergeometric Function \\
                 \\
                 7.1 Introduction / 284 \\
                 7.2 Integral Representations / 284 \\
                 7.3 Elementary Relations / 285 \\
                 7.3.1 Derivatives / 285 \\
                 7.3.2 Contiguous Relations / 285 \\
                 7.3.3 Products of Confluent Functions / 286 \\
                 7.4 Differential Equations / 287 \\
                 7.5 The Complete Solution and Wronskians / 288 \\
                 7.6 Asymptotic Expansions / 291 \\
                 7.7 Expansions in Series of Chebyshev Polynomials / 293
                 \\
                 7.8 Expansions in Series of Besse! Functions / 294 \\
                 7.9 Inequalities / 295 \\
                 7.10 Other Notations and Related Functions / 295 \\
                 7.11 Bibliographic and Numerical Data / 296 \\
                 7.11.1 References / 296 \\
                 7.11.2 Description of and References to Tables and
                 Other Approximations / 296 \\
                 \\
                 VIII. Identification of the $_pF_q$, and $G$-Functions
                 with the Special Functions \\
                 \\
                 8.1 Introduction / 298 \\
                 8.2 Named Special Functions Expressed as $_pF_q$'s /
                 298 \\
                 8.2.1 Elementary Functions / 298 \\
                 8.2.2 The Incomplete Gamma Function and Related
                 Functions / 298 \\
                 8.2.3 The Gaussian Hypergeometric Function / 298 \\
                 8.2.4 Legendre Functions / 299 \\
                 8.2.5 Orthogonal Polynomials / 299 \\
                 8.2.6 Complete Elliptic Integrals / 299 \\
                 8.2.7 Confluent Hypergeometric Functions, Whittaker
                 Functions and Bessel Functions / 300 \\
                 8.3 Named Functions Expressed in Terms of the
                 $G$-Function / 300 \\
                 8.4 The $G$-Function Expressed as a Named Function /
                 306 \\
                 \\
                 IX. Bessel Functions and Their Integrals \\
                 \\
                 9.1 Introduction / 311 \\
                 9.2 Definitions, Connecting Relations and Power Series
                 / 311 \\
                 9.3 Difference--Differential Formulas / 313 \\
                 9.4 Products of Bessel Functions / 314 \\
                 9.5 Asymptotic Expansions for Large Variable / 315 \\
                 9.6 Integrals of Bessel Functions / 315 \\
                 9.7 Expansions in Series of Chebyshev Polynomials / 316
                 \\
                 9.8 Expansions in Series of Bessel Functions / 360 \\
                 9.9 Rational Approximations / 361 \\
                 9.9.1 Introduction / 361 \\
                 9.9.2 $I_\nu(z)$, $z$ Small / 361 \\
                 9.9.3 $K_\nu(z)$, $z$ Large / 366 \\
                 9.10 Computation of Bessel Functions by Use of
                 Recurrence Formulas / 380 \\
                 9.10.1 Introduction / 380 \\
                 9.10.2 Backward Recurrence Schemata for Generating
                 $I_\nu(z)$ / 380 \\
                 9.10.3 Closed Form Expressions / 382 \\
                 9.10.4 Expressions for $J_\nu(z)$ / 389 \\
                 9.10.5 Numerical Examples / 392 \\
                 9.11 Evaluation of Bessel Functions by Application of
                 Trapezoidal Type Integration Formulas / 395 \\
                 9.12 Inequalities / 399 \\
                 9.13 Bibliographic and Numerical Data / 403 \\
                 9.13.1 References / 403 \\
                 9.13.2 Description of and References to Tables / 404
                 \\
                 9.13.3 Description of and References to Other
                 Approximations and Expansions / 410 \\
                 \\
                 X. Lommel Functions, Struve Functions, and Associated
                 Bessel Functions \\
                 \\
                 10.1 Definitions, Connecting Relations and Power Series
                 / 413 \\
                 10.2 Asymptotic Expansions / 415 \\
                 10.3 Expansions in Series of Chebyshev Polynomials and
                 Bessel Functions / 415 \\
                 10.4 Rational Approximations for $H_\nu(z) - Y_\nu(z)$
                 and the Errors in These Approximations / 422 \\
                 10.5 Bibliographic and Numerical Data / 426 \\
                 10.5.1 References / 426 \\
                 10.5.2 Description of and References to Tables / 426
                 \\
                 \\
                 XI. Orthogonal Polynomials \\
                 \\
                 11.1 Introduction / 428 \\
                 11.2 Orthogonal Properties / 428 \\
                 11.3 Jacobi Polynomials / 436 \\
                 11.3.1 Expansion Formulae / 436 \\
                 11.3.2 Difference--Differential Formulae / 439 \\
                 11.3.3 Integrals / 439 \\
                 11.3.4 Expansion of $x^\rho$ in Series of Jacobi
                 Polynomials / 440 \\
                 11.3.5 Convergence Theorems for the Expansion of
                 Arbitrary Functions in Series of Jacobi Polynomials /
                 442 \\
                 11.3.6 Evaluation and Estimation of the Coefficients in
                 the Expansion of a Given Function $f(x)$ in Series of
                 Jacobi Polynomials / 443 \\
                 11.4 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ /
                 453 \\
                 11.5 The Chebyshev Polynomials $T_n^*(x)$ and
                 $U_n^*(x)$ / 459 \\
                 11.6 Coefficients for Expansion of Integrals of
                 Functions in Series of Chebyshev Polynomials of the
                 First Kind / 464 \\
                 11.6.1 Introduction / 464 \\
                 11.6.2 Series of Shifted Chebyshev Polynomials / 464
                 \\
                 11.6.3 Series of Chebyshev Polynomials of Even Order /
                 468 \\
                 11.6.4 Series of Chebyshev Polynomials of Odd Order /
                 468 \\
                 11.7 Orthogonality Properties of Chebyshev Polynomials
                 with Respect to Summation / 469 \\
                 11.8 A Nesting Procedure for the Computation of
                 Expansions in Series of Functions Where the Functions
                 Satisfy a Linear Finite Difference Equation / 475 \\
                 \\
                 XII. Computation by Use of Recurrence Formulas \\
                 \\
                 12.1 Introduction / 483 \\
                 12.2 Homogeneous Difference Equations / 483 \\
                 12.3 Inhomogeneous Difference Equations / 487 \\
                 \\
                 XIII. Some Aspects of Rational and Polynomial
                 Approximations \\
                 \\
                 13.1 Introduction / 490 \\
                 13.2 Approximations in Series of Chebyshev Polynomials
                 of the First Kind / 490 \\
                 13.3 The Pad{\'e} Table / 493 \\
                 13.4 Approximation of Functions Defined by a
                 Differential Equation --- The $\tau$-Method / 495 \\
                 13.5 Approximations of Functions Defined by a Series /
                 499 \\
                 13.6 Solution of Differential Equations in Series of
                 Chebyshev Polynomials of the First Kind / 500 \\
                 \\
                 XIV. Miscellaneous Topics \\
                 \\
                 14.1 Introduction / 505 \\
                 14.2 Bernoulli Polynomials and Numbers / 505 \\
                 14.3 $D$ and $\delta$ Operators / 507 \\
                 14.4 Computation and Check of the Tables / 509 \\
                 14.5 Mathematical Constants / 512 \\
                 14.6 Late Bibliography / 516 \\
                 \\
                 Bibliography / 517 \\
                 \\
                 Notation Index / 545 \\
                 \\
                 Subject Index / 551",
}

@Article{Luke:1975:SRU,
  author =       "Y. L. Luke",
  title =        "Some remarks on uniform asymptotic expansions for
                 {Bessel} functions",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "1",
  number =       "3--4",
  pages =        "285--290",
  month =        "????",
  year =         "1975",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:12 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122175900279",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Book{Masser:1975:EFT,
  author =       "D. W. Masser",
  title =        "Elliptic Functions and Transcendence",
  volume =       "437",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "112 (est.)",
  year =         "1975",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0069432",
  ISBN =         "3-540-07136-9 (print), 3-540-37410-8 (e-book)",
  ISBN-13 =      "978-3-540-07136-5 (print), 978-3-540-37410-7
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  LCCN =         "QA3 .L28 no. 437",
  MRclass =      "11J81 (14K22; 33E05; 11G15; 11J17; 11-02)",
  bibdate =      "Tue May 6 14:52:13 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1975.bib",
  series =       ser-LECT-NOTES-MATH,
  URL =          "http://link.springer.com/book/10.1007/BFb0069432;
                 http://www.springerlink.com/content/978-3-540-37410-7",
  ZMnumber =     "0312.10023",
  acknowledgement = ack-nhfb,
  series-URL =   "http://link.springer.com/bookseries/304",
}

@Article{Midy:1975:ICG,
  author =       "P. Midy",
  title =        "An improved calculation of the general elliptic
                 integral of the second kind in the neighbourhood of $ x
                 = 0 $",
  journal =      j-NUM-MATH,
  volume =       "25",
  number =       "1",
  pages =        "99--101",
  month =        mar,
  year =         "1975",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 16:12:48 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation)",
  corpsource =   "Centre de Calcul Paris Sud Informatique, Univ. Paris
                 XI, Orsay, France",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "elliptic integral; integration; Landen transformation;
                 second kind",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Miller:1975:CCN,
  author =       "Webb Miller",
  key =          "Miller",
  title =        "Computational Complexity and Numerical Stability",
  journal =      j-SIAM-J-COMPUT,
  volume =       "4",
  number =       "2",
  pages =        "97--107",
  month =        jun,
  year =         "1975",
  CODEN =        "SMJCAT",
  DOI =          "https://doi.org/10.1137/0204009",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  bibdate =      "Mon Nov 29 10:58:08 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/4/2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjcomput.bib;
                 Parallel/Multi.bib; Theory/Matrix.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
  keywords =     "complexity; number of multiplications to evaluate a
                 polynomial; numerical analysis; rounding error",
}

@TechReport{Morris:1975:LRS,
  author =       "Robert Morris",
  title =        "A Library of Reference Standard Mathematical
                 Subroutines",
  type =         "Technical Memorandum",
  number =       "1074 (TM 75-1271-6)",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  pages =        "??",
  day =          "1",
  month =        may,
  year =         "1975",
  bibdate =      "Tue Jun 06 08:07:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  abstract =     "This memo describes a set of mathematical library
                 functions to use arbitrary accuracy. Relevant error
                 analysis and subroutines listings are given.",
  acknowledgement = ack-nhfb,
  author-dates = "Robert Morris (25 July 1932--26 June 2011)",
}

@Article{Ng:1975:CCM,
  author =       "Edward W. Ng",
  title =        "A Comparison of Computational Methods and Algorithms
                 for the Complex Gamma Function",
  journal =      j-TOMS,
  volume =       "1",
  number =       "1",
  pages =        "56--70",
  month =        mar,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355626.355635",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "52 #2148",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "R. H. Bartels",
}

@Article{Oliver:1975:SME,
  author =       "J. Oliver",
  title =        "Stable methods for evaluating the points $ \cos (i \pi
                 / n) $",
  journal =      j-J-INST-MATH-APPL,
  volume =       "16",
  number =       "2",
  pages =        "247--257",
  month =        oct,
  year =         "1975",
  CODEN =        "JMTAA8",
  DOI =          "https://doi.org/10.1093/imamat/16.2.247",
  ISSN =         "0020-2932",
  ISSN-L =       "0020-2932",
  MRclass =      "65D05",
  MRnumber =     "52 #12292 (391471)",
  MRreviewer =   "C. W. Clenshaw",
  bibdate =      "Mon Nov 13 08:14:42 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib",
  ZMnumber =     "0308.65011",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Institute of Mathematics and its
                 Applications",
  journal-URL =  "http://imamat.oxfordjournals.org/content/by/year",
  reviewer-dates = "Charles William Clenshaw (15 March 1926--23
                 September 2004)",
}

@Article{Prince:1975:AAF,
  author =       "P. J. Prince",
  title =        "{Algorithm 498}: {Airy} Functions Using {Chebyshev}
                 Series Approximations",
  journal =      j-TOMS,
  volume =       "1",
  number =       "4",
  pages =        "372--379",
  month =        dec,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355656.355663",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:24:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Razaz:1981:RAF}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: FORTRAN routines of fixed 10D precision for
                 the two Airy functions and their derivatives are
                 given.",
}

@Article{Rudnicki-Bujnowski:1975:EFC,
  author =       "Georges Rudnicki-Bujnowski",
  title =        "Explicit Formulas for {Clebsch--Gordan} Coefficients",
  journal =      j-COMP-PHYS-COMM,
  volume =       "10",
  number =       "4",
  pages =        "245--250",
  month =        oct,
  year =         "1975",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(75)90069-7",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sun Feb 12 14:24:38 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465575900697",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  remark =       "Fullerton: A PL/I-FORMAC procedure is discussed.",
}

@Article{Skovgaard:1975:RAJ,
  author =       "Ove Skovgaard",
  title =        "Remark on ``{Algorithm 332}: {Jacobi} Polynomials''",
  journal =      j-CACM,
  volume =       "18",
  number =       "2",
  pages =        "116--117",
  year =         "1975",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:22:18 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Skovgaard75;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Witte:1968:AAJ}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Skovgaard75",
  remark =       "Fullerton: Modifications to an adjustable-precision
                 FORTRAN routine.",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Skovgaard75",
}

@Article{Skovgaard:1975:RBF,
  author =       "Ove Skovgaard",
  title =        "Remark on ``{Algorithm 236: Bessel Functions of the
                 First Kind [S17]}''",
  journal =      j-TOMS,
  volume =       "1",
  number =       "3",
  pages =        "282--284",
  month =        sep,
  year =         "1975",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:26:43 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Gautschi:1964:AAB}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Temme:1975:NEM,
  author =       "N. M. Temme",
  title =        "On the Numerical Evaluation of the Modified {Bessel}
                 Function of the Third Kind",
  journal =      j-J-COMPUT-PHYS,
  volume =       "19",
  number =       "3",
  pages =        "324--337",
  month =        nov,
  year =         "1975",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(75)90082-0",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sat Oct 30 11:20:31 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Temme:1975:UAE,
  author =       "N. M. Temme",
  title =        "Uniform asymptotic expansions of the incomplete gamma
                 functions and the incomplete beta function",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "132",
  pages =        "1109--1114",
  month =        oct,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Dept. of Appl. Math., Amsterdam, Netherlands",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "asymptotic expansions; asymptotic series;
                 complementary error function; function approximation;
                 incomplete beta function; incomplete gamma functions;
                 uniform",
  treatment =    "T Theoretical or Mathematical",
}

@Book{VanBuren:1975:TAS,
  author =       "A. L. (Arnie Lee) {Van Buren} and others",
  title =        "Tables of Angular Spheroidal Wave Functions",
  publisher =    "Naval Research Laboratory",
  address =      "Washington, DC, USA",
  pages =        "????",
  year =         "1975",
  LCCN =         "QC174.26.W3 T27",
  bibdate =      "Sat Apr 1 14:32:29 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Wave functions; Tables; Spheroidal functions",
  tableofcontents = "v. 1. Prolate, m = O \\
                 v. 2. Oblate, m = O",
}

@TechReport{Warner:1975:PDG,
  author =       "D. D. Warner",
  title =        "A partial derivative generator",
  type =         "Computing Science Technical Report",
  number =       "28",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  year =         "1975",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Theory/auto.diff.bib",
  abstract =     "A precompiler is described which takes a specification
                 of a function as input and produces a Fortran
                 subroutine which will evaluate the component functions
                 and the corresponding Jacobian. Many of the Fortran
                 elementary functions are provided, as well as a
                 facility which allows the user to specify their own
                 differentiation rules.",
  acknowledgement = ack-nhfb,
  keywords =     "differentiation arithmetic; precompiler.",
  referred =     "[Carl86a]; [Hali83a]; [Hill82a]; [Spee80a].",
}

@Article{Assmus:1976:NFS,
  author =       "E. F. {Assmus, Jr.} and H. F. {Mattson, Jr.} and
                 Howard E. Sachar",
  title =        "A New Form of the Square Root Bound",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "30",
  number =       "2",
  pages =        "352--354",
  month =        mar,
  year =         "1976",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classification = "B0250 (Combinatorial mathematics); C1160
                 (Combinatorial mathematics)",
  corpsource =   "Dept. of Math., Lehigh Univ., Bethlehem, PA, USA",
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  keywords =     "combinatorial mathematics; linear codes; square root
                 bound; sufficient combinatorial conditions",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Badhe:1976:NAN,
  author =       "Sahadeo K. Badhe",
  title =        "New approximation of the normal distribution
                 function",
  journal =      j-COMMUN-STAT-SIMUL-COMPUT,
  volume =       "5",
  number =       "4",
  pages =        "173--176",
  year =         "1976",
  CODEN =        "CSSCDB",
  DOI =          "https://doi.org/10.1080/03610917608812017",
  ISSN =         "0361-0918",
  ISSN-L =       "0361-0918",
  bibdate =      "Sat Jan 30 06:32:08 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/communstatsimulcomput1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Simulation and
                 Computation",
  journal-URL =  "http://www.tandfonline.com/loi/lssp20",
}

@Article{Baker:1976:SFB,
  author =       "P. W. Baker",
  title =        "Suggestion for a fast binary sine\slash cosine
                 generator",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "11",
  pages =        "1134--1136",
  month =        nov,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674566",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674566",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "$\cos(x)$; $\sin(x)$; elementary function",
}

@Article{Barnett:1976:MRC,
  author =       "A. R. Barnett",
  title =        "{RCWFF} --- Modification of the Real {Coulomb}
                 Wavefunction Program {RCWFN}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "11",
  number =       "1",
  pages =        "141--142",
  month =        jan # "\slash " # feb,
  year =         "1976",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(76)90045-X",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Oct 29 21:24:02 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Barnett:1976:RMR,
  author =       "A. R. Barnett",
  title =        "{RCWFF} --- Modification of the Real {Coulomb}
                 Wavefunction Program {RCWFN}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "11",
  number =       "1",
  pages =        "141--142",
  month =        jan # "\slash " # feb,
  year =         "1976",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(76)90045-X",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 06:01:19 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/001046557690045X",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  xxtitle =      "{RCWFF} --- a modification of the real {Coulomb}
                 wavefunction program {RCWFN}",
}

@Article{Blagoveshchenskii:1976:MCM,
  author =       "Yu V. Blagoveshchenskii and B. A. Popov and G. S.
                 Tesler",
  title =        "Methods for computing mutually inverse functions",
  journal =      j-CYBER,
  volume =       "11",
  number =       "2",
  pages =        "252--256",
  month =        mar,
  year =         "1976",
  CODEN =        "CYBNAW",
  DOI =          "https://doi.org/10.1007/BF01069867",
  ISSN =         "0011-4235 (print), 2375-0189 (electronic)",
  ISSN-L =       "0011-4235",
  bibdate =      "Tue Jan 24 08:29:23 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/index/10.1007/BF01069867",
  acknowledgement = ack-nhfb,
  fjournal =     "Cybernetics",
  journal-URL =  "http://link.springer.com/journal/10559",
  remark =       "Translated from \booktitle{Kibernetika}, No. 2, pp.
                 69--72, March--April, 1975.",
}

@Article{Blair:1976:RCA,
  author =       "J. M. Blair and C. A. Edwards and J. H. Johnson",
  title =        "Rational {Chebyshev} approximations for the inverse of
                 the error function",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "136",
  pages =        "827--830",
  month =        oct,
  year =         "1976",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Atomic Energy of Canada Ltd., Chalk River Nuclear
                 Lab., Chalk River, Ont., Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Chebyshev approximation; Chebyshev approximations;
                 error function; inverse; rational",
  remark =       "Fullerton: With microfiche supplement.",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Brent:1976:FMP,
  author =       "Richard P. Brent",
  title =        "Fast Multiple-Precision Evaluation of Elementary
                 Functions",
  journal =      j-J-ACM,
  volume =       "23",
  number =       "2",
  pages =        "242--251",
  month =        apr,
  year =         "1976",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321941.321944",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "68A20 (68A10)",
  MRnumber =     "52 \#16111",
  MRreviewer =   "Amnon Barak",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Let $ f(x) $ be one of the usual elementary functions
                 ($ \exp $, $ \log $, $ \artan $, $ \sin $, $ \cosh $,
                 etc.), and let $ M(n) $ be the number of
                 single-precision operations required to multiply
                 $n$-bit integers. It is shown that $ f(x) $ can be
                 evaluated, with relative error $ O(2 - n) $, in $
                 O(M(n)l o g (n)) $ operations as $ n \rightarrow \infty
                 $, for any floating-point number $x$ (with an $n$-bit
                 fraction) in a suitable finite interval. From the
                 Sch{\"o}nhage--Strassen bound on $ M(n) $, it follows
                 that an $n$-bit approximation to $ f(x) $ may be
                 evaluated in $ O(n \log_(n) \log \log (n)) $
                 operations. Special cases include the evaluation of
                 constants such as $ \pi $ $e$, and $ e^\pi $. The
                 algorithms depend on the theory of elliptic integrals,
                 using the arithmetic-geometric mean iteration and
                 ascending Landen transformations.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  classification = "723",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
  keywords =     "computational complexity; computer arithmetic;
                 computer programming",
}

@InProceedings{Brent:1976:MPZ,
  author =       "Richard P. Brent",
  title =        "Multiple-precision zero-finding methods and the
                 complexity of elementary function evaluation",
  crossref =     "Traub:1976:ACC",
  pages =        "151--176",
  year =         "1976",
  MRclass =      "68A20",
  MRnumber =     "54 \#11843",
  MRreviewer =   "Claus-Peter Schnorr",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Buschman:1976:IHF,
  author =       "R. G. Buschman",
  title =        "Inequalities for Hypergeometric Functions",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "134",
  pages =        "303--305",
  month =        apr,
  year =         "1976",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0220 (Mathematical analysis); C1120 (Mathematical
                 analysis)",
  corpsource =   "Dept. of Math. and Statistics, Univ. of Guelph,
                 Guelph, Ont., Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; classical orthogonal polynomials;
                 confluence; dominant diagonal matrix; function;
                 functions; Gauss' hypergeometric; hypergeometric
                 functions; Kummer's hypergeometric function; modified
                 Bessel function; principle",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Davies:1976:IPS,
  author =       "M. Davies and B. Dawson",
  title =        "The incrementation parameter in square root
                 iteration",
  journal =      j-J-INST-MATH-APPL,
  volume =       "17",
  number =       "2",
  pages =        "219--223",
  year =         "1976",
  CODEN =        "JMTAA8",
  ISSN =         "0020-2932",
  MRclass =      "65H05",
  MRnumber =     "55 #9514",
  MRreviewer =   "Luciano Biasini",
  bibdate =      "Fri Apr 5 07:38:01 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0319.65039",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Institute of Mathematics and its
                 Applications",
  journal-URL =  "http://imamat.oxfordjournals.org/content/by/year",
}

@Article{Deuflhard:1976:ASC,
  author =       "P. Deuflhard",
  title =        "On Algorithms for the Summation of Certain Special
                 Functions",
  journal =      j-COMPUTING,
  volume =       "17",
  number =       "1",
  pages =        "37--48",
  month =        mar,
  year =         "1976",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/BF02252258",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:52 MST 2001",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. f{\"u}r Math., Tech. Univ. M{\"u}nchen,
                 M{\"u}nchen, West Germany",
  citedby =      "Fullerton:1980:BEM",
  classification = "723; 921; B0290B; B0290H; C4110; C4140",
  description =  "error analysis; linear algebra",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput (Vienna/NY)",
  keywords =     "algorithms; backward error analysis; computer
                 programming; graph representation; mathematical
                 techniques; special functions; stability; summation",
  remark =       "Fullerton: An extension of Clenshaw's summation method
                 is discussed. Spherical harmonic sums are considered as
                 a special case.",
}

@Article{Eckhardt:1976:RAW,
  author =       "Ulrich Eckhardt",
  title =        "A Rational Approximation to {Weierstrass}' $ \wp
                 $-Function",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "136",
  pages =        "818--826",
  month =        oct,
  year =         "1976",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "A0260 (Numerical approximation and analysis); C4130
                 (Interpolation and function approximation)",
  corpsource =   "Nuclear Res. Center, Central Inst. for Appl. Math.,
                 Julich, West Germany",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "equianharmonic; function approximation; rational
                 approximation; unit period parallelogram; Weierstrass'
                 elliptic function; Weierstrass' p function",
  remark =       "Fullerton: A complex FORTRAN algorithm with accuracy
                 down to $ 10^{-18} $ is given.",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Ellacott:1976:RCA,
  author =       "S. Ellacott and Jack Williams",
  title =        "Rational {Chebyshev} Approximation in the Complex
                 Plane",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "13",
  number =       "3",
  pages =        "310--323",
  month =        jun,
  year =         "1976",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}

@Article{elLozy:1976:RAC,
  author =       "Mohamed el Lozy",
  title =        "Remark on {``Algorithm 299: Chi-Squared Integral
                 [S15]''}",
  journal =      j-TOMS,
  volume =       "2",
  number =       "4",
  pages =        "393--395",
  month =        dec,
  year =         "1976",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Jul 05 16:47:38 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Hill:1967:ACS,Hill:1985:RCS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fettis:1976:CR,
  author =       "Henry E. Fettis",
  title =        "Complex Roots of $ \sin z = a z, \cos z = a z $, and $
                 \cosh z = a z $",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "135",
  pages =        "541--545",
  month =        jul,
  year =         "1976",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0220 (Mathematical analysis); C1120 (Mathematical
                 analysis)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "complex roots; cos z=az; cosh z=az; functional
                 equations; sin z=az",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Fullerton:1976:AEM,
  author =       "L. W. Fullerton and G. A. {Rinker, Jr.}",
  title =        "Accurate and Efficient Methods for the Evaluation of
                 Vacuum-Polarization Potentials of Order {$ Z \alpha $}
                 and {$ Z \alpha^2 $}",
  journal =      j-PHYS-REV-A,
  volume =       "13",
  number =       "3",
  pages =        "1283--1287",
  month =        mar,
  year =         "1976",
  CODEN =        "PLRAAN",
  ISSN =         "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519",
  ISSN-L =       "1050-2947",
  bibdate =      "Sat Oct 30 06:32:26 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Physical Review A (Atomic, Molecular, and Optical
                 Physics)",
  journal-URL =  "http://pra.aps.org/browse",
  remark =       "Fullerton: Nine-figure approximations to $ K_n(x) =
                 \int_1^\infty e^{-x t} t^n (1 / r^3 + 1 / (2 r^5)) (r^2
                 - 1)^{1 / 2} \, d t $ for $ n = 0, 1, 3 $, and $5$.",
}

@Article{Ikebe:1976:CZB,
  author =       "Y. Ikebe",
  title =        "Computing Zeros of {Bessel} and Regular {Coulomb} Wave
                 Functions and of Their Derivatives by Matrix Theoretic
                 Approach --- Practical Accuracy Criteria",
  journal =      j-SIAM-REVIEW,
  volume =       "18",
  number =       "4",
  pages =        "810--810",
  month =        "????",
  year =         "1976",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@Article{Kerridge:1976:YAS,
  author =       "D. F. Kerridge and G. W. Cook",
  title =        "Yet Another Series for the Normal Integral",
  journal =      j-BIOMETRIKA,
  volume =       "63",
  number =       "2",
  pages =        "401--403",
  month =        aug,
  year =         "1976",
  CODEN =        "BIOKAX",
  DOI =          "https://doi.org/10.2307/2335636",
  ISSN =         "0006-3444 (print), 1464-3510 (electronic)",
  ISSN-L =       "0006-3444",
  bibdate =      "Sat Jun 21 14:34:06 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00063444.html;
                 http://www.jstor.org/stable/i315483;
                 https://www.math.utah.edu/pub/tex/bib/biometrika1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2335636",
  acknowledgement = ack-nhfb,
  fjournal =     "Biometrika",
  journal-URL =  "http://www.jstor.org/journals/00063444.html",
}

@Article{Kononova:1976:CEF,
  author =       "N. F. Kononova",
  title =        "The computation of elementary functions by means of
                 polynomial approximations by the method of {V. K.
                 Dzjadik}. ({Russian})",
  journal =      "Vy{\v{c}}isl. Prikl. Mat. (Kiev)",
  volume =       "29",
  pages =        "27--39",
  year =         "1976",
  ISSN =         "0321-4117",
  MRclass =      "151. 65D15",
  MRnumber =     "57 \#18026",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Lentz:1976:GBF,
  author =       "William J. Lentz",
  title =        "Generating {Bessel} Functions in {Mie} Scattering
                 Calculations Using Continued Fractions",
  journal =      j-APPL-OPTICS,
  volume =       "15",
  number =       "3",
  pages =        "668--671",
  month =        mar,
  year =         "1976",
  CODEN =        "APOPAI",
  DOI =          "https://doi.org/10.1364/AO.15.000668",
  ISSN =         "0003-6935",
  bibdate =      "Sat Oct 30 08:41:40 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "A new method of generating the Bessel functions and
                 ratios of Bessel functions necessary for Mie
                 calculations is presented. Accuracy is improved while
                 eliminating the need for extended precision word
                 lengths or large storage capability. The algorithm uses
                 a new technique of evaluating continued fractions that
                 starts at the beginning rather than the tail and has a
                 built-in error check. The continued fraction
                 representations for both spherical Bessel functions and
                 ratios of Bessel functions of consecutive order are
                 presented.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Applied Optics",
  journal-URL =  "http://www.osapublishing.org/ao/browse.cfm",
}

@Article{Luke:1976:CER,
  author =       "Yudell L. Luke",
  title =        "{Chebyshev} expansions and rational approximations",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "2",
  number =       "2",
  pages =        "85--93",
  month =        jun,
  year =         "1976",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:14 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0771050X76900139",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Morris:1976:RDF,
  author =       "Robert Morris",
  title =        "Remark on ``{Algorithm 490}: The Dilogarithm Function
                 of a Real Argument [{S22}]''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "112--112",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355666.355680",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Ginsberg:1975:AAD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Paul:1976:SEF,
  author =       "George Paul and M. Wayne Wilson",
  title =        "Should the Elementary Function Library Be Incorporated
                 Into Computer Instruction Sets?",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "132--142",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pike:1976:RIB,
  author =       "Malcolm C. Pike and Jennie SooHoo and N. E. Bosten",
  title =        "Remark on {``Algorithm 179: Incomplete Beta Ratio
                 [S14]''}",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "207--208",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Jul 05 16:45:39 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Ludwig:1963:AIB,Bosten:1974:RAI}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pomeranz:1976:REC,
  author =       "J. Pomeranz",
  title =        "Remark on ``{Algorithm 487: Exact Cumulative
                 Distribution of the Kolmogorov--Smirnov Statistic for
                 Small Samples [S14]}''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "111--111",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:05 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Pomeranz:1974:AAE}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Redding:1976:CPC,
  author =       "R. W. Redding and W. P. Latham",
  title =        "On the calculation of the parabolic cylinder
                 functions. {II}. {The} function {$ V(a, x) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "20",
  number =       "2",
  pages =        "256--258",
  month =        feb,
  year =         "1976",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(76)90071-1",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:20 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999176900711",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Salamin:1976:CUA,
  author =       "Eugene Salamin",
  title =        "Computation of $ \pi $ Using Arithmetic-Geometric
                 Mean",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "135",
  pages =        "565--570",
  month =        jul,
  year =         "1976",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Charles Stark Draper Lab., Cambridge, MA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "arithmetic geometric mean; convergence; elliptic
                 integrals; error analysis; fast Fourier transform
                 multiplication; function evaluation; Landen's;
                 Legendre's relation; numerical computation of pi;
                 transformation",
  remark =       "Fullerton: A quadratically convergent algorithm.",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@InCollection{Salimov:1976:OCE,
  author =       "F. I. Salimov",
  booktitle =    "Probabilistic methods and cybernetics",
  title =        "The organization of calculations of elementary
                 functions into tables. ({Russian})",
  volume =       "12--13",
  publisher =    "Kazan University",
  address =      "Kazan, USSR",
  pages =        "77--90",
  year =         "1976",
  MRclass =      "65A05",
  MRnumber =     "58 \#31706",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Schett:1976:PTS,
  author =       "Alois Schett",
  title =        "Properties of the {Taylor} series expansion
                 coefficients of the {Jacobian} elliptic functions",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "133",
  pages =        "143--147",
  month =        jan,
  year =         "1976",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290P (Differential equations); C4170 (Differential
                 equations)",
  corpsource =   "CENS, Gif-sur-Yvette, France",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "differential equations; Jacobian elliptic functions;
                 randomisation distributions; series (mathematics);
                 Taylor series expansion",
  remark =       "Fullerton: The first several coefficients are
                 tabulated.",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Schonfelder:1976:PSF,
  author =       "J. L. Schonfelder",
  title =        "The Production of Special Function Routines for a
                 Multi-Machine Library",
  journal =      j-SPE,
  volume =       "6",
  number =       "1",
  pages =        "71--82",
  month =        jan # "\slash " # mar,
  year =         "1976",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat May 31 13:36:16 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  remark =       "Fullerton: The design of transportable routines for
                 the NAG library is discussed.",
}

@Article{Schulten:1976:REC,
  author =       "K. Schulten and R. G. Gordon",
  title =        "Recursive Evaluation of $ 3 j $ and $ 6 j $
                 Coefficients",
  journal =      j-COMP-PHYS-COMM,
  volume =       "11",
  number =       "2",
  pages =        "269--278",
  month =        mar # "\slash " # may,
  year =         "1976",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(76)90058-8",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Oct 30 10:32:44 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Shanks:1976:TER,
  author =       "D. Shanks",
  title =        "Table errata: {``Regular continued fractions for $ \pi
                 $ and $ \gamma $'', (Math. Comp. {\bf 25} (1971), 403);
                 ``Rational approximations to $ \pi $'' (ibid. {\bf 25}
                 (1971), 387--392) by K. Y. Choong, D. E. Daykin and C.
                 R. Rathbone}",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "134",
  pages =        "381--381",
  year =         "1976",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1976-0386215-4",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05 (10-04 10F20)",
  MRnumber =     "0386215 (52 \#7073)",
  bibdate =      "Wed Jan 14 13:22:34 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  URL =          "http://www.ams.org/journals/mcom/1976-30-134/S0025-5718-1976-0386215-4",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "The second paper in the title is actually a review of
                 a report containing table of partial quotients for a
                 simple continued fraction for $ \pi $.",
}

@Article{Sheorey:1976:DCE,
  author =       "V. B. Sheorey",
  title =        "Double {Chebyshev} Expansions for Wave Functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "12",
  number =       "2",
  pages =        "125--134",
  month =        nov,
  year =         "1976",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(76)90061-8",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Oct 30 10:38:43 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465576900618",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Siemieniuch:1976:PCR,
  author =       "J. L. Siemieniuch",
  title =        "Properties of certain rational approximations to $
                 e^{-z} $",
  journal =      j-BIT,
  volume =       "16",
  number =       "2",
  pages =        "172--191",
  month =        jun,
  year =         "1976",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01931369",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:14 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=2&spage=172",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "elefunt; elementary functions",
}

@Article{Stegun:1976:ACM,
  author =       "I. A. Stegun and R. Zucker",
  title =        "Automatic Computing Methods for Special Functions.
                 {Part III}. {The} Sine, Cosine, Exponential Integrals,
                 and Related Functions",
  journal =      j-J-RES-NATL-BUR-STAND-1934,
  volume =       "80B",
  number =       "2",
  pages =        "291--311",
  month =        apr,
  year =         "1976",
  ISSN =         "0091-0635",
  bibdate =      "Sat Oct 30 11:07:19 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Research of the National Bureau of
                 Standards (1934)",
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Fullerton: Adjustable double precision FORTRAN.
                 routines for $ \operatorname {Si} $, $ \operatorname
                 {Ci} $, $ \operatorname {Ei} $, $ \operatorname {Shi}
                 $, and $ \operatorname {Chi} $.",
}

@Article{Temme:1976:NEO,
  author =       "Nico M. Temme",
  title =        "On the numerical evaluation of the ordinary {Bessel}
                 function of the second kind",
  journal =      j-J-COMPUT-PHYS,
  volume =       "21",
  number =       "3",
  pages =        "343--350",
  month =        jul,
  year =         "1976",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(76)90032-2",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:21 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999176900322",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Tugov:1976:MCA,
  author =       "I. I. Tugov and Yu. L. Shitkov",
  title =        "A Method of Calculating the {Appell} Functions $
                 {F}_a(\alpha; \beta, \beta '; \gamma; x, y) $",
  journal =      j-USSR-COMP-MATH-MATH-PHYS,
  volume =       "16",
  number =       "6",
  pages =        "1587--1590",
  year =         "1976",
  CODEN =        "CMMPA9",
  ISSN =         "0041-5553, 0502-9902",
  ISSN-L =       "0041-5553",
  bibdate =      "Sat Oct 30 11:38:05 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "U.S.S.R. Computational Mathematics and Mathematical
                 Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00415553",
  remark =       "Fullerton: [English] translation of Russian-language
                 Zhurnal Vychislitel'noi Matematikii Matemancheskoi
                 Fiziki (1976).",
}

@Article{Alexander:1977:SRR,
  author =       "V. L. Alexander",
  title =        "Square Root Routine",
  journal =      j-IBM-TDB,
  volume =       "20",
  number =       "3",
  pages =        "1222",
  month =        aug,
  year =         "1977",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@Article{Amos:1977:ACS,
  author =       "D. E. Amos and S. L. Daniel and M. K. Weston",
  title =        "{Algorithm 511}: {CDC} 6600 Subroutines {IBESS} and
                 {JBESS} for {Bessel} Functions {$ I_\nu (x) $} and {$
                 J_\nu (x) $}, {$ x \ge 0, \nu \ge 0 $} [{S18}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "93--95",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355727",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 29 15:14:12 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See erratum \cite{Amos:1978:ECS}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Amos:1977:CSI,
  author =       "D. E. Amos and S. L. Daniel and M. K. Weston",
  title =        "{CDC} 6600 Subroutines {IBESS} and {JBESS} for
                 {Bessel} Functions {$ I_\nu (x) $} and {$ J_\nu (x) $},
                 {$ x \ge 0, \nu \ge 0 $}",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "76--92",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355726",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "55 #6781",
  bibdate =      "Tue Sep 06 19:20:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Sven-{\AA}ke Gustafson",
}

@Article{Ardill:1977:BFC,
  author =       "R. W. B. Ardill and K. J. M. Moriarty",
  title =        "The {Bessel} Functions {$ J_0 $} and {$ J_1 $} of
                 Complex Argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "13",
  number =       "1",
  pages =        "17--24",
  month =        may,
  year =         "1977",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(77)90023-6",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Oct 29 21:19:09 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465577900236",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Manual{Arnold:1977:SMF,
  author =       "Mark G. Arnold",
  title =        "{SCELBAL} Mathematical Functions Supplement
                 (8008\slash 8080)",
  organization = "Scelbi Computer Consulting. Inc.",
  address =      "1322 Rear --- Boston Post Road, Milford, CT 0646,
                 USA",
  pages =        "31",
  year =         "1977",
  bibdate =      "Fri Dec 01 16:04:29 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.scelbi.com/files/docs/scelbal/SCELBAL%20Mathematical%20Functions%20Supplement.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Brief description of implementations of cos, sin, exp,
                 log, and atn functions.",
}

@Book{Brezinski:1977:ACA,
  author =       "Claude Brezinski",
  title =        "Acc{\'e}l{\'e}ration de la convergence en analyse
                 num{\'e}rique. ({French}) [{Convergence} acceleration
                 in numerical analysis]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "313",
  year =         "1977",
  ISBN =         "0-387-08241-7, 3-540-08241-7",
  ISBN-13 =      "978-0-387-08241-7, 978-3-540-08241-5",
  LCCN =         "????",
  bibdate =      "Thu Dec 1 10:17:17 MST 2011",
  bibsource =    "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
  language =     "French",
}

@Article{Carlson:1977:EIF,
  author =       "B. C. Carlson",
  title =        "Elliptic Integrals of the First Kind",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "8",
  number =       "2",
  pages =        "231--242",
  month =        "????",
  year =         "1977",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRnumber =     "MR 0430341 (55:3346)",
  bibdate =      "Fri Oct 29 22:03:28 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@Book{Carlson:1977:SFA,
  author =       "Bille Chandler Carlson",
  title =        "Special Functions of Applied Mathematics",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xv + 335",
  year =         "1977",
  ISBN =         "0-12-160150-1",
  ISBN-13 =      "978-0-12-160150-8",
  LCCN =         "QA351 .C32",
  bibdate =      "Fri Jan 22 10:33:57 MST 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special",
}

@Article{Cody:1977:CRF,
  author =       "W. J. Cody and Rose M. Motley and L. Wayne Fullerton",
  title =        "The Computation of Real Fractional Order {Bessel}
                 Functions of the Second Kind",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "232--239",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355747",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 20 18:24:22 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Danilcenko:1977:ETC,
  author =       "L. S. Danil'{\v{c}}enko",
  title =        "An efficient technique for the construction of
                 rational approximations of elementary functions.
                 ({Russian}) Optimization of computations (approximation
                 and minimization of functions)",
  journal =      "Akad. Nauk Ukrain. SSR Inst. Kibernet. Preprint",
  volume =       "18",
  pages =        "17--21",
  year =         "1977",
  MRclass =      "65D15",
  MRnumber =     "80b:65016",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{deAPMartins:1977:DSB,
  author =       "Pedro {de A.P.Martins}",
  title =        "Determination of spherical {Bessel} functions of an
                 order larger than the argument",
  journal =      j-J-COMPUT-PHYS,
  volume =       "25",
  number =       "2",
  pages =        "194--198",
  month =        oct,
  year =         "1977",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(77)90021-3",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:26 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999177900213",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
  xxtitle =      "Determination of spherical {Bessel}'s functions of an
                 order larger than the argument",
}

@Article{Derenzo:1977:AHC,
  author =       "Stephen E. Derenzo",
  title =        "Approximations for Hand Calculators Using Small
                 Integer Coefficients",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "137",
  pages =        "214--222",
  month =        jan,
  year =         "1977",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "B0290D (Functional analysis); B0290F (Interpolation
                 and function approximation); C4120 (Functional
                 analysis); C4130 (Interpolation and function
                 approximation); C7310 (Mathematics computing)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximations; function approximation; function
                 evaluation; hand calculators; programmable calculators;
                 small integer coefficients",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Dijkstra:1977:CFE,
  author =       "D. Dijkstra",
  title =        "A continued fraction expansion for a generalization of
                 {Dawson}'s integral",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "138",
  pages =        "503--510",
  month =        apr,
  year =         "1977",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4110 (Error analysis in numerical methods); C4120
                 (Functional analysis); C4160 (Numerical integration and
                 differentiation)",
  corpsource =   "Dept. of Math., Tech. Univ. Twente, Enschede,
                 Netherlands",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "confluent hypergeometric; continued fraction
                 expansion; Dawson's; error analysis; function; function
                 evaluation; generalization; integral; integration;
                 truncation error",
  remark =       "Fullerton: An expansion for $ F(p, x) = e^{-x^2}
                 \int_0^x e^{t^2} \, d t $ is given.",
  treatment =    "T Theoretical or Mathematical",
}

@TechReport{Dzjadyk:1977:TPA,
  author =       "V. K. Dzjadyk and S. F. Karpenko",
  title =        "Tables of polynomials for the approximate solution of
                 elementary functions. ({Russian})",
  number =       "28",
  institution =  "Akad. Nauk Ukrain. SSR Inst. Mat. Preprint",
  pages =        "28",
  year =         "1977",
  MRclass =      "65A05 (65D20)",
  MRnumber =     "58 \#19016",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@TechReport{Dzyadyk:1977:OPM,
  author =       "V. K. Dzjadyk and Z. V. Zarickaja and S. F. Karpenko
                 and N. F. Kononova",
  title =        "{{\cyr Ob {\`e}ffektivnom priblizhenii mnogochlenami
                 {\`e}lementarnykh funktsi{\u\i}.}} ({Russian})
                 [Efficient approximation by polynomials of elementary
                 functions]",
  type =         "Preprint",
  number =       "IM-77-21",
  institution =  "Akad. Nauk Ukrain. SSR Inst. Mat.",
  address =      "Kiev, USSR",
  pages =        "42",
  year =         "1977",
  MRclass =      "65L99",
  MRnumber =     "57 \#11075",
  MRreviewer =   "B. D. Donevski",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Eckhardt:1977:RAW,
  author =       "Ulrich Eckhardt",
  title =        "A rational approximation to {Weierstrass}' elliptic
                 function. {II}. {The} lemniscatic case",
  journal =      j-COMPUTING,
  volume =       "18",
  number =       "4",
  pages =        "341--349",
  year =         "1977",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:53 MST 2001",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-nhfb,
  affiliation =  "Zentralinst. f{\"u}r Angewandte Math., Julich, West
                 Germany",
  citedby =      "Fullerton:1980:BEM",
  classification = "C4130",
  description =  "function approximation",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "elliptic functions; lemniscatic case; rational
                 approximation; Weierstrass elliptic function",
  remark =       "Fullerton: Weierstrass' function and its derivative
                 are approximated in the complex plane to 16 S.",
}

@Article{Egbert:1977:PCAa,
  author =       "W. E. Egbert",
  title =        "Personal calculator algorithms. {I}. Square roots",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "28",
  number =       "9",
  pages =        "22--23",
  month =        may,
  year =         "1977",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  bibdate =      "Tue Mar 25 14:12:15 MST 1997",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5420 (Mainframes and minicomputers); C7310
                 (Mathematics computing)",
  fjournal =     "Hewlett-Packard Journal: technical information from
                 the laboratories of Hewlett-Packard Company",
  keywords =     "electronic calculators; HP personal calculator; square
                 root algorithm",
  treatment =    "A Application; T Theoretical or Mathematical",
  xxpages =      "22--24",
}

@Article{Ercegovac:1977:GHO,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "A General Hardware-Oriented Method for Evaluation of
                 Functions and Computations in a Digital Computer",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "667--680",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674900",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674900",
  abstract =     "A parallel computational method, amenable for
                 efficient hardware-level implementation, is described.
                 It provides a simple and fast algorithm for the
                 evaluation of polynomials, certain rational functions
                 and arithmetic expressions, solving a class of systems
                 of linear equations, or performing the basic arithmetic
                 operations in a fixed-point number representation
                 system. The time required to perform the computation is
                 of the order of $m$ carry-free addition operations, $m$
                 being the number of digits in the solution. In
                 particular, the method is suitable for fast evaluation
                 of mathematical functions in hardware.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Arithmetic expressions; digital computer arithmetic;
                 E-method; evaluation of real-valued functions;
                 fixed-point representation; hardware-level
                 implementation; integral powers; linear systems;
                 on-line algorithms; parallel computation; polynomials;
                 rational functions; redundant number systems",
}

@TechReport{Fox:1977:PMS,
  author =       "P. A. Fox and A. D. Hall and N. L. Schryer",
  title =        "The {PORT} Mathematical Subroutine Library",
  type =         "Computing Science Technical Report",
  number =       "47",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  pages =        "ii + 50",
  day =          "22",
  month =        mar,
  year =         "1977",
  bibdate =      "Fri Sep 01 09:08:27 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  URL =          "http://history.siam.org/%5C/sup/Fox_bell_subroutine.pdf",
  abstract =     "The development at Bell Laboratories of PORT, a
                 library of portable Fortran programs for numerical
                 computation, is discussed.\par

                 Portability is achieved by careful language
                 specification, together with the key technique of
                 specifying computer classes by means of pre-defined
                 machine constants.\par

                 The library is built around an automatic error-handling
                 facility and a dynamic storage allocation scheme, both
                 of which are implemented portably. These, together with
                 the modular structure of the library, lead to
                 simplified calling sequences and ease of use.",
  acknowledgement = ack-nhfb,
  remark =       "May 1977 revision of version of September 1976.",
  tableofcontents = "Part 1: Description \\
                 Part 2: Utility program listings: \\
                 Machine constants \\
                 Error handling \\
                 Stack allocation",
}

@InProceedings{Fullerton:1977:PSF,
  author =       "L. W. Fullerton",
  title =        "Portable Special Function Routines",
  crossref =     "Cowell:1977:PMS",
  pages =        "452--483",
  year =         "1977",
  bibdate =      "Sat Oct 30 06:40:00 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@Article{Gautschi:1977:ACC,
  author =       "Walter Gautschi",
  title =        "Anomalous convergence of a continued fraction for
                 ratios of {Kummer} functions",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "140",
  pages =        "994--999",
  month =        oct,
  year =         "1977",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C1120 (Mathematical analysis); C4170 (Differential
                 equations)",
  corpsource =   "Dept. of Computer Sci., Purdue Univ., Lafayette, IN,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "apparent; Bessel functions; continued fraction;
                 convergence; differential equations; gamma functions;
                 Kummer functions; wrong limit",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Gautschi:1977:ERI,
  author =       "Walter Gautschi",
  title =        "Evaluation of Repeated Integrals of the Coerror
                 Function",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "240--252",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355748",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 22:26:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: An arbitrary-accuracy method for evaluating
                 $ i^n \erfc (x) $ is given.",
}

@Article{Harris:1977:CAT,
  author =       "F. E. Harris",
  title =        "Convergence acceleration technique for lattice sums
                 arising in electronic-structure studies of crystalline
                 solids",
  journal =      j-J-MATH-PHYS,
  volume =       "18",
  number =       "12",
  pages =        "2377--2381",
  month =        dec,
  year =         "1977",
  CODEN =        "JMAPAQ",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Jan 2 14:59:17 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "A0260 (Numerical approximation and analysis); A6150L
                 (Crystal binding)",
  corpsource =   "Dept. of Chem., Univ. of Hawaii, Honolulu, HI, USA",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "convergence acceleration; convergence of numerical
                 methods; crystalline solids; electronic structure;
                 Laplace transform; Laplace transforms; lattice energy;
                 lattice sums; Poisson's summation formula",
  pubcountry =   "USA",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Henrici:1977:ART,
  author =       "Peter Henrici",
  title =        "{Analytische Rechenverfahren f{\"u}r den
                 Taschenrechner HP-25}. ({German}) [{Analytical}
                 Calculations for the {HP-25} Calculator]",
  publisher =    "Oldenbourg",
  address =      "M{\"u}nchen, West Germany",
  pages =        "280",
  year =         "1977",
  ISBN =         "0-471-02938-6",
  ISBN-13 =      "978-0-471-02938-0",
  LCCN =         "????",
  bibdate =      "Mon Jan 28 08:25:06 MST 2019",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1923--1987",
  language =     "German",
  subject =      "Numerische Mathematik; Programmierung <EDV>;
                 Kleinrechner",
  tableofcontents = "Einleitung / 9 \\
                 Teil I: Zahlentheorie / 13 \\
                 Primfaktorzerlegung / 14 \\
                 Euklidscher Algorithmus / 18 \\
                 Rationale Binomialkoeffizienten / 22 \\
                 Kettenbruchdarstellungen reeller Zahlen / 28 \\
                 Genaue Kettenbruchdarstellungen von quadratischen
                 Irrationalit{\"a}ten / 33 \\
                 Teil II: Iteration / 39 \\
                 Iteration / 40 \\
                 Iteration mit Aitken-Beschleunigung / 45 \\
                 Aitken--Steffensen-Iteration / 50 \\
                 Newton-Iteration f{\"u}r Wurzeln komplexer Zahlen / 55
                 \\
                 Teil III: Polynome / 61 \\
                 Der Horner-Algorithmus 6 / 2 \\
                 Das Newton-Verfahren bei Polynomen / 66 \\
                 Bernoulli-Verfahren: Eine reelle dominante Nullstelle /
                 71 \\
                 Bernoulli-Verfahren: Zwei konjugiert komplexe dominante
                 Nullstellen / 76 \\
                 Der Quotienten--Differenzen-Algorithmus / 82 \\
                 Der Routh-Algorithmus / 87 \\
                 Der Schur--Cohn-Algorithmus I / 92 \\
                 Der Schur--Cohn-Algorithmus II / 97 \\
                 Teil IV: Potenzreihen / 101 \\
                 Reziproke Potenzreihe / 102 \\
                 Potenz einer Potenzreihe / 111 \\
                 Exponentiation einer Potenzreihe / 118 \\
                 Teil V: Integration / 123 \\
                 Numerische Integration mit Schrittverfeinerung / 124
                 \\
                 Der Romberg-Algorithmus / 129 \\
                 Die Planasche Summationsformel / 136 \\
                 Eine Differentialgleichung erster Ordnung: Trapezregel
                 / 143 \\
                 Autonome Differentialgleichung zweiter Ordnung ohne
                 erste Ableitung / 150 \\
                 Lineare Differentialgleichung zweiter Ordnung / 155 \\
                 Teil VI: Spezielle Konstanten und Funktionen / 161 \\
                 Log-Arcsinus-Algorithmus / 162 \\
                 Die Gamma-Funktion / 167 \\
                 Unvollst{\"a}ndige Gamma-Funktion / 174 \\
                 Die Fehlerfunktion / 181 \\
                 Vollst{\"a}ndige elliptische Integrale / 187 \\
                 Besselfunktionen ganzzahliger Ordnung / 191 \\
                 Besselfunktionen beliebiger Ordnung / 196 \\
                 Besselfunktionen: Asymptotische Reihe / 201 \\
                 Die Riemannsche Zetafunktion auf der kritischen Geraden
                 / 207 \\
                 Stichwortverzeichnis / 213",
}

@Book{Higgins:1977:CBP,
  author =       "John Rowland Higgins",
  title =        "Completeness and basis properties of sets of special
                 functions",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "x + 134",
  year =         "1977",
  ISBN =         "0-521-21376-2 (hardcover), 0-521-60488-5 (paperback)",
  ISBN-13 =      "978-0-521-21376-9 (hardcover), 978-0-521-60488-8
                 (paperback)",
  LCCN =         "????",
  bibdate =      "Sat Oct 30 16:52:55 MDT 2010",
  bibsource =    "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hill:1977:AIB,
  author =       "G. W. Hill",
  title =        "{Algorithm 518}: Incomplete {Bessel} Function {$ I_0
                 $}. {The von Mises} Distribution [{S14}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "279--284",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355753",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 24 15:46:06 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: Adjustable-accuracy 50-statement FORTRAN
                 subprogram.",
}

@Article{Hinden:1977:PAR,
  author =       "Harvey J. Hinden",
  title =        "Phi Again: a Relationship Between the Golden Ratio and
                 the Limit of a Ratio of Modified {Bessel} Functions",
  journal =      j-FIB-QUART,
  volume =       "15",
  number =       "2",
  pages =        "112, 152",
  month =        apr,
  year =         "1977",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:17 MDT 2011",
  bibsource =    "http://www.fq.math.ca/15-2.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/15-2/hinden-a.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Ismail:1977:IRC,
  author =       "Mourad E. H. Ismail",
  title =        "Integral representations and complete monotonicity of
                 various quotients of {Bessel} functions",
  journal =      j-CAN-J-MATH,
  volume =       "29",
  number =       "??",
  pages =        "1198--1207",
  month =        "????",
  year =         "1977",
  CODEN =        "CJMAAB",
  DOI =          "https://doi.org/10.4153/CJM-1977-119-5",
  ISSN =         "0008-414X (print), 1496-4279 (electronic)",
  ISSN-L =       "0008-414X",
  bibdate =      "Sat Sep 10 15:38:50 MDT 2011",
  bibsource =    "http://cms.math.ca/cjm/v29/;
                 https://www.math.utah.edu/pub/tex/bib/canjmath1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Canadian Journal of Mathematics = Journal canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cjm/",
}

@Article{Jansen:1977:RLF,
  author =       "J. K. M. Jansen",
  title =        "Remark on ``{Algorithm 259: Legendre Functions for
                 Arguments Larger than One}''",
  journal =      j-TOMS,
  volume =       "3",
  number =       "2",
  pages =        "204--250",
  month =        jun,
  year =         "1977",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:08 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Gautschi:1965:ALF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Book{Luke:1977:ACM,
  author =       "Yudell L. Luke",
  title =        "Algorithms for the Computation of Mathematical
                 Functions",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xiii + 284",
  year =         "1977",
  ISBN =         "0-12-459940-0",
  ISBN-13 =      "978-0-12-459940-6",
  LCCN =         "QA351 .L7961",
  bibdate =      "Wed Dec 15 10:38:19 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface / xi \\
                 1: Basic Formulas / 1 \\
                 1.1 Introduction / 1 \\
                 1.2 The Generalized Hypergeometric Function and the
                 $G$-Function / 1 \\
                 1.3 Expansion of $_pF_q(z)$ and $G^{q - r, 1}_{p + 1,
                 q}(z)$, $r = 0$ or $r = 1$, in Series of Chebyshev
                 Polynomials of the First Kind / 4 \\
                 1.4 Efficient Evaluation of Series of Chebyshev
                 Polynomials / 17 \\
                 1.5 Rational Approximations for Generalized
                 Hypergeometric Functions / 20 \\
                 1.6 The Pad{\'e} Table / 27 \\
                 1.7 Computations of and Checks on Coefficients and
                 Tables / 29 \\
                 1.8 Tables of the Functions $e^{-\zeta}$, and
                 $e^{-\xi}$ / 35 \\
                 2: Identification of Functions / 41 \\
                 2.1 Introduction / 41 \\
                 2.2 The Generalized Hypergeometric Function $_pF_q(z)$
                 / 41 \\
                 2.3 The G-Function / 47 \\
                 2.4 Miscellaneous Functions / 48 \\
                 3: General Remarks on the Algorithms and Programs / 49
                 \\
                 3.1 Introduction / 49 \\
                 3.2 Precision and Complex Arithmetic / 49 \\
                 4: Chebyshev Coefficients for $_2F_1(a.b;c;z)$ / 52 \\
                 5: Coefficients for the Expansion of the Confluent
                 Hypergeometric Function $_1F_1(a;c;z)$ in Ascending
                 Series of Chebyshev Polynomials / 70 \\
                 6: Chebyshev Coefficients for $_0F_1(c;z)$ / 77 \\
                 7: Coefficients for the Expansion of $_1F_2(a;b,c;z)$
                 in Ascending Series of Chebyshev Polynomials / 82 \\
                 8: Coefficients for the Expansion of the Confluent
                 Hypergeometric Functions $U(a;c;z)$ and $_1F_1(a;c;-z)$
                 in Descending Series of Chebyshev Polynomials / 88 \\
                 9: Coefficients for the Expansion of the Functions
                 $G^{m,1}_{1,3}(z^2/4|^1_{a,b,c})$, $m = 3$ or $m = 2$,
                 in Descending Series of Chebyshev Polynomials / 101 \\
                 10: Differential and Integral Properties of Expansions
                 in Series of Chebyshev Polynomials of the First Kind /
                 116 \\
                 11: Expansion of Exponential Type Integrals in Series
                 of Chebyshev Polynomials of the First Kind / 126 \\
                 11.1 Introduction / 126 \\
                 11.2 The Representation for $g(x)$ / 127 \\
                 11.3 The Representation for $G(x)$ / 129 \\
                 11.4 Exponential Type Integrals Involving Logarithms /
                 133 \\
                 11.5 Numerical Examples / 135 \\
                 11.6 Errata / 139 \\
                 12: Conversion of a Power Series into a Series of
                 Chebyshev Polynomials of the First Kind / 154 \\
                 13: Rational Approximations for $_2F_1(a,b;c;-z)$ / 159
                 \\
                 14: Pad{\'e} Approximations for $_2F_1(1,b;c;-z)$ / 174
                 \\
                 15: Rational Approximations for $_1F_1(a;c;-z)$ / 182
                 \\
                 16: Pad{\'e} Approximations for $_1F_1(1;c;-z)$ / 192
                 \\
                 17: Rational Approximations for Bessel Functions of the
                 First Kind / 203 \\
                 18: Pad{\'e} Approximations for $I_{\nu +
                 1}(z)/I_\nu(z)$ / 220 \\
                 19: Evaluation of Bessel Functions of the First Kind by
                 Use of the Backward Recurrence Formula \\
                 19.1 Introduction / 230 \\
                 19.2 Backward Recurrence Schemata for $I_\nu(z)$ and
                 $J_\nu(z)$ / 230 \\
                 19.3 Numerical Examples / 240 \\
                 19.4 Mathematical Description of Programs / 243 \\
                 19.4.1 Evaluation of Functions Related to $I_{m +
                 \nu}(z)$ and $J_{m + \nu}(z)$ / 243 \\
                 19.4.2 Evaluation of Functions Related to $e^{-l}I_{m +
                 \nu}(z)$ / 245 \\
                 20: Rational Approximations for $z^aU(a;1 + a - b;z)$ /
                 252 \\
                 21: Pad{\'e} Approximations for $z U(1;2-b;z)$ / 265
                 \\
                 Appendices \\
                 Bibliography / 280 \\
                 Notation Index / 281 \\
                 Subject Index / 283",
  wrongisbn =    "0-12-459940-6",
}

@Article{Marsaglia:1977:SMG,
  author =       "George Marsaglia",
  title =        "The squeeze method for generating gamma variates",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "3",
  number =       "4",
  pages =        "321--325",
  year =         "1977",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(77)90089-X",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65C10",
  MRnumber =     "58 \#13613",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  ZMnumber =     "0384.65005",
  abstract =     "This paper describes an exact method for computer
                 generation of random variables with a gamma
                 distribution. The method is based on the
                 Wilson--Hilferty transformation and an improvement on
                 the rejection technique. The idea is to ``squeeze'' a
                 target density between two functions, the top one easy
                 to sample from, the bottom one easy to evaluate.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  ZMclass =      "*65C10 Random number generation 60E05 General theory
                 of probability distributions",
}

@Article{McCarthy:1977:OAE,
  author =       "D. P. McCarthy",
  title =        "The optimal algorithm to evaluate $ x^n $ using
                 elementary multiplication methods",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "137",
  pages =        "251--256",
  month =        jan,
  year =         "1977",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4120 (Functional analysis); C4240 (Programming and
                 algorithm theory)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computational complexity; function evaluation; optimal
                 multiplication chains; symbolic algebraic
                 manipulation",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Ng:1977:CAL,
  author =       "E. W. Ng",
  title =        "Computations and Applications of Linear Hypergeometric
                 Transformations",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "3",
  number =       "1",
  pages =        "65--70",
  year =         "1977",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(77)90115-8",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Sat Oct 30 09:27:55 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Linear transformations are well-known in the theory of
                 hypergeometric functions. In this note, it is
                 indicated, both by analyses and by supporting numerical
                 experiments, how these transformations can be applied
                 to the computation of Legendre's functions, the
                 incomplete Beta function, and the variance-ratio
                 probability distribution function. It is shown that a
                 simple transformation can in many cases cause dramatic
                 improvement in computation.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Page:1977:MAC,
  author =       "E. Page",
  title =        "Miscellanea: Approximations to the Cumulative Normal
                 Function and its Inverse for Use on a Pocket
                 Calculator",
  journal =      j-APPL-STAT,
  volume =       "26",
  number =       "1",
  pages =        "75--76",
  year =         "1977",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  bibdate =      "Sat Apr 21 10:21:55 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/as1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}

@Article{Pexton:1977:RTTa,
  author =       "Robert L. Pexton and Arno D. Steiger",
  title =        "Roots of two transcendental equations involving
                 spherical {Bessel} functions",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "139",
  pages =        "752--753",
  month =        jul,
  year =         "1977",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1110 (Algebra)",
  corpsource =   "Univ. of California, Livermore, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; root; spherical Bessel functions;
                 transcendental equations",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Randazzo:1977:DFE,
  author =       "D. J. Randazzo",
  booktitle =    "Numerical analysis ({Proceedings of the Colloquium,
                 Lausanne, 1976})",
  title =        "Data fits with exponential functions",
  volume =       "37",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "77--94",
  year =         "1977",
  ISBN =         "3-7643-0939-3",
  ISBN-13 =      "978-3-7643-0939-8",
  MRclass =      "65D15",
  MRnumber =     "468111",
  MRreviewer =   "C. W. Clenshaw",
  bibdate =      "Mon Nov 13 08:14:42 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Internat. Ser. Numer. Math.",
  acknowledgement = ack-nhfb,
  reviewer-dates = "Charles William Clenshaw (15 March 1926--23
                 September 2004)",
}

@Article{Schett:1977:RFT,
  author =       "Alois Schett",
  title =        "Recurrence formula of the {Taylor} series expansion
                 coefficients of the {Jacobian} elliptic functions",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "140",
  pages =        "1003--1005",
  month =        oct,
  year =         "1977",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C1110 (Algebra)",
  corpsource =   "CENS, Gif-sur-Yvette, France",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "elliptic functions; functions; Jacobian elliptic;
                 peak; recurrence formula; run up; Taylor series
                 expansion coefficients",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Schindler:1977:CCS,
  author =       "Susan Schindler and R. Mirman",
  title =        "The {Clebsch--Gordan} coefficients of {$ S_n $}",
  journal =      j-J-MATH-PHYS,
  volume =       "18",
  number =       "8",
  pages =        "1697--1704",
  month =        aug,
  year =         "1977",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.523470",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Jan 2 14:59:17 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Ordering schemes for the frames and tableaux of $ S_n
                 $ are presented, and some results, expressible in terms
                 of these, are developed. A formula is derived for the
                 sign function on tableaux. A table of the nonzero
                 Clebsch--Gordon coefficients for the ''working
                 triplets'' is given. Methods are described, and a
                 needed table supplied, for finding the other
                 coefficients from the tabulated ones. The values are
                 for $ n = 2, \ldots {}, 6 $, with the coefficients for
                 $ n = 6 $ relegated to PAPS.",
  acknowledgement = ack-nhfb,
  classification = "A0365F (Algebraic methods in quantum theory); A1130L
                 (Other internal and higher symmetries in particle
                 physics)",
  corpsource =   "Baruch Coll., City Univ. of New York, NY, USA",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "$S_n$ group; Clebsch Gordan coefficients;
                 Clebsch--Gordan coefficients; working triplets",
  pubcountry =   "USA",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Schonfelder:1977:PTS,
  author =       "J. L. Schonfelder",
  title =        "The Production and Testing of Special Function
                 Software in the {NAG} Library",
  crossref =     "Cowell:1977:PMS",
  pages =        "425--451",
  year =         "1977",
  bibdate =      "Sat Oct 30 10:24:29 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}

@Article{Sharma:1977:GMA,
  author =       "R. R. Sharma and Bahman Zohuri",
  title =        "A general method for an accurate evaluation of
                 exponential integrals {$ E_1 (x), x > 0 $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "25",
  number =       "2",
  pages =        "199--204",
  month =        oct,
  year =         "1977",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(77)90022-5",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:26 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999177900225",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Verma:1977:CSF,
  author =       "Arun Verma",
  title =        "Certain summation formulae for basic hypergeometric
                 series",
  journal =      j-CAN-MATH-BULL,
  volume =       "20",
  number =       "??",
  pages =        "369--376",
  month =        "????",
  year =         "1977",
  CODEN =        "CMBUA3",
  DOI =          "https://doi.org/10.4153/CMB-1977-055-8",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  bibdate =      "Thu Sep 8 10:04:41 MDT 2011",
  bibsource =    "http://cms.math.ca/cmb/v20/;
                 https://www.math.utah.edu/pub/tex/bib/canmathbull.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Canadian mathematical bulletin = Bulletin canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cmb/",
}

@Article{Amos:1978:ECS,
  author =       "Donald E. Amos",
  title =        "Erratum: ``{Algorithm 511}: {CDC} 6600 Subroutines
                 {IBESS} and {JBESS} for {Bessel} Functions {$ I_\nu (x)
                 $} and {$ J_\nu (x) $}, {$ x \ge 0, \nu \ge 0 $}
                 [{S18}]''",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "411--411",
  month =        dec,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356502.356501",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Amos:1977:ACS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Andrews:1978:EFM,
  author =       "M. Andrews and S. F. McCormick and G. D. Taylor",
  title =        "Evaluation of Functions on Microcomputers: Square
                 Root",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "4",
  number =       "4",
  pages =        "359--367",
  year =         "1978",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Thu Sep 15 18:40:29 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  xxmonth =      "(none)",
}

@Article{Andrews:1978:UEF,
  author =       "M. Andrews and T. Mraz",
  title =        "Unified elementary function generator",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "2",
  number =       "5",
  pages =        "270--273",
  month =        oct,
  year =         "1978",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Thu Sep 1 10:15:39 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessors and Microsystems",
}

@Article{Ardill:1978:SBF,
  author =       "R. W. B. Ardill and K. J. M. Moriarty",
  title =        "Spherical {Bessel} functions $ j_n $ and $ y_n $ of
                 integer order and real argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "14",
  number =       "3--4",
  pages =        "261--265",
  month =        may # "\slash " # jun,
  year =         "1978",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(78)90019-X",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Apr 24 10:35:27 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/001046557890019X",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Benton:1978:CZT,
  author =       "T. C. Benton and H. D. Knoble",
  title =        "Common Zeros of Two {Bessel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "142",
  pages =        "533--535",
  month =        apr,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1110 (Algebra)",
  corpsource =   "Pennsylvania State Univ., University Park, PA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; common zeros; poles and zeros;
                 positive zeros; zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Blair:1978:RCA,
  author =       "J. M. Blair and C. A. Edwards and J. H. Johnson",
  title =        "Rational {Chebyshev} approximations for the {Bickley}
                 functions {$ K i_n(x) $}",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "143",
  pages =        "876--886",
  month =        jul,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Atomic Energy of Canada Ltd., Chalk River, Ont.,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximation; Bessel functions; Bickley functions;
                 Chebyshev approximation; Chebyshev approximations;
                 function; recurrence; relation",
  remark =       "Fullerton: Approximations accurate to 23 digits of
                 repeated integrals of the Bessel function $ K_0 (x) $
                 for $ n = 1, 2, \ldots {}, 10 $.",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Bowman:1978:ASS,
  author =       "K. O. Bowman and L. R. Shenton",
  title =        "Asymptotic series and {Stieltjes} continued fractions
                 for a gamma function ratio",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "4",
  number =       "2",
  pages =        "105--111",
  month =        jun,
  year =         "1978",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:17 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0771050X78900347",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Book{Brezinski:1978:AAC,
  author =       "Claude Brezinski",
  title =        "Algorithmes d'acc{\'e}l{\'e}ration de la convergence:
                 {\'e}tude num{\'e}rique. ({French}) [Algorithms for
                 convergence acceleration: numerical study]",
  publisher =    "{\'E}ditions Technip",
  address =      "Paris, France",
  pages =        "xi + 392",
  year =         "1978",
  ISBN =         "2-7108-0341-0 (paperback)",
  ISBN-13 =      "978-2-7108-0341-6 (paperback)",
  LCCN =         "????",
  bibdate =      "Thu Dec 1 10:20:23 MST 2011",
  bibsource =    "carmin.sudoc.abes.fr:210/ABES-Z39-PUBLIC;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
  language =     "French",
}

@Article{Brezinski:1978:CAS,
  author =       "C. Brezinski",
  title =        "Convergence acceleration of some sequences by the $
                 \epsilon $-algorithm",
  journal =      j-NUM-MATH,
  volume =       "29",
  number =       "2",
  pages =        "173--177",
  month =        jan,
  year =         "1978",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  classification = "C4140 (Linear algebra)",
  corpsource =   "UER d'IEEA-Informatique, Univ. de Lille I, Villeneuve
                 d'Ascq, France",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "acceleration; converge; convergence acceleration;
                 convergence of numerical methods; epsilon-algorithm;
                 sequences",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Brezinski:1978:SCA,
  author =       "C. Brezinski",
  title =        "Survey on convergence acceleration methods in
                 numerical analysis",
  journal =      j-MATH-STUDENT,
  volume =       "46",
  number =       "1",
  pages =        "28--41 (1979)",
  year =         "1978",
  CODEN =        "MTHSBH",
  ISSN =         "0025-5742",
  MRclass =      "65B99",
  MRnumber =     "698176 (84d:65003)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematics Student",
  keywords =     "convergence acceleration",
}

@Article{Chin:1978:DAD,
  author =       "R. C. Y. Chin and G. W. Hedstrom",
  title =        "A dispersion analysis for difference schemes: tables
                 of generalized {Airy} functions",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "144",
  pages =        "1163--1170",
  month =        oct,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation);
                 C4170 (Differential equations)",
  corpsource =   "Univ. of California, Lawrence Livermore Lab.,
                 Livermore, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "artificial viscosity; difference schemes; dispersion
                 analysis; function approximation; functions;
                 generalized Airy; linear hyperbolic equation",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Coleman:1978:RSN,
  author =       "John P. Coleman",
  title =        "Remark on {``Algorithm 49: Spherical Neumann
                 Function''}",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "295--295",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500",
  bibdate =      "Sat Jul 05 16:48:40 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Herndon:1961:ASN}.",
  acknowledgement = ack-nhfb,
  keywords =     "Neumann functions; special functions",
}

@Article{DiDonato:1978:AR,
  author =       "A. R. DiDonato",
  title =        "An Approximation for $ \int^\infty_x e^{-t^2 / 2} t^p
                 d t, x > 0, p $ Real",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "141",
  pages =        "271--275",
  month =        jan,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4160 (Numerical integration and differentiation)",
  corpsource =   "Naval Surface Weapons Center, Dahlgren, VA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "integral approximation; integration; numerical
                 analysis",
  remark =       "Fullerton: Closely related to the complementary
                 incomplete gamma function.",
  treatment =    "A Application; N New Development; T Theoretical or
                 Mathematical",
}

@Article{Drezner:1978:CBN,
  author =       "Z. Drezner",
  title =        "Computation of the Bivariate Normal Integral",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "141",
  pages =        "277--279",
  month =        jan,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation)",
  corpsource =   "Faculty of Business, McMaster Univ., Hamilton, Ont.,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "bivariate normal integral; computation; Gauss
                 quadrature method; integration; numerical analysis",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Dzjadyk:1978:CRP,
  author =       "V. K. Dzjadyk and L. {\=I}. F{\'\i}lozof",
  title =        "The convergence rate of {Pad{\'e}} approximants for
                 some elementary functions. ({Russian})",
  journal =      "Mat. Sb. (N.S.)",
  volume =       "107(149)",
  number =       "3",
  pages =        "347--363, 463",
  year =         "1978",
  ISSN =         "0368-8666",
  MRclass =      "41A21 (30E10 41A25)",
  MRnumber =     "81b:41043",
  MRreviewer =   "B. D. Donevski",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@InProceedings{Ercegovac:1978:LSR,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "An On-Line Square Rooting Algorithm",
  crossref =     "IEEE:1978:PSC",
  pages =        "183--189",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac.pdf",
  abstract =     "An on-line algorithm for computing square roots in a
                 radix 2, normalized floating-point number system with
                 the redundant digit set $ \{ - 1, 0, 1 \} $ is
                 described. The algorithm has on-line delay of one and
                 it is amenable for modular implementation. A systematic
                 approach, used in deriving this algorithm, is presented
                 in detail.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@Book{Feinsilver:1978:SFP,
  author =       "Philip J. (Philip Joel) Feinsilver",
  title =        "Special functions, probability semigroups, and
                 {Hamiltonian} flows",
  volume =       "696",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "vi + 112",
  year =         "1978",
  ISBN =         "0-387-09100-9",
  ISBN-13 =      "978-0-387-09100-6",
  LCCN =         "QA3 .L28 no. 696; QA273",
  bibdate =      "Sat Oct 30 19:22:05 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Lecture notes in mathematics",
  acknowledgement = ack-nhfb,
  subject =      "probabilities; semigroups; functions, special;
                 Hamiltonian systems",
}

@InProceedings{Frankowski:1978:RME,
  author =       "Krzysztof S. Frankowski",
  title =        "A Realistic Model for Error Estimates in the
                 Evaluation of Elementary Functions",
  crossref =     "IEEE:1978:PSC",
  pages =        "70--74",
  year =         "1978",
  MRclass =      "65G05 (65D20)",
  MRnumber =     "80g:65050",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Gautschi:1978:CMB,
  author =       "Walter Gautschi and Josef Slavik",
  title =        "On the computation of modified {Bessel} function
                 ratios",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "143",
  pages =        "865--875",
  month =        jul,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C1120 (Mathematical analysis); C4130 (Interpolation
                 and function approximation)",
  corpsource =   "Dept. of Computer Sci., Purdue Univ., Lafayette, IN,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel; Bessel functions; continued fraction;
                 fraction; function approximation; functions; Gauss'
                 continued; modified Bessel function ratios; Perron's
                 continued fraction",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Gustafson:1978:ATC,
  author =       "S.-{\AA}. Gustafson",
  title =        "Algorithm $ 38 $. {Two} computer codes for convergence
                 acceleration",
  journal =      j-COMPUTING,
  volume =       "21",
  number =       "1",
  pages =        "87--91",
  year =         "1978",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65B10",
  MRnumber =     "83a:65005",
  bibdate =      "Tue Jan 2 17:40:53 MST 2001",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 INSPEC Axiom database (1968--date); MathSciNet
                 database",
  acknowledgement = ack-nhfb,
  affiliation =  "Australian Nat. Univ., Canberra, ACT, Australia",
  classification = "723; C4140",
  description =  "convergence of numerical methods",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "codes, symbolic; convergence acceleration; power
                 series sum",
}

@Article{Gustafson:1978:CAG,
  author =       "S.-{\AA}. Gustafson",
  title =        "Convergence acceleration on a general class of power
                 series",
  journal =      j-COMPUTING,
  volume =       "21",
  number =       "1",
  pages =        "53--69",
  year =         "1978",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65B10 (40A05)",
  MRnumber =     "83m:65005",
  MRreviewer =   "A. M. Cohen",
  bibdate =      "Tue Jan 2 17:40:53 MST 2001",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 INSPEC Axiom database (1968--date); MathSciNet
                 database",
  acknowledgement = ack-nhfb,
  affiliation =  "Australian Nat. Univ., Canberra, ACT, Australia",
  classification = "C4120",
  description =  "convergence of numerical methods; function
                 evaluation",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "algorithms; convergence acceleration; power series",
}

@Article{Hamaker:1978:MAC,
  author =       "Hugo C. Hamaker",
  title =        "Miscellanea: Approximating the Cumulative Normal
                 Distribution and its Inverse",
  journal =      j-APPL-STAT,
  volume =       "27",
  number =       "1",
  pages =        "76--77",
  month =        jan,
  year =         "1978",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  bibdate =      "Sat Apr 21 10:22:12 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/as1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}

@InProceedings{Hull:1978:DFP,
  author =       "T. E. Hull",
  title =        "Desirable Floating-Point Arithmetic and Elementary
                 Functions for Numerical Computation",
  crossref =     "IEEE:1978:PSC",
  pages =        "63--69",
  year =         "1978",
  bibdate =      "Thu Sep 01 12:14:34 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}

@Article{Katholi:1978:CVP,
  author =       "Charles R. Katholi",
  title =        "On the computation of values of the psi function from
                 rapidly converging power series expansions",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "8",
  number =       "1",
  pages =        "25--42",
  year =         "1978",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949657808810245",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Tue Apr 22 09:10:43 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
}

@Article{Ling:1978:EWZ,
  author =       "Chin-Bing Ling",
  title =        "Evaluation of {Weierstrass} Zeta Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "20",
  number =       "1",
  pages =        "183--183",
  month =        "????",
  year =         "1978",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1020017",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:52:48 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/20/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "January 1978",
}

@Article{Morita:1978:CCE,
  author =       "T. Morita",
  title =        "Calculation of the complete elliptic integrals with
                 complex modulus",
  journal =      j-NUM-MATH,
  volume =       "29",
  number =       "2",
  pages =        "233--236",
  month =        jan,
  year =         "1978",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classification = "C4160 (Numerical integration and differentiation)",
  corpsource =   "Dept. of Appl. Sci., Faculty of Engng., Tohoku Univ.,
                 Sendai, Japan",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "complete elliptic integrals; complex modulus;
                 integration",
  remark =       "Fullerton: Addendum to a paper by Morita and
                 Horiguchi.",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Pexton:1978:RTT,
  author =       "Robert L. Pexton and Arno D. Steiger",
  title =        "Roots of two transcendental equations as functions of
                 a continuous real parameter",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "142",
  pages =        "511--518",
  month =        apr,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1110 (Algebra)",
  corpsource =   "Lawrence Livermore Lab., Univ. of California,
                 Livermore, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "continuous real parameter; equations; roots; spherical
                 Bessel functions; transcendental equations",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Preston:1978:NAT,
  author =       "F. S. Preston",
  title =        "A New Algorithm for the Tangent",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "2",
  pages =        "167--167",
  month =        feb,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675052",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:26 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675052",
  abstract =     "A new mathematical algorithm has been developed for
                 the tangent. The form of the equation guarantees that
                 the error is zero at $ 0^\circ $, $ 45^\circ $, and $
                 90^\circ $ corresponding to tangents of $0$, $1$, and
                 infinity. With only one constant the error is brought
                 to zero at two more points and the maximum error is
                 less than one part in $ 3000 $. By adding a second
                 constant, the error is reduced to less than one in $
                 720 \, 000 $. Further terms improve the accuracy
                 geometrically.",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Schindler:1978:GCG,
  author =       "Susan Schindler and R. Mirman",
  title =        "Generation of the {Clebsch-Gordan} coefficients for {$
                 S_n $}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "15",
  number =       "1--2",
  pages =        "131--145",
  month =        sep,
  year =         "1978",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(78)90087-5",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sun Oct 31 09:20:58 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Schmidt:1978:EI,
  author =       "Paul W. Schmidt",
  title =        "Evaluation of the Integral $ \int^\infty_0 \frac {t^{2
                 \alpha - 1} J_\nu (x \sqrt {1 + t^2})(1 + t^2)^{\alpha
                 + \beta - 1}} d t $",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "141",
  pages =        "265--269",
  month =        jan,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290M (Numerical integration and differentiation);
                 C4160 (Numerical integration and differentiation)",
  corpsource =   "Phys. Dept., Univ. of Missouri, Columbia, MO, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "cylinder diameter distribution; first kind Bessel
                 function; integral evaluation; integration; long
                 circular; neutron scattering data; numerical analysis;
                 power series expansions; recurrence; relations",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Schoene:1978:RMI,
  author =       "Andrew Y. Schoene",
  title =        "Remark on ``{Algorithm 435}: Modified Incomplete Gamma
                 Function [{S14}]''",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "296--304",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355791.355803",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Fullerton:1972:MIG}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Schonfelder:1978:CEE,
  author =       "J. L. Schonfelder",
  title =        "{Chebyshev} expansions for the error and related
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "144",
  pages =        "1232--1240",
  month =        oct,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4110 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation)",
  corpsource =   "Computer Centre, Univ. of Birmingham, Birmingham, UK",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximations; Chebyshev approximation; Chebyshev
                 expansions; error analysis; error function; mappings;
                 NAG library",
  remark =       "Fullerton: Approximations for $ \erf (x) $, $ \erfc
                 (x) $, and probability functions $ P(x) $, $ Q(x) $
                 with accuracy down to $ 10^{-30} $.",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Skovgaard:1978:RCE,
  author =       "Ove Skovgaard",
  title =        "Remark on ``{Algorithm 149: Complete Elliptic Integral
                 [S21]}''",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "95--95",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:13 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Merner:1962:AAC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Slepian:1978:PSW,
  author =       "D. Slepian",
  title =        "Prolate Spheroidal Wave Functions, {Fourier} Analysis,
                 and Uncertainty --- {V}: The Discrete Case",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "57",
  number =       "5",
  pages =        "1371--1430",
  month =        may # "--" # jun,
  year =         "1978",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  bibdate =      "Tue Nov 9 11:15:56 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1978/BSTJ.1978.5705.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol57/bstj57-5-1371.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}

@Article{Temme:1978:UAE,
  author =       "N. M. Temme",
  title =        "Uniform asymptotic expansions of confluent
                 hypergeometric functions",
  journal =      j-J-INST-MATH-APPL,
  volume =       "22",
  number =       "2",
  pages =        "215--223",
  year =         "1978",
  CODEN =        "JMTAA8",
  ISSN =         "0020-2932",
  MRclass =      "33A30",
  MRnumber =     "80a:33004",
  MRreviewer =   "F. W. J. Olver",
  bibdate =      "Fri Apr 5 05:48:27 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Institute of Mathematics and its
                 Applications",
  journal-URL =  "http://imamat.oxfordjournals.org/content/by/year",
}

@Article{Alt:1979:SRD,
  author =       "H. Alt",
  title =        "Square Rooting Is as Difficult as Multiplication",
  journal =      j-COMPUTING,
  volume =       "21",
  number =       "3",
  pages =        "221--232",
  month =        sep,
  year =         "1979",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "68C25",
  MRnumber =     "82m:68081",
  bibdate =      "Tue Jan 2 17:40:54 MST 2001",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date); MathSciNet
                 database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Math. \& Information, Univ. of Saarlandes,
                 Saarbrucken, West Germany",
  classification = "723; C5230",
  description =  "digital arithmetic",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "algorithm; computer programming; square rooting",
}

@Article{Ardill:1979:ABF,
  author =       "R. W. B. Ardill and K. J. M. Moriarty",
  title =        "Accurate {Bessel} functions {$ J_n(z) $}, {$ Y_n(z)
                 $}, {$ H_n^{(1)}(z) $} and {$ H_n^{(2)}(z) $} of
                 integer order and complex argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "17",
  number =       "3",
  pages =        "321--336",
  month =        jun,
  year =         "1979",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(79)90060-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Apr 24 10:35:27 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  remark =       "Fullerton: Description of a program with accuracy
                 about $ 10^{-10} $.",
}

@Article{Atkins:1979:FSC,
  author =       "D. E. Atkins",
  title =        "{Fourth Symposium on Computer Arithmetic}: crunching
                 with quality and {LSI}",
  journal =      j-COMPUTER,
  volume =       "12",
  number =       "4",
  pages =        "94--97",
  month =        apr,
  year =         "1979",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Thu Dec 12 07:20:54 MST 1996",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Computer arithmetic problems --- faster computation
                 rates and more efficient representations of real
                 numbers --- are considered in the paper. Floating-point
                 arithmetic standardization, novel implementation of
                 basic arithmetic operators, evaluation of elementary
                 functions --- these are the main considerations of the
                 conference review.",
  acknowledgement = ack-nhfb,
  classification = "722; 723",
  fjournal =     "Computer",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  journalabr =   "Computer",
  keywords =     "computer arithmetic; computer systems, digital; data
                 processing --- data description; mathematical
                 techniques --- digital arithmetic",
}

@Article{Babb:1979:OEC,
  author =       "Stanley E. {Babb, Jr.} and James W. Cafky",
  title =        "Operational evaluation of certain infinite {Bessel}
                 function integrals",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1033--1039",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "44A99",
  MRnumber =     "80e:44002",
  MRreviewer =   "L. Arteaga",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4180 (Integral equations)",
  corpsource =   "Dept. of Phys. and Astron., Univ. of Oklahoma, Norman,
                 OK, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel function integral; integration; numerical
                 methods; Schafheitlin method; trigonometric function;
                 Weber",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Borjesson:1979:SAE,
  author =       "P. B{\"o}rjesson and C.-E. Sundberg",
  title =        "Simple Approximations of the Error Function {$ Q(x) $}
                 for Communications Applications",
  journal =      j-IEEE-TRANS-COMM,
  volume =       "27",
  number =       "3",
  pages =        "639--643",
  month =        mar,
  year =         "1979",
  CODEN =        "IECMBT",
  DOI =          "https://doi.org/10.1109/tcom.1979.1094433",
  ISSN =         "0090-6778 (print), 1558-0857 (electronic)",
  ISSN-L =       "0090-6778",
  bibdate =      "Sat Dec 16 15:29:00 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Communications",
}

@Article{Campbell:1979:BFR,
  author =       "J. B. Campbell",
  title =        "{Bessel} functions {$ J_\nu (x) $} and {$ Y_\nu (x) $}
                 of real order and real argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "18",
  number =       "1",
  pages =        "133--142",
  month =        sep,
  year =         "1979",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(79)90030-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 06:01:26 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465579900304",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Carlson:1979:CEI,
  author =       "B. C. Carlson",
  title =        "Computing elliptic integrals by duplication",
  journal =      j-NUM-MATH,
  volume =       "33",
  number =       "1",
  pages =        "1--16",
  month =        mar,
  year =         "1979",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65D20",
  MRnumber =     "80h:65008",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Logarithms, arctangents, and elliptic integrals of all
                 three kinds (including complete integrals) are
                 evaluated numerically by successive applications of the
                 duplication theorem. When the convergence is improved
                 by including a fixed number of terms of Taylor's
                 series, the error ultimately decreases by a factor of
                 4096 in each cycle of iteration. Except for Cauchy
                 principal values there is no separation of cases
                 according to the values of the variables, and no
                 serious cancellations occur if the variables are real
                 and nonnegative. Only rational operations and square
                 roots are required. An appendix contains a recurrence
                 relation and two new representations (in terms of
                 elementary symmetric functions and power sums) for
                 $R$-polynomials, as well as an upper bound for the
                 error made in truncating the Taylor series of an
                 $R$-function.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classification = "C4180 (Integral equations)",
  corpsource =   "Dept. of Math. and Phys., Iowa Univ., Ames, IA, USA",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "convergence; duplication theory; elliptic integral;
                 integration; numerical methods; R-polynomial; Taylor
                 series",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Cole:1979:EI,
  author =       "R. J. Cole and C. Pescatore",
  title =        "Evaluation of the Integral $ \int_0^\infty t^n \exp (
                 - t^2 - x / t) \, d t $",
  journal =      j-J-COMPUT-PHYS,
  volume =       "32",
  number =       "2",
  pages =        "280--287",
  month =        aug,
  year =         "1979",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(79)90135-9",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:34 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999179901359",
  abstract =     "The main purpose of this paper is to provide a unified
                 approach to the treatment of linear recurrence
                 relations for single or pairs of order statistics.
                 Suppose such a relation has been proved in the simplest
                 case when $ X_1, \ldots {}, X_n $ are independent
                 variates having an arbitrary absolutely continuous
                 distribution. It is pointed out that the same relation
                 continues to hold when the $X$'s are exchangeable,
                 whether continuous or not. As has recently become well
                 known, further generalizations are possible when the
                 $X$'s have any joint distribution. Attention is also
                 drawn to a useful nonlinear recurrence relation due to
                 Boncelet (1987).",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Conde:1979:Z,
  author =       "S. Conde and Shyam L. Kalla",
  title =        "The $ \nu $-zeros of {$ J_{- \nu }(x) $}",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "145",
  pages =        "423--426",
  month =        jan,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20",
  MRnumber =     "80b:65021",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4170 (Differential equations); C4190 (Other numerical
                 methods)",
  corpsource =   "Facultad de Ingenieria, Univ. del Zulia, Maracaibo,
                 Venezuela",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel function; boundary value; boundary-value
                 problems; J/sub -v/(x); partial differential equations;
                 poles and zeros; problems; transforms; v-zeros",
  remark =       "Fullerton: With a microfiche supplement.",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Delic:1979:CSS,
  author =       "G. Delic",
  title =        "{Chebyshev} series for the spherical {Bessel} function
                 $ j_l(r) $",
  journal =      j-COMP-PHYS-COMM,
  volume =       "18",
  number =       "1",
  pages =        "73--86",
  month =        sep,
  year =         "1979",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(79)90025-0",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 06:01:26 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465579900250",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Divgi:1979:CUB,
  author =       "D. R. Divgi",
  title =        "Calculation of Univariate and Bivariate Normal
                 Probability Functions",
  journal =      j-ANN-STAT,
  volume =       "7",
  number =       "4",
  pages =        "903--910",
  month =        jul,
  year =         "1979",
  CODEN =        "ASTSC7",
  DOI =          "https://doi.org/10.1214/aos/1176344739",
  ISSN =         "0090-5364 (print), 2168-8966 (electronic)",
  ISSN-L =       "0090-5364",
  bibdate =      "Wed Jun 4 06:39:50 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annstat1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://projecteuclid.org/euclid.aos/1176344739",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aos/",
}

@Article{Einarsson:1979:BEN,
  author =       "Bo Einarsson",
  title =        "Bibliography on the evaluation of numerical software",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "5",
  number =       "2",
  pages =        "145--159",
  month =        jun,
  year =         "1979",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0771-050X(79)90011-1",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Thu Oct 28 17:14:49 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This bibliography on the evaluation of numerical
                 software has been written at the request of the IFIP
                 Working Group on Numerical Software (IFIP WG 2.5), and
                 is divided into nine different sections. Within each
                 section the references are given in alphabetical order
                 by the first author. The aim of the bibliography is to
                 be useful in the production and evaluation of good
                 software for numerical mathematics.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  tableofcontents = "2. Miscellaneous evaluations \\
                 3. Linear algebra \\
                 4. Optimization and nonlinear equations \\
                 5. Functions \\
                 6. Quadrature \\
                 7. Integral equations \\
                 8. Ordinary differential equations \\
                 9. Partial differential equations",
}

@Article{elLozy:1979:RAS,
  author =       "Mohamed el Lozy",
  title =        "Remark on ``{Algorithm 395: Student's
                 $t$-Distribution}'' and Remark on ``{Algorithm 396:
                 Student's Quantiles [S14]}''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "238--239",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:16 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See
                 \cite{Hill:1970:AASa,Hill:1970:AASb,Hill:1981:RSD,Hill:1985:RCS}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: The algorithms are corrected for computers
                 with anomalously small word lengths (e.g., IBM and
                 Interdata).",
}

@Article{Epstein:1979:STE,
  author =       "H. I. Epstein and B. F. Caviness",
  title =        "A structure theorem for the elementary functions and
                 its application to the identity problem",
  journal =      j-INT-J-COMPUT-INF-SCI,
  volume =       "8",
  number =       "1",
  pages =        "9--37",
  year =         "1979",
  CODEN =        "IJCIAH",
  ISSN =         "0091-7036",
  MRclass =      "12H05 (68C05)",
  MRnumber =     "80k:12032",
  MRreviewer =   "Michael F. Singer",
  bibdate =      "Sat Apr 26 12:45:53 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Computer and Information
                 Sciences",
  journal-URL =  "http://link.springer.com/journal/10766",
}

@Article{Fettis:1979:AEU,
  author =       "Henry E. Fettis",
  title =        "An asymptotic expansion for the upper percentage
                 points of the $ \chi^2 $-distribution",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1059--1064",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "62E20",
  MRnumber =     "80h:62014",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4130 (Interpolation and function approximation)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximation theory; asymptotic expansion; upper
                 percentage point",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Gabutti:1979:HPM,
  author =       "Bruno Gabutti",
  title =        "On high precision methods for computing integrals
                 involving {Bessel} functions",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1049--1057",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D30",
  MRnumber =     "80c:65048",
  MRreviewer =   "K. Jetter",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4180 (Integral equations); C4240 (Programming and
                 algorithm theory)",
  corpsource =   "Istituto di Calcoli Numerici, Univ. di Torino, Torino,
                 Italy",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel function integral; computational complexity;
                 exponential function integral; integration",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Gargantini:1979:NSS,
  author =       "Irene Gargantini",
  title =        "The Numerical Stability of Simultaneous Iterations Via
                 Square-Rooting",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "5",
  number =       "1",
  pages =        "25--31",
  month =        "????",
  year =         "1979",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(81)90136-X",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812218190136X",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Gautschi:1979:AIG,
  author =       "W. Gautschi",
  title =        "{Algorithm 542}: Incomplete Gamma Functions [{S14}]",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "482--489",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355864",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:39:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: FORTRAN routines of adjustable accuracy.",
}

@Article{Gautschi:1979:CPI,
  author =       "Walter Gautschi",
  title =        "A Computational Procedure for Incomplete Gamma
                 Functions",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "466--481",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355863",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:32:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Fullerton: Algorithms for the incomplete gamma
                 function, $ \gamma (a, x) $, the complementary
                 function, $ \Gamma (a, x) $, and Tricomi's form, $
                 \gamma '(a, x) $, are given.",
}

@Article{Glasser:1979:NI,
  author =       "M. L. Glasser",
  title =        "A Note on the Integral $ \int^\infty_0 t^{2 \alpha -
                 1}(1 + t^2)^{1 - \alpha - \beta } {J}_\nu (x \sqrt {1 +
                 t^2}) d t $",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "146",
  pages =        "792--793",
  month =        apr,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A40",
  MRnumber =     "80d:33004",
  MRreviewer =   "T. Erber",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C1120 (Mathematical analysis); C4180 (Integral
                 equations)",
  corpsource =   "Math. and Computer Sci. Dept., Clarkson Coll. of
                 Technol., Potsdam, NY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; hypergeometric series; integral;
                 integral equations",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Haavie:1979:GNT,
  author =       "Tore H{\aa}vie",
  title =        "Generalized {Neville} type extrapolation schemes",
  journal =      j-BIT,
  volume =       "19",
  number =       "2",
  pages =        "204--213",
  month =        jun,
  year =         "1979",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01930850",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65B05 (65D05 65D30)",
  MRnumber =     "80f:65005",
  MRreviewer =   "Siegfried Filippi",
  bibdate =      "Wed Jan 4 18:52:16 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=19&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=19&issue=2&spage=204",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Johnson:1979:RAF,
  author =       "Donald B. Johnson and Webb Miller and Brian Minnihan
                 and Celia Wrathall",
  title =        "Reducibility Among Floating-Point Graphs",
  journal =      j-J-ACM,
  volume =       "26",
  number =       "4",
  pages =        "739--760",
  month =        oct,
  year =         "1979",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65G05",
  MRnumber =     "80i:65045",
  bibdate =      "Fri Dec 08 11:55:10 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The graph-theoretic models of this paper can be used
                 to compare the rounding-error behavior of numerical
                 programs. The models follow the approach, popularized
                 by Wilkinson, of assuming independent rounding errors
                 in each arithmetic operation. Models constructed on
                 this assumption are more tractable than would be the
                 case under more realistic assumptions. There are
                 identified two easily tested conditions on programs
                 which guarantee that error analyses are relatively
                 insensitive to the particular graph model employed. The
                 development has the additional benefit of sometimes
                 providing an elementary proof that one program is
                 comparable in stability to another. Examples of such
                 results are given.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
}

@Article{Kusterer:1979:SEP,
  author =       "Roland Kusterer and Manfred Reimer",
  title =        "Stable Evaluation of Polynomials in Time $ \log n $",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1019--1031",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1979-0528054-X;
                 https://doi.org/10.2307/2006075",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65G05 (68C25)",
  MRnumber =     "80d:65050 (528054)",
  MRreviewer =   "C. W. Clenshaw",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Math. Inst., University of Dortmund, Dortmund, West
                 Germany",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "algorithm; approximation theory; number of
                 multiplications to evaluate a polynomial; polynomials",
  reviewer-dates = "Charles William Clenshaw (15 March 1926--23
                 September 2004)",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Leung:1979:AFE,
  author =       "K. V. Leung and S. S. Ghaderpanah",
  title =        "An application of the finite element approximation
                 method to find the complex zeros of the modified
                 {Bessel} function $ {K}_n(z) $",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "148",
  pages =        "1299--1306",
  month =        oct,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (33-04)",
  MRnumber =     "80e:65024",
  MRreviewer =   "R. P. Boas, Jr.",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4140 (Linear algebra)",
  corpsource =   "Dept. of Computer Sci., Concordia Univ., Montreal,
                 Que., Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel function; complex zeros; finite element
                 analysis; finite element approximation method;
                 iterative optimisation scheme; modified; poles and
                 zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Lindstrom:1979:MSM,
  author =       "F. T. Lindstrom",
  title =        "A Modified $3$-Spline Method for Evaluating the
                 {Euler} Digamma Function",
  journal =      j-TECHNOMETRICS,
  volume =       "21",
  number =       "3",
  pages =        "307--311",
  month =        aug,
  year =         "1979",
  CODEN =        "TCMTA2",
  DOI =          "https://doi.org/10.2307/1267752",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  bibdate =      "Sat Jun 21 13:18:50 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00401706.html;
                 http://www.jstor.org/stable/i254300;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/technometrics1970.bib",
  URL =          "http://www.jstor.org/stable/1267752",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
  journal-URL =  "http://www.jstor.org/journals/00401706.html",
}

@Article{Ling:1979:EWZ,
  author =       "C. B. Ling",
  title =        "Evaluation of {Weierstrass} Zeta Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "21",
  number =       "1",
  pages =        "146--147",
  month =        "????",
  year =         "1979",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1021020",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@Article{Maurone:1979:ABD,
  author =       "Philip A. Maurone and Alain J. Phares",
  title =        "On the asymptotic behavior of the derivatives of
                 {Airy} functions",
  journal =      j-J-MATH-PHYS,
  volume =       "20",
  number =       "11",
  pages =        "2191--2191",
  month =        nov,
  year =         "1979",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.523997",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "33A60",
  MRnumber =     "80j:33014",
  bibdate =      "Sat Oct 29 11:28:40 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1975.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v20/i11/p2191_s1",
  acknowledgement = ack-nhfb,
  classification = "A0230 (Function theory, analysis); A0365D
                 (Functional analytical methods in quantum theory);
                 A1235 (Composite models of particles)",
  corpsource =   "Dept. of Phys., Villanova Univ., Villanova, PA, USA",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "Airy functions; angular momentum theory; asymptotic
                 behavior; derivatives; functional analysis;
                 noniterative functional solution; quantum theory; quark
                 confinement; recursion relation",
  onlinedate =   "29 July 2008",
  pagecount =    "1",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Morris:1979:DFR,
  author =       "Robert Morris",
  title =        "The Dilogarithm Function of a Real Argument",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "146",
  pages =        "778--787",
  month =        apr,
  year =         "1979",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1979-0521291-X",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (33A70)",
  MRnumber =     "80e:65025",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C4240 (Programming and algorithm theory)",
  corpsource =   "Bell Labs., Murray Hill, NJ, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "algorithm theory; dilogarithm function; real
                 argument",
  received =     "22 May 1978",
  remark =       "Fullerton: Relative errors down to $ 10^{-24} $ for $
                 \operatorname {Li}_2 (z) = - \int_0^z \frac {\log (1 -
                 z)z} \, d z $. $ \operatorname {Li}_2 (z) $ is a form
                 of Spence's integral.",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Pexton:1979:DRT,
  author =       "Robert L. Pexton and Arno D. Steiger",
  title =        "Degenerate roots of three transcendental equations
                 involving spherical {Bessel} functions",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1041--1048",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "loose microfiche suppl. 65H10 (65D20)",
  MRnumber =     "80g:65057",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Lawrence Livermore Lab., Univ. of California,
                 Livermore, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "function approximation; spherical Bessel function;
                 transcendental equation",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Phillips:1979:FAC,
  author =       "G. Phillips",
  title =        "A fast approximation to the complementary error
                 function for use in fitting gamma-ray peaks",
  journal =      j-NUCL-INSTR-METH,
  volume =       "164",
  number =       "??",
  pages =        "561--563",
  month =        sep,
  year =         "1979",
  CODEN =        "NUIMAL",
  DOI =          "https://doi.org/10.1016/0029-554X(79)90094-6",
  ISSN =         "0029-554x (print), 1878-3759 (electronic)",
  ISSN-L =       "0029-554X",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://adsabs.harvard.edu/abs/1979NucIM.164..561P",
  abstract =     "A fast approximation to the complementary error
                 function has been programmed and tested for use in the
                 peak-shape function for fitting peaks in gamma-ray
                 spectra. The function was compared for speed and
                 accuracy on the NRL ASC 7 computer to the mathematical
                 library version of the complementary error function.
                 The approximation has resulted in a 50\% time savings
                 in the computer program HYPERMET which was developed at
                 NRL for automatic analysis of gamma-ray spectra from
                 germanium detectors.",
  acknowledgement = ack-nhfb,
  fjournal =     "Nuclear Instruments and Methods",
}

@Article{Risch:1979:APE,
  author =       "Robert H. Risch",
  title =        "Algebraic properties of the elementary functions of
                 analysis",
  journal =      j-AM-J-MATH,
  volume =       "101",
  number =       "4",
  pages =        "743--759",
  year =         "1979",
  CODEN =        "AJMAAN",
  ISSN =         "0002-9327 (print), 1080-6377 (electronic)",
  ISSN-L =       "0002-9327",
  MRclass =      "12H05",
  MRnumber =     "81b:12029",
  MRreviewer =   "J. L. Johnson",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Mathematics",
}

@Article{Schulten:1979:AEC,
  author =       "Z. (or K. ??) Schulten and D. G. M. Anderson and R. G.
                 Gordon",
  title =        "An Algorithm for the Evaluation of the Complex {Airy}
                 Functions",
  journal =      j-J-COMPUT-PHYS,
  volume =       "31",
  number =       "1",
  pages =        "60--75",
  month =        apr,
  year =         "1979",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(79)90062-7",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sat Oct 30 10:34:34 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
  remark =       "Fullerton: Simple formulae over the whole complex
                 plane are presented.",
}

@Article{Smith:1979:ALL,
  author =       "David A. Smith and William F. Ford",
  title =        "Acceleration of Linear and Logarithmic Convergence",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "16",
  number =       "2",
  pages =        "223--240",
  month =        apr,
  year =         "1979",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65B10",
  MRnumber =     "82a:65012",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}

@Article{Takemasa:1979:CFC,
  author =       "T. Takemasa and T. Tamura and H. H. Wolter",
  title =        "{Coulomb} Functions with Complex Angular Momenta",
  journal =      j-COMP-PHYS-COMM,
  volume =       "17",
  number =       "4",
  pages =        "351--355",
  month =        jul # "\slash " # aug,
  year =         "1979",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(79)90097-3",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Oct 30 11:14:02 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  remark =       "Fullerton: Description of program CCOULOM, which works
                 only in the part of the $ (\rho, \eta) $-plane where $
                 \eta^2 \ll \rho $ and $ | \ell |^2 \ll \rho $.",
}

@Article{Temme:1979:AAP,
  author =       "N. M. Temme",
  title =        "An Algorithm with {ALGOL 60} Program for the
                 Computation of the Zeros of Ordinary {Bessel} Functions
                 and those of their Derivatives",
  journal =      j-J-COMPUT-PHYS,
  volume =       "32",
  number =       "2",
  pages =        "270--279",
  month =        aug,
  year =         "1979",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(79)90134-7",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sat Oct 30 11:23:13 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
  remark =       "Fullerton: An adjustable-accuracy 100 line Algol
                 procedure is discussed.",
}

@Article{Temme:1979:AEI,
  author =       "N. M. Temme",
  title =        "The asymptotic expansion of the incomplete gamma
                 functions",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "10",
  number =       "4",
  pages =        "757--766",
  month =        jul,
  year =         "1979",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33A15",
  MRnumber =     "80i:33002",
  MRreviewer =   "E. Rieksti\lfhook n{\v{s}}",
  bibdate =      "Sun Nov 28 19:22:16 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/10/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@Article{Terras:1979:DIG,
  author =       "Riho Terras",
  title =        "The determination of incomplete gamma functions
                 through analytic integration",
  journal =      j-J-COMPUT-PHYS,
  volume =       "31",
  number =       "1",
  pages =        "146--151",
  month =        apr,
  year =         "1979",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(79)90066-4",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 09:15:33 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999179900664",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Thacher:1979:NBR,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "New Backward Recurrences for {Bessel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "146",
  pages =        "744--764",
  month =        apr,
  year =         "1979",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (33A40)",
  MRnumber =     "81b:65019",
  MRreviewer =   "R. G. Langebartel",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "C1120 (Mathematical analysis)",
  corpsource =   "Dept. of Computer Sci., Univ. of Kentucky, Lexington,
                 KY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "backward recurrences; Bessel functions; converges",
  treatment =    "N New Development; T Theoretical or Mathematical",
}

@Article{Brent:1980:SNA,
  author =       "Richard P. Brent and Edwin M. McMillan",
  title =        "Some new algorithms for high-precision computation of
                 {Euler}'s constant",
  journal =      j-MATH-COMPUT,
  volume =       "34",
  number =       "149",
  pages =        "305--312",
  month =        jan,
  year =         "1980",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "10-04 (10A40 68C05)",
  MRnumber =     "82g:10002",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Univ. of California, Berkeley, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; computation; Euler's constant;
                 function evaluation; high precision",
  remark =       "Fullerton: Calculation to 30,100 places is discussed,
                 but only a 3-digit value appears in the paper.",
  treatment =    "N New Development; T Theoretical or Mathematical",
}

@InProceedings{Brent:1980:UAE,
  author =       "R. P. Brent",
  title =        "Unrestricted Algorithms for Elementary and Special
                 Functions",
  crossref =     "Lavington:1980:IPP",
  pages =        "613--619",
  year =         "1980",
  bibdate =      "Thu Sep 01 11:55:31 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://maths-people.anu.edu.au/~brent/pub/pub052.html",
  acknowledgement = ack-nj,
  remark =       "From the author's Web site: Errata for original
                 version:\par Page 615, remove the absolute value signs
                 in equation (13) and the following paragraph (x should
                 be large and positive here).\par

                 Page 616, second half of equation (26): insert a minus
                 sign after the equals sign.\par

                 Page 617, equation (39): delete `` / j ! ''.\par

                 Page 617, equation (42): the assumption ``j < k''
                 should be added. Also, the contour C needs to be
                 enlarged slightly.\par

                 Page 617, left-hand-side of equation (44): replace
                 ``Sj,k'' by ``S2j,k''.\par

                 Page 617, ten lines after equation (44): replace
                 ``O(jn2)'' by ``O(j2n)''.",
}

@Article{Brezinski:1980:GEA,
  author =       "C. Brezinski",
  title =        "A general extrapolation algorithm",
  journal =      j-NUM-MATH,
  volume =       "35",
  number =       "2",
  pages =        "175--187",
  month =        jun,
  year =         "1980",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65B05",
  MRnumber =     "81j:65015",
  MRreviewer =   "L. Fox",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  classification = "C4130 (Interpolation and function approximation)",
  corpsource =   "UER IEEA, Univ. de Lille 1, Villeneuve d'Ascq,
                 France",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "convergence acceleration; extrapolation; extrapolation
                 algorithm; linear extrapolation; rational
                 extrapolation; recursive algorithm; sequence
                 transformations",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Char:1980:SCF,
  author =       "Bruce W. Char",
  title =        "On {Stieltjes}' continued fraction for the gamma
                 function",
  journal =      j-MATH-COMPUT,
  volume =       "34",
  number =       "150",
  pages =        "547--551",
  month =        apr,
  year =         "1980",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05 (65D20)",
  MRnumber =     "81b:65008",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: The first 41 coefficients to 40 digits are
                 given.",
}

@Article{Clenshaw:1980:UAE,
  author =       "C. W. Clenshaw and Frank W. J. Olver",
  title =        "An unrestricted algorithm for the exponential
                 function",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "17",
  number =       "2",
  pages =        "310--331",
  month =        apr,
  year =         "1980",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0717026",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65D20",
  MRnumber =     "567276",
  MRreviewer =   "A. M. Cohen",
  bibdate =      "Sun Nov 12 06:18:24 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "An algorithm is presented for the computation of the
                 exponential function of real argument. There are no
                 restrictions on the range of the argument or on the
                 precision that may be demanded in the results.",
  acknowledgement = ack-nhfb,
  author-dates = "Charles William Clenshaw (15 March 1926--23 September
                 2004); Frank William John Olver (15 December 1924--23
                 April 2013)",
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}

@Book{Cody:1980:SME,
  author =       "William J. {Cody, Jr.} and William Waite",
  title =        "Software Manual for the Elementary Functions",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "x + 269",
  year =         "1980",
  ISBN =         "0-13-822064-6",
  ISBN-13 =      "978-0-13-822064-8",
  LCCN =         "QA331 .C635 1980",
  bibdate =      "Tue Dec 14 23:28:38 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Preface / ix \\
                 1. Introduction / 1 \\
                 2. Preliminaries / 3 \\
                 3. Performance Testing / 11 \\
                 4. SQRT / 17 \\
                 5. ALOG/ALOG10 / 35 \\
                 6. EXP / 60 \\
                 7. POWER (**) / 84 \\
                 8. SIN/COS / 125 \\
                 9. TAN/COT / 150 \\
                 10. ASIN/ACOS / 174 \\
                 11. ATAN/ATAN2 / 194 \\
                 12. SINH/COSH / 217",
  tableofcontents = "Preface / ix \\
                 1. Introduction / 1 \\
                 2. Preliminaries / 3 \\
                 3. Performance Testing / 11 \\
                 4. SQRT / 17 \\
                 a. General Discussion / 17 \\
                 b. Flow Chart for SQRT(X) / 18 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 19 \\
                 d. Implementation Notes, Binary Floating-Point Machines
                 / 23 \\
                 e. Implementation Notes, Non-Binary Floating-Point
                 Machines / 25 \\
                 f. Testing / 28 \\
                 5. ALOG/ALOG10 / 35 \\
                 a. General Discussion / 35 \\
                 b. Flow Chart for ALOG(X)/ALOG10(X) / 37 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 38 \\
                 d. Implementation Notes, Non-Decimal Floating-Point
                 Machines / 42 \\
                 e. Implementation Notes, Decimal Floating-Point
                 Machines / 46 \\
                 f. Testing / 49 \\
                 6. EXP / 60 \\
                 a. General Discussion / 60 \\
                 b. Flow Chart for EXP(X) / 62 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 63 \\
                 d. Implementation Notes, Non-Decimal Floating-Point
                 Machines / 67 \\
                 e. Implementation Notes, Decimal Floating-Point
                 Machines / 71 \\
                 f. Testing / 75 \\
                 7. POWER (**) / 84 \\
                 a. General Discussion / 84 \\
                 b. Flow Chart for POWER(X,Y) / 88 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 90 \\
                 d. Implementation Notes, Non-Decimal Floating-Point
                 Machines / 97 \\
                 e. Implementation Notes, Decimal Floating-Point
                 Machines / 106 \\
                 f. Testing / 113 \\
                 8. SIN/COS / 125 \\
                 a. General Discussion / 125 \\
                 b. Flow Chart for SIN(X)/COS(X) / 127 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 129 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 134 \\
                 e. Testing / 139 \\
                 9. TAN/COT / 150 \\
                 a. General Discussion / 150 \\
                 b. Flow Chart for TAN(X)/COTAN(X) / 152 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 154 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 159 \\
                 e. Testing / 164 \\
                 10. ASIN/ACOS / 174 \\
                 a. General Discuss i on / 174 \\
                 b. Flow Chart for AS IN(X)/ACOS(X) / 176 \\
                 c. Implementation Not es, Non-Decimal Fixed-Point
                 Machines / 177 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 181 \\
                 e. Testing / 185 \\
                 11. ATAN/ATAN2 / 194 \\
                 a. General Discussion / 194 \\
                 b. Flow Chart for ATAN(X)/ATAN2(V,U) / 196 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 198 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 203 \\
                 e. Testing / 207 \\
                 12. SINH/COSH / 217 \\
                 a. General Discussion / 217 \\
                 b. Flow Chart for SINH(X)/COSH(X) / 220 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 221 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 225 \\
                 e. Testing / 229",
}

@Article{Coleman:1980:FSB,
  author =       "J. P. Coleman",
  title =        "A {Fortran} subroutine for the {Bessel} function {$
                 J_n(x) $} of order $0$ to $ 10 $",
  journal =      j-COMP-PHYS-COMM,
  volume =       "21",
  number =       "1",
  pages =        "109--118",
  day =          "1",
  month =        dec,
  year =         "1980",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(80)90080-6",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 06:01:19 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465580900806",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Delahaye:1980:RNA,
  author =       "J. P. Delahaye and B. Germain-Bonne",
  title =        "{R}{\'e}sultats n{\'e}gatifs en acc{\'e}l{\'e}ration
                 de la convergence. ({French}) [{Negative} results in
                 convergence acceleration]",
  journal =      j-NUM-MATH,
  volume =       "35",
  number =       "4",
  pages =        "443--457",
  month =        nov,
  year =         "1980",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65B99 (40A99)",
  MRnumber =     "81k:65007",
  MRreviewer =   "Claude Brezinski",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "C4130 (Interpolation and function approximation);
                 C4240 (Programming and algorithm theory)",
  corpsource =   "Univ. des Sci. et Tech. de Lille I, Villeneuve d'Ascq,
                 France",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "acceleration; algorithm; approximation theory;
                 computational complexity; convergence; convergence
                 acceleration; convergence of numerical methods",
  language =     "French",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Ditkin:1980:CSF,
  author =       "V. A. Ditkin and K. A. Karpov and M. K. Kerimov",
  title =        "The computation of special functions",
  journal =      j-USSR-COMP-MATH-MATH-PHYS,
  volume =       "20",
  number =       "5",
  pages =        "3--12",
  year =         "1980",
  CODEN =        "CMMPA9",
  ISSN =         "0041-5553, 0502-9902",
  ISSN-L =       "0041-5553",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.2.1; G.1.2",
  CRclass =      "G.2.1 Combinatorics; G.2.1 Generating functions; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, DISCRETE MATHEMATICS,
                 Combinatorics, Generating functions; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  fjournal =     "U.S.S.R. Computational Mathematics and Mathematical
                 Physics",
  genterm =      "algorithms; design",
  guideno =      "09092",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00415553",
  journalabr =   "USSR Comput. Math. Math. Phys",
  jrldate =      "1980",
  subject =      "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Eckhardt:1980:AWE,
  author =       "Ulrich Eckhardt",
  title =        "{Algorithm 549}: {Weierstrass}' Elliptic Functions
                 [{S21}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "1",
  pages =        "112--120",
  month =        mar,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355873.355884",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:31:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Weierstrass' elliptic functions",
  remark =       "Fullerton: A complex FORTRAN algorithm with accuracy
                 down to $ 10^{-18} $ is given",
}

@Article{Fransen:1980:HPV,
  author =       "Arne Frans{\'e}n and Staffan Wrigge",
  title =        "High-precision values of the gamma function and of
                 some related coefficients",
  journal =      j-MATH-COMPUT,
  volume =       "34",
  number =       "150",
  pages =        "553--566",
  month =        apr,
  year =         "1980",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05 (65D20)",
  MRnumber =     "81f:65004",
  MRreviewer =   "F. W. J. Olver",
  bibdate =      "Sat Apr 01 10:12:58 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  note =         "See addendum and corrigendum
                 \cite{Fransen:1981:ACH}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 80D values of coefficients in the Taylor
                 series for $ \Gamma^m(s + x) $ are given.",
}

@TechReport{Fullerton:1980:BEM,
  author =       "L. W. Fullerton",
  title =        "A Bibliography on the Evaluation of Mathematical
                 Functions",
  type =         "Technical report",
  number =       "TM 80-1274-4 and CSTR 86",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  month =        sep,
  year =         "1980",
  bibdate =      "Sat Feb 05 17:39:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Gargantini:1980:PSR,
  author =       "Irene Gargantini",
  title =        "Parallel Square-Root Iterations for Multiple Roots",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "6",
  number =       "3",
  pages =        "279--288",
  month =        "????",
  year =         "1980",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122180900358",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
}

@Unpublished{Kahan:1980:SPI,
  author =       "W. Kahan",
  title =        "Software $ \sqrt x $ for the Proposed {IEEE
                 Floating-Point Standard}",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "????",
  day =          "25",
  month =        aug,
  year =         "1980",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
  mynote =       "Dated August 25 1980",
}

@Article{Kasperkovitz:1980:AAM,
  author =       "P. Kasperkovitz",
  title =        "Asymptotic approximations for modified {Bessel}
                 functions",
  journal =      j-J-MATH-PHYS,
  volume =       "21",
  number =       "1",
  pages =        "6--13",
  month =        jan,
  year =         "1980",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.524310",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "33A40",
  MRnumber =     "81a:33012",
  MRreviewer =   "N. Hayek Calil",
  bibdate =      "Sat Oct 29 18:18:22 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1980.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v21/i1/p6_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  onlinedate =   "21 July 2008",
  pagecount =    "8",
}

@Article{Langebartel:1980:FER,
  author =       "R. G. Langebartel",
  title =        "{Fourier} expansions of rational fractions of elliptic
                 integrals and {Jacobian} elliptic functions",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "11",
  number =       "3",
  pages =        "506--513",
  month =        may,
  year =         "1980",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "42A16 (33A25)",
  MRnumber =     "81e:42008",
  MRreviewer =   "R. C. Varma",
  bibdate =      "Sat Dec 5 18:14:13 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@InProceedings{Maksymiv:1980:APT,
  author =       "E. M. Maksymiv",
  booktitle =    "Differentsialnye Uravneniya i ikh Prilozhen",
  title =        "Approximate properties of {Thiele}'s formula in a
                 class of elementary functions. ({Russian})",
  volume =       "141",
  publisher =    "Vestnik L'vov. Politekhn. Inst.",
  address =      "L'vov, USSR",
  pages =        "55--56",
  year =         "1980",
  MRclass =      "119.65D20",
  MRnumber =     "81i:65021",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Moran:1980:CND,
  author =       "P. A. P. Moran",
  title =        "Calculation of the Normal Distribution Function",
  journal =      j-BIOMETRIKA,
  volume =       "67",
  number =       "3",
  pages =        "675--676",
  month =        dec,
  year =         "1980",
  CODEN =        "BIOKAX",
  DOI =          "https://doi.org/10.1093/biomet/67.3.675;
                 https://doi.org/10.2307/2335138",
  ISSN =         "0006-3444 (print), 1464-3510 (electronic)",
  ISSN-L =       "0006-3444",
  MRclass =      "62E30",
  MRnumber =     "601106 (82d:62044)",
  MRreviewer =   "G. P. Bhattacharjee",
  bibdate =      "Sat Jun 21 14:34:26 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00063444.html;
                 http://www.jstor.org/stable/i315495;
                 https://www.math.utah.edu/pub/tex/bib/biometrika1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2335138",
  acknowledgement = ack-nhfb,
  fjournal =     "Biometrika",
  journal-URL =  "http://biomet.oxfordjournals.org/content/by/year;
                 http://www.jstor.org/journals/00063444.html",
}

@Article{OBrien:1980:SBF,
  author =       "D. M. O'Brien",
  title =        "Spherical {Bessel} functions of large order",
  journal =      j-J-COMPUT-PHYS,
  volume =       "36",
  number =       "1",
  pages =        "128--132",
  month =        jun,
  year =         "1980",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(80)90177-1",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:01 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999180901771",
  abstract =     "This note introduces functions $ b_n(x) $, related to
                 spherical Bessel functions $ j_n(x) $ and $ y_n(x) $.
                 They are scaled so that they are bounded functions of
                 $n$ and polynomially bounded functions of $x$, and
                 therefore avoid the problems of underflow and overflow
                 which are so common with Bessel functions. They can be
                 generated from a stable recurrence relation for which
                 starting values are readily computable.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@InProceedings{Olver:1980:UAG,
  author =       "F. W. J. Olver",
  title =        "Unrestricted algorithms for generating elementary
                 functions",
  crossref =     "Alefeld:1980:PSE",
  pages =        "131--140",
  year =         "1980",
  MRclass =      "65G05 (65D15)",
  MRnumber =     "82b:65034",
  MRreviewer =   "John Todd",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Pedersen:1980:HBM,
  author =       "P. W. Pedersen",
  title =        "Hvordan beregner man kvadratroden? \toenglish {How do
                 you calculate the square root?} \endtoenglish",
  journal =      "Elektronik (Denmark)",
  volume =       "??",
  number =       "4",
  pages =        "18--21",
  month =        apr,
  year =         "1980",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Book{Popov:1980:PFD,
  author =       "B. A. Popov and G. S. Tesler",
  title =        "Priblizhenie funktsii dlya tekhnicheskikh prilozhenii.
                 ({Russian}) [{Approximation} of functions for technical
                 applications]",
  publisher =    "Naukova Dumka",
  address =      "Kiev, USSR",
  pages =        "351",
  year =         "1980",
  MRclass =      "65D15 (41-02 65D07)",
  MRnumber =     "602955",
  bibdate =      "Tue Jan 24 08:23:12 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Nauka i tekhnicheskii progress. [Science and technical
                 progress]",
  acknowledgement = ack-nhfb # " and " # ack-mv,
}

@Article{Rengarajan:1980:MFI,
  author =       "S. R. Rengarajan and J. E. Lewis",
  title =        "{Mathieu} Functions of Integral Order and Real
                 Arguments",
  journal =      j-IEEE-TRANS-MICROWAVE-THEORY-TECH,
  volume =       "28",
  number =       "3",
  pages =        "276--277",
  month =        mar,
  year =         "1980",
  CODEN =        "IETMAB",
  DOI =          "https://doi.org/10.1109/TMTT.1980.1130060",
  ISSN =         "0018-9480 (print), 1557-9670 (electronic)",
  ISSN-L =       "0018-9480",
  bibdate =      "Sat Oct 30 10:09:01 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "To compute Mathieu functions, modified Mathieu
                 functions and related parameters for integral orders
                 and real arguments, encountered in wave propagation
                 involving elliptic geometries.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "IEEE transactions on microwave theory and techniques",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=22",
  remark =       "Fullerton: A long FORTRAN program is very briefly
                 described. This work is superior to that of Clemm
                 (1969), because $q$ may be negative.",
}

@Article{Schell:1980:AEU,
  author =       "Hans-Joachim Schell",
  title =        "{Asymptotische Entwicklungen f{\"u}r die
                 unvollst{\"a}ndige Gammafunktion}. ({German})
                 [{Asymptotic} developments for the incomplete gamma
                 function]",
  journal =      "{Wissenschaftliche Zeitschrift der Technischen
                 Hochschule Karl-Marx-Stadt}",
  volume =       "22",
  number =       "5",
  pages =        "477 485",
  month =        "????",
  year =         "1980",
  bibdate =      "Sat Feb 18 15:11:46 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "{Wiss. Schr. Tech. Univ. Karl-Marx-Stadt}",
  keywords =     "incomplete gamma function; uniform asymptotic
                 expansions",
  language =     "German",
}

@Article{Schonfelder:1980:VHA,
  author =       "J. L. Schonfelder",
  title =        "Very high accuracy {Chebyshev} expansions for the
                 basic trigonometric functions",
  journal =      j-MATH-COMPUT,
  volume =       "34",
  number =       "149",
  pages =        "237--244",
  month =        jan,
  year =         "1980",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20",
  MRnumber =     "81f:65016",
  MRreviewer =   "Claude Carasso",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 40D coefficients for the sine, cosine and
                 tangent are given.",
}

@Book{Sneddon:1980:SFM,
  author =       "Ian Naismith Sneddon",
  title =        "Special Functions of Mathematical Physics and
                 Chemistry",
  publisher =    "Longman",
  address =      "London, UK",
  edition =      "Third",
  pages =        "ix + 182",
  year =         "1980",
  ISBN =         "0-582-44396-2 (paperback)",
  ISBN-13 =      "978-0-582-44396-9 (paperback)",
  LCCN =         "QA351 .S64 1980",
  bibdate =      "Sat Oct 30 18:25:01 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Longman mathematical texts",
  acknowledgement = ack-nhfb,
  remark =       "See first edition \cite{Sneddon:1956:SFM} and second
                 edition \cite{Sneddon:1961:SFM}.",
  subject =      "Functions, Special",
}

@InCollection{Tretjakov:1980:PSE,
  author =       "V. A. Tret'jakov",
  booktitle =    "Mathematical analysis and the theory of functions
                 ({Russian})",
  title =        "On the properties of some elementary functions that
                 are defined on the algebra of bicomplex numbers.
                 ({Russian})",
  publisher =    "Moskov. Oblast. Ped. Inst.",
  address =      "Moscow, USSR",
  pages =        "99--106",
  year =         "1980",
  MRclass =      "30G35 (78A35)",
  MRnumber =     "82i:30069",
  MRreviewer =   "Toma V. Tonev",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Tretter:1980:ASA,
  author =       "Marietta J. Tretter and G. W. Walster",
  title =        "Analytic subtraction applied to the incomplete gamma
                 and beta functions",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "1",
  number =       "3",
  pages =        "321--326",
  month =        sep,
  year =         "1980",
  CODEN =        "SIJCD4",
  DOI =          "https://doi.org/10.1137/0901022",
  ISSN =         "0196-5204",
  ISSN-L =       "0196-5204",
  MRclass =      "65D20 (33A15)",
  MRnumber =     "81m:65029",
  MRreviewer =   "Anton Hut'a",
  bibdate =      "Mon Mar 31 09:58:49 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific and Statistical Computing",
  journal-URL =  "http://epubs.siam.org/loi/sjoce3",
  keywords =     "analytic subtraction; continued fraction; incomplete
                 beta function; incomplete gamma function",
  onlinedate =   "September 1980",
}

@PhdThesis{vonGudenberg:1980:EAR,
  author =       "J. Wolff {von Gudenberg}",
  title =        "{Einbettung allgemeiner Rechnerarithmetik in Pascal
                 mittels eines Operatorkonzepts und Implementierung der
                 Standardfunktionen mit optimaler Genauigkeit}
                 \toenglish {Embedding a General Computer Arithmetic in
                 Pascal by Means of an Operator Concept and the
                 Implementation of Elementary Functions with Optimal
                 Accuracy} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  year =         "1980",
  bibdate =      "Sun Oct 25 10:29:29 1998",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}

@Article{Waldecker:1980:NSR,
  author =       "D. E. Waldecker",
  title =        "Nonrestoring Square Root with Simplified Answer
                 Generation",
  journal =      j-IBM-TDB,
  volume =       "22",
  number =       "11",
  pages =        "4807--4808",
  month =        apr,
  year =         "1980",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@Article{Andrews:1981:EFM,
  author =       "M. Andrews and D. Jaeger and S. F. McCormick and G. D.
                 Taylor",
  title =        "Evaluation of Functions on Microcomputers: $ \exp (x)
                 $",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "7",
  number =       "6",
  pages =        "503--508",
  month =        "????",
  year =         "1981",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:21 MST 2017",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122181900341",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
  xxmonth =      "(none)",
}

@Article{Arscott:1981:LBB,
  author =       "F. M. Arscott",
  title =        "The land beyond {Bessel}: a survey of higher special
                 functions",
  journal =      j-LECT-NOTES-MATH,
  volume =       "846",
  pages =        "26--45",
  year =         "1981",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0089822",
  ISBN =         "3-540-10569-7 (print), 3-540-38538-X (e-book)",
  ISBN-13 =      "978-3-540-10569-5 (print), 978-3-540-38538-7
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  bibdate =      "Fri May 9 19:07:31 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1980.bib",
  URL =          "http://link.springer.com/chapter/10.1007/BFb0089822/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0089819",
  book-URL =     "http://www.springerlink.com/content/978-3-540-38538-7",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
}

@Article{Banuelos:1981:PCF,
  author =       "Alicia Ba{\~n}uelos and Ricardo Angel Depine and
                 Roberto Claudio Mancini",
  title =        "A program for computing the {Fermi--Dirac} functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "21",
  number =       "3",
  pages =        "315--322",
  month =        jan,
  year =         "1981",
  CODEN =        "CPHCBZ",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Wed Feb 5 09:02:18 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
                 https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465581900126",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655/",
}

@Article{Baratella:1981:ABF,
  author =       "P. Baratella and M. Garetto and G. Vinardi",
  title =        "Approximation of the {Bessel} function {$ J_\nu (x) $}
                 by numerical integration",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "7",
  number =       "2",
  pages =        "87--91",
  month =        jun,
  year =         "1981",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:21 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0771050X81900401",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Barnett:1981:ARI,
  author =       "A. R. Barnett",
  title =        "An algorithm for regular and irregular {Coulomb} and
                 {Bessel} functions of real order to machine accuracy",
  journal =      j-COMP-PHYS-COMM,
  volume =       "21",
  number =       "3",
  pages =        "297--314",
  month =        jan,
  year =         "1981",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(81)90011-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Apr 24 10:35:27 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "We describe an algorithm to evaluate a wide class of
                 functions and their derivatives, to extreme precision
                 (25--30S) if required, which does not use any function
                 calls other than square root. The functions are the
                 Coulomb functions of positive argument ($ F_\lambda (x,
                 \eta) $, $ G_\lambda (x, \eta) $, $ x > 0 $, $ \eta $,
                 $ \lambda $ real) and hence, as special cases with $
                 \eta = 0 $, the cylindrical Bessel functions ($ J_\mu
                 (x) $, $ Y_\mu (x) $, $ x > 0 $, $ \mu $ real), the
                 spherical Bessel functions ($ i_\lambda (x) $, $
                 y_\lambda (x) $, $ x > 0 $, $ \lambda $ real), Airy
                 functions of negative argument $ \textrm {Ai}( - x) $,
                 $ \textrm {Bi}( - x) $ and others. The present method
                 has a number of attractive features: both the regular
                 and irregular solution are calculated, all others of
                 the functions can be produced from a specified minimum
                 (not necessarily zero) to a specified maximum,
                 functions of a single order can be found without all of
                 the orders from zero, the derivatives of the functions
                 arise naturally in the solution and are readily
                 available, the results are available to different
                 precisions from the same subroutine (in contrast to
                 rational approximation techniques) and the methods can
                 be used for estimating final accuracies. In addition,
                 the sole constant required in the algorithm is $ \pi $,
                 no precalculated arrays of coefficients are needed, and
                 the final accuracy is not dependent on that of other
                 subroutines. The method works most efficiently in the
                 region $ x \approx 0.5 $ to $ x \approx 1000 $ but
                 outside this region the results are still reliable,
                 even though the number of iterations within the
                 subroutine rises. Even in these more asymptotic regions
                 the unchanged algorithm can be used with known accuracy
                 to test other specific subroutines more appropriate to
                 these regions. The algorithm uses the recursion
                 relations satisfied by the Coulomb functions and
                 contains a significant advance over Miller's method for
                 evaluating the ratio of successive minimal solutions ($
                 F_\lambda + 1 / F_\lambda $ ). It relies on the
                 evaluation of two continued fractions and no infinite
                 series is required for normalisation: instead the
                 Wronskian is used.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Bice:1981:AAS,
  author =       "P. K. Bice",
  title =        "Algorithm adds square root to micro's arithmetic
                 capability",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "29",
  number =       "11",
  pages =        "146",
  month =        may,
  year =         "1981",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
}

@Article{Branrers:1981:RAZ,
  author =       "M. Branrers and R. Piessens and M. {De Meue}",
  title =        "Rational approximations for zeros of {Bessel}
                 functions",
  journal =      j-J-COMPUT-PHYS,
  volume =       "42",
  number =       "2",
  pages =        "403--405",
  month =        aug,
  year =         "1981",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(81)90253-9",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:07 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999181902539",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Campbell:1981:BFR,
  author =       "J. B. Campbell",
  title =        "{Bessel} functions {$ I_\nu (z) $} and {$ K_\nu (z) $}
                 of real order and complex argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "24",
  number =       "1",
  pages =        "97--105",
  month =        sep # "\slash " # oct,
  year =         "1981",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(81)90109-0",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:27:59 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465581901090",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Carlson:1981:AAI,
  author =       "B. C. Carlson and Elaine M. Notis",
  title =        "{Algorithm 577}: Algorithms for Incomplete Elliptic
                 Integrals [{S21}]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "398--403",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355970",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 22:58:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "$R$-functions; elliptic integrals; inverse circular
                 functions; inverse hyperbolic functions; logarithms",
}

@Article{Chen:1981:AFD,
  author =       "Gang Chen",
  title =        "An attempt to find the derivatives of elementary
                 functions using the algorithmic language {BCY}.
                 ({Chinese})",
  journal =      "Zhejiang Daxue Xuebao",
  volume =       "3",
  pages =        "141--149",
  year =         "1981",
  MRclass =      "26A09",
  MRnumber =     "714 524",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Davis:1981:EFA,
  author =       "Diane F. Davis",
  title =        "Elementary Functions on an Array Processor",
  crossref =     "IEEE:1981:PIS",
  pages =        "170--178",
  year =         "1981",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Delahaye:1981:ACS,
  author =       "J.-P. Delahaye",
  title =        "Acc{\'e}l{\'e}ration de la convergence des suites dont
                 le rapport des erreurs est born{\'e}. ({French})
                 [{Convergence} acceleration for sequences with bounded
                 error ratios]",
  journal =      j-CALCOLO,
  volume =       "18",
  number =       "2",
  pages =        "1--116",
  year =         "1981",
  CODEN =        "CDABAE",
  DOI =          "https://doi.org/10.1007/BF02576491",
  ISSN =         "0008-0624 (print), 1126-5434 (electronic)",
  ISSN-L =       "0008-0624",
  MRclass =      "65B05",
  MRnumber =     "647821 (83a:65004)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Calcolo",
  journal-URL =  "http://link.springer.com/journal/10092",
  keywords =     "convergence acceleration",
  language =     "{French}",
}

@Article{Drachman:1981:TTH,
  author =       "B. Drachman and C. I. Chuang",
  title =        "A table of two hundred zeros of the derivative of the
                 modified {Bessel} function {$ K_n(z) $} and a graph of
                 their distribution",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "7",
  number =       "3",
  pages =        "167--171",
  month =        sep,
  year =         "1981",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:22 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0771050X81900140",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Farmwald:1981:HBE,
  author =       "P. Michael Farmwald",
  title =        "High Bandwidth Evaluation of Elementary Functions",
  crossref =     "IEEE:1981:PIS",
  pages =        "139--142",
  year =         "1981",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Fettis:1981:TEHb,
  author =       "Henry E. Fettis",
  title =        "Table errata: {{\em Handbook of elliptic integrals for
                 engineers and physicists} [second edition, Springer,
                 New York, 1971 and MR {\bf 43} \#3506] by P. F. Byrd
                 and M. D. Friedman}",
  journal =      j-MATH-COMPUT,
  volume =       "36",
  number =       "153",
  pages =        "317--317",
  month =        jan,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05",
  MRnumber =     "82a:65008a",
  bibdate =      "Sat Apr 12 15:32:35 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Fettis:1981:TETb,
  author =       "Henry E. Fettis",
  title =        "Table errata: {{\em A table of the complete elliptic
                 integral of the first kind for complex values of the
                 modulus, Part I} [Rep. No. ARL 69-0172, Aerospace Res.
                 Lab., Wright--Patterson Air Force Base, Ohio, 1969; MR
                 {\bf 40} \#6725] by Fettis and J. C. Caslin}",
  journal =      j-MATH-COMPUT,
  volume =       "36",
  number =       "153",
  pages =        "318",
  month =        jan,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "318.65A05",
  MRnumber =     "82a:65010",
  bibdate =      "Sat Jan 11 13:29:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Fransen:1981:ACH,
  author =       "Arne Frans{\'e}n",
  title =        "Addendum and corrigendum to: {``High-precision values
                 of the gamma function and of some related
                 coefficients''} {[Math. Comp. {\bf 34} (1980), no. 150,
                 553--566, MR 81f:65004] by Frans{\'e}n and S. Wrigge}",
  journal =      j-MATH-COMPUT,
  volume =       "37",
  number =       "155",
  pages =        "233--235",
  month =        jul,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05 (65D20)",
  MRnumber =     "82m:65002",
  bibdate =      "Sat Apr 01 10:12:58 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  note =         "See \cite{Fransen:1980:HPV}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Fredette:1981:RES,
  author =       "G. Fredette",
  title =        "68000 routine extracts square roots",
  journal =      j-EDN,
  volume =       "26",
  number =       "16",
  pages =        "185--194",
  month =        aug,
  year =         "1981",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@TechReport{Fullerton:1981:FUMa,
  author =       "L. W. Fullerton",
  title =        "{FNLIB} User's Manual Explanatory Table of Contents",
  type =         "Technical report",
  number =       "CSTR 92",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  month =        mar,
  year =         "1981",
  bibdate =      "Sat Feb 05 17:39:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Fullerton:1981:FUMb,
  author =       "L. W. Fullerton",
  title =        "{FNLIB} User's Manual",
  type =         "Technical report",
  number =       "CSTR 95",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  month =        mar,
  year =         "1981",
  bibdate =      "Sat Feb 05 17:39:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Gasper:1981:SFB,
  author =       "George Gasper",
  title =        "Summation Formulas for Basic Hypergeometric Series",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "12",
  number =       "2",
  pages =        "196--200",
  month =        mar,
  year =         "1981",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33A30",
  MRnumber =     "82a:33005",
  MRreviewer =   "L. J. Slater",
  bibdate =      "Sun Nov 28 19:22:39 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/12/2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@Article{Gatto:1981:NEM,
  author =       "M. A. Gatto and J. B. Seery",
  title =        "Numerical evaluation of the modified {Bessel}
                 functions {$I$} and {$K$}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "7",
  number =       "3",
  pages =        "203--209",
  month =        "????",
  year =         "1981",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:20 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122181900808",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
}

@Article{Glasser:1981:CBS,
  author =       "M. L. Glasser",
  title =        "A Class of {Bessel} Summations",
  journal =      j-MATH-COMPUT,
  volume =       "37",
  number =       "156",
  pages =        "499--501",
  month =        oct,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A40 (42A16 44A15)",
  MRnumber =     "82j:33015",
  MRreviewer =   "B. D. Agrawal",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0220 (Mathematical analysis); C1120 (Mathematical
                 analysis)",
  corpsource =   "Dept. of Math. and Computer Sci., Clarkson Coll.,
                 Potsdam, NY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; Bessel summations; infinite series",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Haavie:1981:RUT,
  author =       "Tore H{\aa}vie",
  title =        "Remarks on a unified theory for classical and
                 generalized interpolation and extrapolation",
  journal =      j-BIT,
  volume =       "21",
  number =       "4",
  pages =        "465--474",
  month =        dec,
  year =         "1981",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01932843",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "41A05 (65D05)",
  MRnumber =     "83d:41004",
  MRreviewer =   "G. M{\"u}hlbach",
  bibdate =      "Wed Jan 4 18:52:17 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=21&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=21&issue=4&spage=465",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Hill:1981:RSD,
  author =       "G. W. Hill",
  title =        "Remark on ``{Algorithm 395: Student's
                 $t$-Distribution}''",
  journal =      j-TOMS,
  volume =       "7",
  number =       "2",
  pages =        "247--249",
  month =        jun,
  year =         "1981",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:18 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See
                 \cite{Hill:1970:AASa,Hill:1970:AASb,elLozy:1979:RAS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hill:1981:RSQ,
  author =       "G. W. Hill",
  title =        "Remark on ``{Algorithm 396: Student's
                 $t$-Quantiles}''",
  journal =      j-TOMS,
  volume =       "7",
  number =       "2",
  pages =        "250--251",
  month =        jun,
  year =         "1981",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:19 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Hill:1970:AASb}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hough:1981:API,
  author =       "D. Hough",
  title =        "Application of the proposed {IEEE 754} standard for
                 floating-point arithmetic",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "3",
  pages =        "70--74",
  year =         "1981",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1981.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  annote =       "Various features of the proposed standard provide an
                 especially convenient environment for programming
                 numerical procedures such as the familiar elementary
                 functions.",
  bydate =       "MB",
  byrev =        "Le",
  country =      "USA",
  date =         "14/06/82",
  descriptors =  "Computer arithmetic; floating point; computation
                 structure; method; application; standard",
  enum =         "1418",
  fjournal =     "Computer",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  location =     "RWTH-AC-DFV: Bibl.",
  references =   "10",
  revision =     "21/04/91",
}

@Article{Iserles:1981:ARA,
  author =       "A. Iserles and M. J. D. Powell",
  title =        "On the {$A$}-acceptability of rational approximations
                 that interpolate the exponential function",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "1",
  number =       "3",
  pages =        "241--251",
  month =        jul,
  year =         "1981",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/1.3.241",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65D15 (30E10)",
  MRnumber =     "83a:65015 (641308)",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  author-dates = "Michael James David Powell (29 July 1936--19 April
                 2015)",
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@Article{James:1981:LTS,
  author =       "D. G. James",
  title =        "Linear transformations of the second elementary
                 function",
  journal =      j-LIN-AND-MULT-ALGEBRA,
  volume =       "10",
  number =       "4",
  pages =        "347--349",
  year =         "1981",
  CODEN =        "LNMLAZ",
  ISSN =         "0308-1087 (print), 1563-5139 (electronic)",
  ISSN-L =       "0308-1087",
  MRclass =      "15A69 (10C15)",
  MRnumber =     "83c:15023",
  MRreviewer =   "E. W. Ellers",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear and Multilinear Algebra",
  journal-URL =  "http://www.tandfonline.com/loi/glma20",
}

@Article{Kunz:1981:QZ,
  author =       "W. Kunz",
  title =        "{Quadratwurzel mit dem $ \mu $P Z80} \toenglish
                 {Square Roots with the Z80 Microprocessor}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "7",
  pages =        "109--110",
  year =         "1981",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronik",
}

@Book{Lewin:1981:PAF,
  author =       "Leonard Lewin",
  title =        "Polylogarithms and Associated Functions",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "xvii + 359",
  year =         "1981",
  ISBN =         "0-444-00550-1",
  ISBN-13 =      "978-0-444-00550-2",
  LCCN =         "QA342 .L47",
  bibdate =      "Fri Jun 16 13:56:23 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "22-Jul-1919--13-Aug-2007",
  author-url =   "https://en.wikipedia.org/wiki/Leonard_Lewin_(telecommunications_engineer)",
  remark =       "Lightly revised and retitled edition of
                 \cite{Lewin:1958:DAF}.",
  subject =      "Logarithmic functions",
}

@InCollection{Longman:1981:DCA,
  author =       "I. M. Longman",
  booktitle =    "{Pad{\'e} approximation and its applications,
                 Amsterdam 1980 (Amsterdam, 1980)}",
  title =        "Difficulties of convergence acceleration",
  volume =       "888",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "273--289",
  year =         "1981",
  MRclass =      "65B10",
  MRnumber =     "649102 (83d:65013)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Lecture Notes in Mathematics",
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
}

@Article{Maino:1981:CPC,
  author =       "G. Maino and E. Menapace and A. Ventura",
  title =        "Computation of parabolic cylinder functions by means
                 of a {Tricomi} expansion",
  journal =      j-J-COMPUT-PHYS,
  volume =       "40",
  number =       "2",
  pages =        "294--304",
  month =        apr,
  year =         "1981",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(81)90211-4",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:06 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999181902114",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Markov:1981:ICE,
  author =       "S. M. Markov",
  title =        "On the interval computation of elementary functions",
  journal =      j-C-R-ACAD-BULGARE-SCI,
  volume =       "34",
  number =       "3",
  pages =        "319--322",
  year =         "1981",
  CODEN =        "DBANAD",
  ISSN =         "0366-8681",
  MRclass =      "65G10",
  MRnumber =     "83e:65084",
  MRreviewer =   "David F. Griffiths",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes rendus de l'Acad{\'e}mie bulgare des
                 sciences",
}

@Article{McCullagh:1981:RCS,
  author =       "Peter McCullagh",
  title =        "A rapidly convergent series for computing $ \psi (z) $
                 and its derivatives",
  journal =      j-MATH-COMPUT,
  volume =       "36",
  number =       "153",
  pages =        "247--248",
  month =        jan,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (33A15)",
  MRnumber =     "81m:65028",
  MRreviewer =   "J. Gregor",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2007741",
  acknowledgement = ack-nhfb,
  classcodes =   "C4120 (Functional analysis)",
  corpsource =   "Imperial Coll. of Sci. and Technol., London, UK",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "(mathematics); convergence; function evaluation; log
                 gamma function; poles; poles and zeros; rapidly
                 convergent series; series; series expansion; uniformly
                 convergent",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Moon:1981:AFC,
  author =       "Wooil Moon",
  title =        "{Airy} function with complex arguments",
  journal =      j-COMP-PHYS-COMM,
  volume =       "22",
  number =       "4",
  pages =        "411--417",
  month =        may,
  year =         "1981",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(81)90138-7",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 09:27:06 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465581901387",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@TechReport{Morris:1981:NDL,
  author =       "Alfred H. {Morris, Jr.}",
  title =        "{NSWC\slash DL} Library of Mathematics Subroutines",
  type =         "Report",
  number =       "NSWC/TR-79-338",
  institution =  "Naval Surface Warfare Center",
  address =      "Dahlgren, VA 22448-5000, USA; Silver Spring, MD
                 20903-5000, USA",
  pages =        "235",
  year =         "1981",
  bibdate =      "Tue Jun 13 08:47:19 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran2.bib",
  note =         "See also later editions
                 \cite{Morris:1990:NLM,Morris:1993:NLM}.",
  URL =          "https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/ADA108106.xhtml",
  abstract =     "The NSWC/DL library is a library of general-purpose
                 FORTRAN subroutines that provide a basic computational
                 capability in a variety of mathematical activities.
                 Although intended for use on the CDC 6000 series
                 computers, emphasis has been placed on the
                 transportability of the codes. Subroutines are
                 available in the following areas: Elementary
                 Operations, Geometry, Special Functions, Polynomials,
                 Solutions of Nonlinear Equations, Vectors, Matrices,
                 Sparse Matrices, Eigenvalues and Eigenvectors, Least
                 Squares Solutions of Linear Equations, Optimization,
                 Transforms, Approximation of Functions, Curve Fitting,
                 Surface Fitting over Rectangular Grids, Surface Fitting
                 over Arbitrarily Positioned Data Points, Numerical
                 Integration, Ordinary Differential Equations/Initial
                 Value Problems, and Random Number Generation.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Peng:1981:AES,
  author =       "Hong Peng",
  title =        "Algorithms for extracting square roots and cube
                 roots",
  crossref =     "IEEE:1981:PSC",
  pages =        "121--126",
  year =         "1981",
  bibdate =      "Thu Sep 01 11:37:17 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Peng.pdf",
  abstract =     "This paper describes a kind of algorithms for fast
                 extracting square roots and cube roots, their
                 mathematical proofs, their revised algorithm formulae,
                 and hardware implementation of the square root
                 algorithm. These algorithms may be of no significance
                 for large scale computer with fast division. But I am
                 sure that it is effective and economical to apply these
                 algorithms to the circuit designs of some mini- and
                 microcomputers with general multiplication and
                 division, such as nonrestoring division.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-5",
}

@Article{Razaz:1981:RAF,
  author =       "M. Razaz and J. L. Schonfelder",
  title =        "Remark on ``{Algorithm} 498: {Airy} Functions Using
                 {Chebyshev} Series Approximations''",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "404--405",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355971",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Prince:1975:AAF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Schulten:1981:NAE,
  author =       "Z. Schulten and R. G. Gordon and D. G. M. Anderson",
  title =        "A numerical algorithm for the evaluation of {Weber}
                 parabolic cylinder functions {$ U(a, x) $}, {$ V(a, x)
                 $}, and {$ W(a, \pm x) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "42",
  number =       "2",
  pages =        "213--237",
  month =        aug,
  year =         "1981",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(81)90241-2",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:07 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999181902412",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Shepherd:1981:CA,
  author =       "M. M. Shepherd and J. G. Laframboise",
  title =        "{Chebyshev} Approximation of $ (1 + 2 x) \exp (x^2)
                 \erfc (x) $ in $ 0 \leq x < \infty $",
  journal =      j-MATH-COMPUT,
  volume =       "36",
  number =       "153",
  pages =        "249--253",
  month =        jan,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20",
  MRnumber =     "83c:65029",
  MRreviewer =   "John P. Coleman",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "York Univ., Toronto, Ont., Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "(1+2x)exp(x/sup 2/)erfc x; Chebyshev approximation;
                 Chebyshev expansion; erfc x; single",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Smith:1981:ERA,
  author =       "J. M. Smith and F. W. J. Olver and D. W. Lozier",
  title =        "Extended-Range Arithmetic and Normalized {Legendre}
                 Polynomials",
  journal =      j-TOMS,
  volume =       "7",
  number =       "1",
  pages =        "93--105",
  month =        mar,
  year =         "1981",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65G05)",
  MRnumber =     "83a:65017",
  bibdate =      "Mon Aug 29 22:02:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://doi.acm.org/10.1145/355934.355940",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "angular momentum; extended-range arithmetic; Legendre
                 polynomials; overflow; underflow",
}

@Article{Steinberg:1981:LSE,
  author =       "D. Steinberg and M. Rodeh",
  title =        "A layout for the shuffle-exchange network with {$
                 O(N^2 / \log^{3 / 2N}) $} area",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-30",
  number =       "12",
  pages =        "977--982",
  month =        dec,
  year =         "1981",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1981.1675738",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "C.1.2; G.1.2",
  CRclass =      "C.1.2 Multiple Data Stream Architectures
                 (Multiprocessors); C.1.2 Interconnection architectures;
                 G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Computer Systems Organization, PROCESSOR
                 ARCHITECTURES, Multiple Data Stream Architectures
                 (Multiprocessors), Interconnection architectures;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "IEEE Transactions on Computers",
  genterm =      "design",
  guideno =      "06519",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  jrldate =      "Dec. 1981",
  subject =      "C. Computer Systems Organization; C.1 PROCESSOR
                 ARCHITECTURES; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}

@Article{Steinhardt:1981:ASF,
  author =       "Paul J. Steinhardt and P. Chaudhari",
  title =        "{Airy} stress function for atomic models",
  journal =      j-J-COMPUT-PHYS,
  volume =       "42",
  number =       "2",
  pages =        "266--276",
  month =        aug,
  year =         "1981",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(81)90244-8",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:07 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999181902448",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@InProceedings{Taylor:1981:CHD,
  author =       "George S. Taylor",
  title =        "Compatible hardware for division and square root",
  crossref =     "IEEE:1981:PSC",
  pages =        "127--134",
  year =         "1981",
  bibdate =      "Mon Sep 16 16:30:51 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Taylor.pdf",
  abstract =     "Hardware for radix four division and radix two square
                 root is shared in a processor designed to implement the
                 proposed IEEE floating-point standard. The division
                 hardware looks ahead to find the next quotient digit in
                 parallel with the next partial remainder. An 8-bit ALU
                 estimates the next remainder's leading bits. The
                 quotient digit look-up table is addressed with a
                 truncation of the estimate rather than a truncation of
                 the full partial remainder. The estimation ALU and the
                 look-up table are asymmetric for positive and negative
                 remainders. This asymmetry reduces the width of the ALU
                 and the number of minterms in the logic equations for
                 the look-up table. The square root algorithm obtains
                 the correctly rounded result in about two division
                 times using small extensions to the division
                 hardware.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Temme:1981:ECH,
  author =       "N. M. Temme",
  title =        "On the expansion of confluent hypergeometric functions
                 in terms of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "7",
  number =       "1",
  pages =        "27--32",
  month =        mar,
  year =         "1981",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:21 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0771050X81900048",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Terras:1981:ASI,
  author =       "Riho Terras",
  title =        "Algorithms for some integrals of {Bessel} functions
                 and multivariate {Gaussian} integrals",
  journal =      j-J-COMPUT-PHYS,
  volume =       "41",
  number =       "1",
  pages =        "192--199",
  month =        may,
  year =         "1981",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(81)90087-5",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:06 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999181900875",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Terras:1981:MAI,
  author =       "Riho Terras",
  title =        "A {Miller} algorithm for an incomplete {Bessel}
                 function",
  journal =      j-J-COMPUT-PHYS,
  volume =       "39",
  number =       "1",
  pages =        "233--240",
  month =        jan,
  year =         "1981",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(81)90147-9",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:04 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999181901479",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Vogelius:1981:DRM,
  author =       "M. Vogelius and I. Babuska",
  title =        "On a dimensional reduction method. {II}. {Some}
                 approximation-theoretic results",
  journal =      j-MATH-COMPUT,
  volume =       "37",
  number =       "155",
  pages =        "47--68",
  month =        jul,
  year =         "1981",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2; G.1.7",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.7 Ordinary Differential Equations;
                 G.1.7 Boundary value problems",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Boundary value problems",
  fjournal =     "Mathematics of Computation",
  genterm =      "theory",
  guideno =      "09396",
  journal-URL =  "http://www.ams.org/mcom/",
  jrldate =      "July 1981",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Book{Wimp:1981:STT,
  author =       "Jet Wimp",
  title =        "Sequence Transformations and Their Applications",
  volume =       "154",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xix + 257",
  year =         "1981",
  ISBN =         "0-08-095662-9 (e-book), 0-12-757940-0",
  ISBN-13 =      "978-0-08-095662-6 (e-book), 978-0-12-757940-5",
  LCCN =         "QA292 .W54",
  bibdate =      "Thu Dec 1 11:08:47 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Mathematics in Science and Engineering",
  URL =          "http://public.eblib.com/EBLPublic/PublicView.do?ptiID=453177",
  acknowledgement = ack-nhfb,
  subject =      "Sequences (Mathematics) Transformations (Mathematics)
                 Numerical analysis; Acceleration of convergence",
  tableofcontents = "Front Cover \\
                 Sequence Transformations and Their Applications \\
                 Copyright Page \\
                 Contents \\
                 Preface \\
                 Acknowledgments \\
                 Notation \\
                 Chapter 1. Sequences and Series \\
                 Chapter 2. Linear Transformations \\
                 Chapter 3. Linear Lozenge Methods \\
                 Chapter 4. Optimal Methods and Methods Based on Power
                 Series \\
                 Chapter 5. Nonlinear Lozenges \\
                 Iteration Sequences \\
                 Chapter 6. The Schmidt Transformation \\
                 The e-Algorithm \\
                 Chapter 7. Aitken's $d^2$-Process and Related Methods
                 \\
                 Chapter 8. Lozenge Algorithms and the Theory of
                 Continued Fractions \\
                 Chapter 9. Other Lozenge Algorithms and Nonlinear
                 MethodsChapter 10. The Brezinski--H{\aa}vie
                 ProtocolChapter 11. The Brezinski--H{\aa}vie Protocol
                 and Numerical Quadrature \\
                 Chapter 12. Probabilistic Methods \\
                 Chapter 13. Multiple Sequences \\
                 Appendix \\
                 Bibliography \\
                 Index",
}

@Article{Andrews:1982:MMS,
  author =       "M. Andrews",
  title =        "Mathematical Microprocessor Software: a $ \sqrt (x) $
                 Comparison",
  journal =      j-IEEE-MICRO,
  volume =       "2",
  number =       "3",
  pages =        "63--79",
  month =        may # "\slash " # jun,
  year =         "1982",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1982.290970",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
                 Science Citation Index database (1980--2000)",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation);
                 C6150G (Diagnostic, testing, debugging and evaluating
                 systems)",
  corpsource =   "Colorado State Univ., Fort Collins, CO, USA",
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "16-bit machines; 8-bit machine; accuracy; Chen method;
                 computer testing; Cordic method; direct method;
                 function approximation; hardware; Intel 8080; Newton
                 method; PDP-11/20; software requirements; speed;
                 square-roots",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Armengou:1982:ASQ,
  author =       "Santiago Zarzuela Armengou",
  title =        "About some questions of differential algebra
                 concerning to elementary functions",
  journal =      "Publ. Sec. Mat. Univ. Aut{\`o}noma Barcelona",
  volume =       "26",
  number =       "1",
  pages =        "5--15",
  year =         "1982",
  MRclass =      "12H05",
  MRnumber =     "86i:12009",
  MRreviewer =   "Michael F. Singer",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Barnett:1982:CCB,
  author =       "A. R. Barnett",
  title =        "{COULFG}: {Coulomb} and {Bessel} functions and their
                 derivatives, for real arguments, by {Steed}'s method",
  journal =      j-COMP-PHYS-COMM,
  volume =       "27",
  number =       "2",
  pages =        "147--166",
  month =        aug,
  year =         "1982",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(82)90070-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:28:03 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465582900704",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Barnett:1982:CFE,
  author =       "A. R. Barnett",
  title =        "Continued-fraction evaluation of {Coulomb} functions
                 {$ F_\lambda (\eta, x) $}, {$ G_\lambda (\eta, x) $}
                 and their derivatives",
  journal =      j-J-COMPUT-PHYS,
  volume =       "46",
  number =       "2",
  pages =        "171--188",
  month =        may,
  year =         "1982",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(82)90012-2",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:11 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999182900122",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Barnett:1982:HPE,
  author =       "A. R. Barnett",
  title =        "High-precision evaluation of the regular and irregular
                 {Coulomb} wavefunctions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "8",
  number =       "1",
  pages =        "29--33",
  month =        mar,
  year =         "1982",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:22 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0771050X82900043",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@TechReport{Bazarov:1982:EEF,
  author =       "M. B. Bazarov and Yu. I. Shokin and Z. Kh. Yuldashev",
  title =        "On the Evaluation of Elementary Functions in Interval
                 Analysis (In {Russian})",
  institution =  "Applied Mathematics and Mechanics, Tashkent State
                 Univ.",
  address =      "Tashkent, USSR",
  pages =        "26--31",
  year =         "1982",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-jr # "\slash " # ack-nhfb,
}

@Article{Belevitch:1982:SIT,
  author =       "V. Belevitch and J. Boersma",
  title =        "On {Stieltjes} integral transforms involving {$ \Gamma
                 $}-functions",
  journal =      j-MATH-COMPUT,
  volume =       "38",
  number =       "157",
  pages =        "223--226",
  month =        jan,
  year =         "1982",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "44A15 (33A15 33A45)",
  MRnumber =     "83d:44001",
  MRreviewer =   "V. M. Bhise",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0230 (Integral transforms); C1130 (Integral
                 transforms)",
  corpsource =   "Philips Res Lab., Brussels, Belgium",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Gamma functions; integral transforms; Stieltjes
                 transforms; systematic classification; transforms",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Borwein:1982:MNT,
  author =       "P. B. Borwein",
  title =        "On a method of {Newman} and a theorem of {Bernstein}",
  journal =      j-J-APPROX-THEORY,
  volume =       "34",
  number =       "1",
  pages =        "37--41",
  month =        jan,
  year =         "1982",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory",
  guideno =      "06012",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  jrldate =      "Jan. 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Brezinski:1982:ASG,
  author =       "C. Brezinski",
  title =        "{Algorithm 585}: a Subroutine for the General
                 Interpolation and Extrapolation Problems",
  journal =      j-TOMS,
  volume =       "8",
  number =       "3",
  pages =        "290--301",
  month =        sep,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356004.356008",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:49:19 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; convergence acceleration; extrapolation;
                 interpolation; least squares approximation;
                 Neville--Aitken scheme",
}

@Article{Brezinski:1982:SNC,
  author =       "Claude Brezinski",
  title =        "Some New Convergence Acceleration Methods",
  journal =      j-MATH-COMPUT,
  volume =       "39",
  number =       "159",
  pages =        "133--145",
  month =        jul,
  year =         "1982",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2007624",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65B05",
  MRnumber =     "658218 (83f:65003)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "convergence acceleration",
}

@Article{Burr:1982:CCR,
  author =       "S. A. Burr",
  title =        "Computing cube roots when a fast square root is
                 available",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "8",
  number =       "3",
  pages =        "181--183",
  month =        "????",
  year =         "1982",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(82)90041-4",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:22 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122182900414",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
}

@Book{Carroll:1982:TST,
  author =       "Robert Wayne Carroll",
  title =        "Transmutation, scattering theory, and special
                 functions",
  volume =       "87; 69",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "x + 457",
  year =         "1982",
  ISBN =         "0-444-86426-1 (paperback)",
  ISBN-13 =      "978-0-444-86426-0 (paperback)",
  LCCN =         "QA1 .N86 no. 87; QA329",
  bibdate =      "Sat Oct 30 18:29:29 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "North-Holland mathematics studies",
  acknowledgement = ack-nhfb,
  subject =      "Transmutation operators; Scattering (Mathematics);
                 Inverse problems (Differential equations); Functions,
                 Special",
}

@Article{Chambers:1982:UBF,
  author =       "Ll. G. Chambers",
  title =        "An upper bound for the first zero of {Bessel}
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "38",
  number =       "158",
  pages =        "589--591",
  month =        apr,
  year =         "1982",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A65",
  MRnumber =     "83h:33011",
  MRreviewer =   "S. Ahmed",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@InProceedings{Cody:1982:TTP,
  author =       "W. J. Cody",
  title =        "Transportable test procedures for elementary function
                 software",
  crossref =     "Mulvey:1982:EMP",
  pages =        "236--247",
  year =         "1982",
  bibdate =      "Thu Nov 17 06:39:08 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-wjc,
}

@Article{Crick:1982:IRB,
  author =       "S. E. Crick",
  title =        "Inclusion relations for {Bernstein} quasi-analytic
                 classes",
  journal =      j-J-APPROX-THEORY,
  volume =       "34",
  number =       "4",
  pages =        "375--379",
  month =        apr,
  year =         "1982",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "algorithms; theory",
  guideno =      "07841",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  jrldate =      "April 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Cruz:1982:ZHF,
  author =       "Andr{\'e}s Cruz and Javier Sesma",
  title =        "Zeros of the {Hankel} function of real order and of
                 its derivative",
  journal =      j-MATH-COMPUT,
  volume =       "39",
  number =       "160",
  pages =        "639--645",
  month =        oct,
  year =         "1982",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A40",
  MRnumber =     "83j:33005",
  MRreviewer =   "S. Ahmed",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); B0290F (Interpolation
                 and function approximation); C4120 (Functional
                 analysis); C4130 (Interpolation and function
                 approximation)",
  corpsource =   "Dept. de Fisica Teorica, Univ. de Zaragoza, Zaragoza,
                 Spain",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximation; derivative; evaluation; function
                 approximation; function evaluation; Hankel function;
                 poles and zeros; real order; trajectories; zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Danielopoulos:1982:CEP,
  author =       "S. D. Danielopoulos",
  title =        "On the Cost of Evaluating Polynomials and Their
                 Derivatives",
  journal =      j-COMPUTING,
  volume =       "29",
  number =       "4",
  pages =        "373--380",
  year =         "1982",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "68C25 (68C20)",
  MRnumber =     "84a:68039",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of Ioannina, Greece",
  catcode =      "G.1.2; G.4; G.1.0",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.4 Algorithm analysis; G.1.0 General;
                 G.1.0 Computer arithmetic",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis; Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic",
  fjournal =     "Computing",
  genterm =      "economics; theory",
  guideno =      "04049",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  jrldate =      "1982",
  keywords =     "mathematical techniques",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Decker:1982:CAN,
  author =       "D. W. Decker and C. T. Kelley",
  title =        "Convergence acceleration for {Newton}'s method at
                 singular points",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "19",
  number =       "1",
  pages =        "219--229",
  month =        feb,
  year =         "1982",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65H05 (58E07 65J15)",
  MRnumber =     "83e:65090",
  MRreviewer =   "Michael Pr{\"u}fer",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  keywords =     "convergence acceleration",
}

@Article{Delahaye:1982:SLC,
  author =       "J. P. Delahaye and B. Germain-Bonne",
  title =        "The set of logarithmically convergent sequences cannot
                 be accelerated",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "19",
  number =       "4",
  pages =        "840--844",
  month =        aug,
  year =         "1982",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65B99",
  MRnumber =     "83f:65005",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  keywords =     "convergence acceleration",
}

@Article{Epstein:1982:UAF,
  author =       "C. Epstein and W. L. Miranker and T. J. Rivlin",
  title =        "Ultra-arithmetic {I}: function data types",
  journal =      j-MATH-COMP-SIM,
  volume =       "24",
  number =       "1",
  pages =        "1--18",
  month =        feb,
  year =         "1982",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1; G.1.2; G.1.2",
  CRclass =      "G.1.5 Roots of Nonlinear Equations; G.1.2
                 Approximation; G.1.2 Chebyshev approximation and
                 theory; G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Chebyshev
                 approximation and theory; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Mathematics and Computers in Simulation",
  genterm =      "algorithms",
  guideno =      "09324",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784754",
  jrldate =      "Feb. 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Epstein:1982:UAI,
  author =       "C. Epstein and W. L. Miranker and T. J. Rivlin",
  title =        "Ultra-arithmetic {II}: intervals of polynomials",
  journal =      j-MATH-COMP-SIM,
  volume =       "24",
  number =       "1",
  pages =        "19--29",
  month =        feb,
  year =         "1982",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2; G.1.1; G.1.0",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.1 Interpolation; G.1.1 Spline and
                 piecewise polynomial interpolation; G.1.0 General;
                 G.1.0 Error analysis",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Spline and piecewise polynomial
                 interpolation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Error analysis",
  fjournal =     "Mathematics and Computers in Simulation",
  genterm =      "algorithms",
  guideno =      "09325",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784754",
  jrldate =      "Feb. 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Fenton:1982:RCM,
  author =       "J. D. Fenton and R. S. Gardiner-Garden",
  title =        "Rapidly-convergent methods for evaluating elliptic
                 integrals and theta and elliptic functions",
  journal =      j-J-AUSTRAL-MATH-SOC-SER-B,
  volume =       "24",
  number =       "1",
  pages =        "47--58",
  month =        jul,
  year =         "1982",
  CODEN =        "JAMMDU",
  DOI =          "https://doi.org/10.1017/S0334270000003301",
  ISSN =         "0334-2700",
  ISSN-L =       "0334-2700",
  bibdate =      "Fri Apr 26 16:13:14 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/anziamj.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.cambridge.org/core/journals/anziam-journal/article/rapidlyconvergent-methods-for-evaluating-elliptic-integrals-and-theta-and-elliptic-functions/2D993C9A7C9EB1D4B61B856E22B45A34",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Austral Math. Soc. Ser. B",
  fjournal =     "Journal of the Australian Mathematical Society. Series
                 B, Applied Mathematics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
  onlinedate =   "17 February 2009",
}

@Article{Fernandez:1982:HCI,
  author =       "F. M. Fern{\'a}ndez and A. Mes{\'o}n and E. A.
                 Castro",
  title =        "Hypervirial calculation of integrals involving
                 {Bessel} functions",
  journal =      j-J-MATH-PHYS,
  volume =       "23",
  number =       "2",
  pages =        "254--255",
  month =        feb,
  year =         "1982",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.525345",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "81C05 (33A40 82A51)",
  MRnumber =     "83c:81010",
  bibdate =      "Sat Oct 29 18:19:03 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1980.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v23/i2/p254_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "2",
}

@Article{Gawronski:1982:ACF,
  author =       "W. Gawronski and U. Stadtm{\"u}ller",
  title =        "Approximation of continuous functions by generalized
                 {Favard} operators",
  journal =      j-J-APPROX-THEORY,
  volume =       "34",
  number =       "4",
  pages =        "384--396",
  month =        apr,
  year =         "1982",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory; algorithms",
  guideno =      "06038",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  jrldate =      "April 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Gessel:1982:SEH,
  author =       "Ira Gessel and Dennis Stanton",
  title =        "Strange Evaluations of Hypergeometric Series",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "13",
  number =       "2",
  pages =        "295--308",
  month =        mar,
  year =         "1982",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33A30",
  MRnumber =     "83c:33002",
  MRreviewer =   "C. L. Parihar",
  bibdate =      "Sun Nov 28 19:22:53 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/13/2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@Article{Gordon:1982:RAN,
  author =       "H. T. Gordon",
  title =        "Rough approximation numerical algorithms",
  journal =      j-DDJ,
  volume =       "7",
  number =       "7",
  pages =        "54--56",
  month =        jul,
  year =         "1982",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.0; G.1.2",
  CRclass =      "G.1.0 General; G.1.0 Numerical algorithms; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  guideno =      "04547",
  jrldate =      "July 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Greaves:1982:AHM,
  author =       "G. Greaves",
  title =        "An algorithm for the {Hausdorff} moment problem",
  journal =      j-NUM-MATH,
  volume =       "39",
  number =       "2",
  pages =        "231--238",
  month =        aug,
  year =         "1982",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Numerische Mathematik",
  genterm =      "algorithms",
  guideno =      "07489",
  journal-URL =  "http://link.springer.com/journal/211",
  jrldate =      "Aug. 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Hawkes:1982:ANT,
  author =       "Alan G. Hawkes",
  title =        "Approximating the Normal Tail",
  journal =      j-J-R-STAT-SOC-SER-D-STATISTICIAN,
  volume =       "31",
  number =       "3",
  pages =        "231--236",
  month =        sep,
  year =         "1982",
  CODEN =        "????",
  DOI =          "https://doi.org/10.2307/2987989",
  ISSN =         "0039-0526 (print), 1467-9884 (electronic)",
  ISSN-L =       "0039-0526",
  bibdate =      "Thu Jan 22 18:10:21 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i349970;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-d-1980.bib",
  URL =          "http://www.jstor.org/stable/2987989",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society. Series D
                 (The Statistician)",
  journal-URL =  "http://www.jstor.org/journals/00390526.html",
}

@Article{Hermann:1982:SAG,
  author =       "Robert Hermann",
  title =        "Some algebraic, geometric, and system-theoretic
                 properties of the {Special Functions} of mathematical
                 physics",
  journal =      j-J-MATH-PHYS,
  volume =       "23",
  number =       "7",
  pages =        "1282--1294",
  month =        jul,
  year =         "1982",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.525511",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Sat Oct 29 18:19:10 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1980.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v23/i7/p1282_s1",
  abstract =     "It is known that many of the Special Functions of
                 mathematical physics appear as matrix elements of Lie
                 group representations. This paper is concerned with a
                 beginning attack on the converse problem, i.e., finding
                 conditions that a given function be a matrix element.
                 The methods used are based on a combination of ideas
                 from system theory, functional analysis, Lie theory,
                 differential algebra, and linear ordinary differential
                 equation theory. A key idea is to attach a symbol as an
                 element of a commutative algebra. In favorable cases,
                 this symbol defines a Riemann surface, and a
                 meromorphic differential form on that surface. The
                 topological and analytical invariants attached to this
                 form play a key role in system theory. The Lie algebras
                 of the groups appear as linear differential operators
                 on this Riemann surface. Finally, it is shown how the
                 Picard--Vessiot--Infeld--Hull theory of factorization
                 of linear differential operators leads to realization
                 of many Special Functions as matrix representations of
                 group representations.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "13",
}

@TechReport{Kahan:1982:BCC,
  author =       "W. Kahan",
  title =        "Branch Cuts for Complex Elementary Functions",
  type =         "Technical Report",
  number =       "PAM-105",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  year =         "1982",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Math/Matrix.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "na, elementary function",
}

@Article{Keener:1982:CLB,
  author =       "L. L. Keener",
  title =        "Characterizing local best {SAIN} approximations",
  journal =      j-J-APPROX-THEORY,
  volume =       "36",
  number =       "1",
  pages =        "55--63",
  month =        sep,
  year =         "1982",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2; G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Chebyshev approximation and
                 theory; G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Chebyshev approximation and theory;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory",
  guideno =      "06074",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  jrldate =      "Sept. 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Lassey:1982:CCI,
  author =       "Keith R. Lassey",
  title =        "On the computation of certain integrals containing the
                 modified {Bessel} function $ {I}_0 (\xi) $",
  journal =      j-MATH-COMPUT,
  volume =       "39",
  number =       "160",
  pages =        "625--637",
  month =        oct,
  year =         "1982",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20",
  MRnumber =     "83j:65029",
  MRreviewer =   "Walter Gautschi",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 B0290M (Numerical integration and differentiation);
                 C4130 (Interpolation and function approximation); C4160
                 (Numerical integration and differentiation)",
  corpsource =   "Inst. of Nuclear Sci., DSIR, Lower Hutt, New Zealand",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximation; approximation theory; convergence of
                 numerical methods; convergent series; function;
                 function approximation; integration; limiting
                 behaviour; modified Bessel; numerical integration;
                 one-dimensional integrals; two-dimensional integrals",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Ling:1982:EIH,
  author =       "Chih Bing Ling and Ming Jing Wu",
  title =        "Evaluation of integrals of {Howland} type involving a
                 {Bessel} function",
  journal =      j-MATH-COMPUT,
  volume =       "38",
  number =       "157",
  pages =        "215--222",
  month =        jan,
  year =         "1982",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05 (65D20)",
  MRnumber =     "82m:65003",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0220 (Mathematical analysis); B0290M (Numerical
                 integration and differentiation); C1120 (Mathematical
                 analysis); C4160 (Numerical integration and
                 differentiation)",
  corpsource =   "Dept. of Maths., Virginia Polytech. Inst. and State
                 Univ., Blacksburg, VA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "10D; 20D; accuracy; Bessel function; Bessel functions;
                 Howland type; integrals; integration; tabulated
                 values",
  treatment =    "T Theoretical or Mathematical",
}

@Article{McCormick:1982:EFM,
  author =       "S. F. McCormick and G. D. Taylor and D. V. Pryor",
  title =        "Evaluation of Functions on Microcomputers: $ \ln (x)
                 $",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "8",
  number =       "5",
  pages =        "389--392",
  month =        "????",
  year =         "1982",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:23 MST 2017",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122182900323",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
  xxmonth =      "(none)",
}

@InCollection{Mori:1982:ARS,
  author =       "S. Mori and C. Y. Suen",
  editor =       "Ching Y. Suen and Renato {De Mori}",
  key =          "Scanners",
  booktitle =    "Computer analysis and perception: vol. I, {Visual}
                 signals",
  title =        "Automatic recognition of symbols and architecture of
                 the recognition unit",
  publisher =    pub-CRC,
  address =      pub-CRC:adr,
  bookpages =    "various",
  pages =        "17--40",
  year =         "1982",
  ISBN =         "0-8493-6305-5 (vol. 1), 0-8493-6306-3 (vol. 2)",
  ISBN-13 =      "978-0-8493-6305-4 (vol. 1), 978-0-8493-6306-1 (vol.
                 2)",
  LCCN =         "TA1650 .C65 1982",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "I.5; G.1.2; C.3; B.7; I.5.4",
  CRclass =      "I.5.2 Design Methodology; G.1.2 Approximation; G.1.2
                 Elementary function approximation; C.3 Signal
                 processing systems; B.7.1 Types and Design Styles;
                 I.5.4 Applications; I.5.4 Signal processing",
  descriptor =   "Computing Methodologies, PATTERN RECOGNITION, Design
                 Methodology; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Computer Systems Organization,
                 SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS, Signal
                 processing systems; Hardware, INTEGRATED CIRCUITS,
                 Types and Design Styles; Computing Methodologies,
                 PATTERN RECOGNITION, Applications, Signal processing",
  genterm =      "documentation; theory; design",
  guideno =      "01691",
  subject =      "I. Computing Methodologies; I.5 PATTERN RECOGNITION;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; C.
                 Computer Systems Organization; C.3 SPECIAL-PURPOSE AND
                 APPLICATION-BASED SYSTEMS; B. Hardware; B.7 INTEGRATED
                 CIRCUITS; I. Computing Methodologies; I.5 PATTERN
                 RECOGNITION",
}

@Article{Oklobdzija:1982:LSR,
  author =       "V. G. Oklobdzija and M. D. Ercegovac",
  title =        "An On-Line Square Root Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "1",
  pages =        "70--75",
  month =        jan,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1675887",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675887",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Ollin:1982:CFE,
  author =       "H. Z. Ollin and I. Gerst",
  title =        "Classes of functions with explicit best uniform
                 approximations",
  journal =      j-J-APPROX-THEORY,
  volume =       "34",
  number =       "3",
  pages =        "264--276",
  month =        mar,
  year =         "1982",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory",
  guideno =      "06030",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  jrldate =      "March 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Book{Patel:1982:HND,
  author =       "Jagdish K. Patel and Campbell B. Read",
  title =        "Handbook of the Normal Distribution",
  volume =       "40",
  publisher =    pub-DEKKER,
  address =      pub-DEKKER:adr,
  pages =        "ix + 337",
  year =         "1982",
  ISBN =         "0-8247-1541-1",
  ISBN-13 =      "978-0-8247-1541-0",
  LCCN =         "QA273.6 .P373",
  bibdate =      "Sat Dec 16 17:22:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Statistics, textbooks and monographs",
  acknowledgement = ack-nhfb,
  subject =      "Gaussian distribution",
}

@Article{Piessens:1982:ABF,
  author =       "R. Piessens and Maria Branders",
  title =        "Approximation for {Bessel} functions and their
                 application in the computation of {Hankel} transforms",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "8",
  number =       "4",
  pages =        "305--311",
  month =        "????",
  year =         "1982",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:22 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122182900128",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
}

@Article{Piessens:1982:ACB,
  author =       "R. Piessens",
  title =        "Automatic computation of {Bessel} function integrals",
  journal =      j-COMP-PHYS-COMM,
  volume =       "25",
  number =       "3",
  pages =        "289--295",
  month =        mar,
  year =         "1982",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(82)90024-8",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:28:01 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465582900248",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Rack:1982:GIV,
  author =       "H.-J Rack",
  title =        "A generalization of an inequality of {V. Markov} to
                 multivariate polynomials",
  journal =      j-J-APPROX-THEORY,
  volume =       "35",
  number =       "1",
  pages =        "94--97",
  month =        may,
  year =         "1982",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory",
  guideno =      "06047",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  jrldate =      "May 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Rix:1982:UQA,
  author =       "P. Rix",
  title =        "{Universeller Quad\-rat\-wurz\-el-Al\-go\-rith\-mus}
                 \toenglish {Universal Square Root Algorithms}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "23",
  pages =        "81--82",
  year =         "1982",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronik",
}

@PhdThesis{Rockey:1982:DMS,
  author =       "S. A. Rockey",
  title =        "Discrete methods of state approximation, parameter
                 identification and optimal control for hereditary
                 systems",
  type =         "{Ph.D} Thesis",
  school =       "Brown University",
  address =      "Providence, RI",
  pages =        "208",
  year =         "1982",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2; G.1.2; G.1.5",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Linear
                 approximation; G.1.5 Roots of Nonlinear Equations;
                 G.1.5 Convergence",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Linear approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
                 Equations, Convergence",
  guideno =      "15449",
  source =       "UMI order no. DA8228325",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Sommer:1982:EPL,
  author =       "M. Sommer",
  title =        "Existence of pointwise-{Lipschitz}-continuous
                 selections of the metric projection for a class of
                 {$Z$}-spaces",
  journal =      j-J-APPROX-THEORY,
  volume =       "34",
  number =       "2",
  pages =        "115--130",
  month =        feb,
  year =         "1982",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory",
  guideno =      "06018",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  jrldate =      "Feb. 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@PhdThesis{Wang:1982:AME,
  author =       "J.-L Wang",
  title =        "Asymptotically minimax estimators for distributions
                 with increasing failure rate",
  type =         "{Ph.D} Thesis",
  school =       "University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "42",
  year =         "1982",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "design",
  guideno =      "15084",
  source =       "UMI order no. DA8300696",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Whitley:1982:MBI,
  author =       "R. Whitley",
  title =        "{Markov} and {Bernstein}'s inequalities, and compact
                 and strictly singular operators",
  journal =      j-J-APPROX-THEORY,
  volume =       "34",
  number =       "3",
  pages =        "277--285",
  month =        mar,
  year =         "1982",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory",
  guideno =      "06031",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  jrldate =      "March 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Book{Wilkes:1982:PPE,
  author =       "M. V. (Maurice Vincent) Wilkes and David J. Wheeler
                 and Stanley Gill",
  title =        "The Preparation of Programs for an Electronic Digital
                 Computer: with Special Reference to the {EDSAC} and the
                 Use of a Library of Subroutines",
  volume =       "1",
  publisher =    pub-TOMASH,
  address =      pub-TOMASH:adr,
  pages =        "xxxi + 167",
  year =         "1982",
  ISBN =         "0-262-23118-2 (MIT Press 1984), 0-938228-03-X",
  ISBN-13 =      "978-0-262-23118-3 (MIT Press 1984),
                 978-0-938228-03-5",
  LCCN =         "QA76.6 .W545 1982",
  bibdate =      "Mon Feb 10 11:33:59 MST 2020",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "With a new introduction by Martin Campbell-Kelly.",
  series =       "Charles Babbage Institute reprint series for the
                 history of computing",
  acknowledgement = ack-nhfb,
}

@Article{Wills:1982:RCA,
  author =       "C. A. Wills and J. M. Blair and P. L. Ragde",
  title =        "Rational {Chebyshev} approximations for the {Bessel}
                 functions $ {J}_0 (x) $, $ {J}_1 (x) $, $ {Y}_0 (x) $,
                 $ {Y}_1 (x) $",
  journal =      j-MATH-COMPUT,
  volume =       "39",
  number =       "160",
  pages =        "617--623",
  month =        oct,
  year =         "1982",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (33A40 41A50)",
  MRnumber =     "83j:65030",
  MRreviewer =   "C. W. Clenshaw",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0260 (Optimisation techniques); B0290F (Interpolation
                 and function approximation); C1180 (Optimisation
                 techniques); C4130 (Interpolation and function
                 approximation)",
  corpsource =   "AEG Ltd., Chalk River Nuclear Labs., Ont., Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximations; Bessel functions; Chebyshev; Chebyshev
                 approximation; formulae; McMahon asymptotic; minimax
                 techniques; near-minimax rational approximation",
  treatment =    "T Theoretical or Mathematical",
}

@PhdThesis{Wimp:1982:CMS,
  author =       "Jet (Jesse Jet) Wimp",
  title =        "Computational methods and special functions",
  type =         "{D.Sc.} thesis",
  school =       "University of Edinburgh",
  address =      "Edinburgh, UK",
  year =         "1982",
  bibdate =      "Thu Dec 01 11:15:32 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Amos:1983:APF,
  author =       "Donald E. Amos",
  title =        "{Algorithm 610}: a Portable {FORTRAN} Subroutine for
                 Derivatives of the Psi Function",
  journal =      j-TOMS,
  volume =       "9",
  number =       "4",
  pages =        "494--502",
  month =        dec,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356056.356065",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "791 979",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.0; G.1; G; D.3.2",
  CRclass =      "G.1.0 General; G.1.0 Numerical algorithms; G.1.m
                 Miscellaneous; D.3.2 Language Classifications; D.3.2
                 FORTRAN",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Miscellaneous; Mathematics of
                 Computing, MISCELLANEOUS; Software, PROGRAMMING
                 LANGUAGES, Language Classifications, FORTRAN",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  genterm =      "ALGORITHMS",
  guideno =      "02212",
  journal-URL =  "https://dl.acm.org/loi/toms",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.m MISCELLANEOUS; D.
                 Software; D.3 PROGRAMMING LANGUAGES",
}

@Article{Benton:1983:CZT,
  author =       "T. C. Benton",
  title =        "Common Zeros of Two {Bessel} Functions. {Part II}.
                 {Approximations} and Tables",
  journal =      j-MATH-COMPUT,
  volume =       "41",
  number =       "163",
  pages =        "203--217",
  month =        jul,
  year =         "1983",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A40 (65A05)",
  MRnumber =     "85a:33010",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0220 (Mathematical analysis); C1120 (Mathematical
                 analysis)",
  corpsource =   "Dept. of Math., Pennsylvania State Univ., University
                 Park, PA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; computer program; poles and zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Bowman:1983:CFP,
  author =       "K. O. Bowman and L. R. Shenton",
  title =        "Continued fractions and the polygamma functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "9",
  number =       "1",
  pages =        "29--39",
  month =        mar,
  year =         "1983",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:24 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042783900262",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Brezinski:1983:CAE,
  author =       "C. Brezinski and J. P. Delahaye and B. Germain-Bonne",
  title =        "Convergence acceleration by extraction of linear
                 subsequences",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "20",
  number =       "6",
  pages =        "1099--1105",
  month =        dec,
  year =         "1983",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0720079",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65B99 (40A05)",
  MRnumber =     "723826 (85g:65014)",
  MRreviewer =   "John H. McCabe",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  keywords =     "convergence acceleration",
}

@Article{Brezinski:1983:ECC,
  author =       "Claude Brezinski",
  title =        "Error control in convergence acceleration processes",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "3",
  number =       "1",
  pages =        "65--80",
  year =         "1983",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/3.1.65",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65B99 (65D32 65G05)",
  MRnumber =     "705081 (85a:65004)",
  MRreviewer =   "John P. Coleman",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "convergence acceleration",
}

@Article{Cash:1983:BRKa,
  author =       "J. R. Cash",
  title =        "Block {Runge--Kutta} Methods for the Numerical
                 Integration of Initial Value Problems in Ordinary
                 Differential Equations. {Part I}. {The} Nonstiff Case",
  journal =      j-MATH-COMPUT,
  volume =       "40",
  number =       "161",
  pages =        "175--191",
  month =        jan,
  year =         "1983",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65L05",
  MRnumber =     "84d:65044a",
  MRreviewer =   "W. C. Rheinboldt",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 B0290M (Numerical integration and differentiation);
                 B0290P (Differential equations); C4130 (Interpolation
                 and function approximation); C4160 (Numerical
                 integration and differentiation); C4170 (Differential
                 equations)",
  corpsource =   "Dept. of Math., Imperial Coll., London, UK",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximate numerical integration; approximation
                 theory; block implicit formulae; block Runge--Kutta
                 formulae; C. W. Gear; differential equations;
                 equations; first order; formulae; initial value;
                 initial value problems; integration; linear multistep
                 methods; nonstiff problems; order; ordinary
                 differential; problems; Runge--Kutta methods;
                 Runge--Kutta starters; stepsize; stiff problems;
                 systems; variable order; variable order block
                 explicit",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Cody:1983:ASM,
  author =       "W. J. Cody",
  title =        "Algorithm 597: Sequence of Modified {Bessel} Functions
                 of the First Kind",
  journal =      j-TOMS,
  volume =       "9",
  number =       "2",
  pages =        "242--245",
  month =        jun,
  year =         "1983",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2; G",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, MISCELLANEOUS",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  genterm =      "algorithms",
  guideno =      "02186",
  journal-URL =  "https://dl.acm.org/loi/toms",
  jrldate =      "June 1983",
  keywords =     "algorithms",
  subject =      "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation G
                 Mathematics of Computing, MISCELLANEOUS",
}

@Article{Coleman:1983:CEB,
  author =       "J. P. Coleman and A. J. Monaghan",
  title =        "{Chebyshev} expansions for the {Bessel} function $
                 {J}_n(z) $ in the complex plane",
  journal =      j-MATH-COMPUT,
  volume =       "40",
  number =       "161",
  pages =        "343--366",
  month =        jan,
  year =         "1983",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05 (30E10 33A40 65D20)",
  MRnumber =     "84c:65013",
  MRreviewer =   "C. W. Clenshaw",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Cruz:1983:MPR,
  author =       "Andr{\'e}s Cruz and Javier Sesma",
  title =        "Modulus and phase of the reduced logarithmic
                 derivative of the {Hankel} function",
  journal =      j-MATH-COMPUT,
  volume =       "41",
  number =       "164",
  pages =        "597--605",
  month =        oct,
  year =         "1983",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A40 (65H05 81F10)",
  MRnumber =     "85b:33006",
  MRreviewer =   "H. E. Fettis",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Cusick:1983:CCL,
  author =       "David Cusick",
  title =        "Computers \& Calculators: a Logarithm Algorithm for
                 Four-Function Calculators",
  journal =      j-TWO-YEAR-COLL-MATH-J,
  volume =       "14",
  number =       "4",
  pages =        "322--324",
  month =        sep,
  year =         "1983",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/00494925.1983.11972706",
  ISSN =         "0049-4925 (print), 2325-9116 (electronic)",
  ISSN-L =       "0049-4925",
  bibdate =      "Thu Feb 14 09:49:45 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/collegemathj.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/00494925.1983.11972706;
                 https://www.jstor.org/stable/3027283",
  acknowledgement = ack-nhfb,
  fjournal =     "Two-Year College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 http://www.jstor.org/journals/00494925.html",
  onlinedate =   "30 Jan 2018",
}

@Article{Demsky:1983:MMC,
  author =       "J. Demsky and M. Schlesinger and R. D. Kent",
  title =        "Micro/mini computer program for calculating the square
                 root of rationals at arbitrary precision",
  journal =      j-COMP-PHYS-COMM,
  volume =       "29",
  number =       "3",
  pages =        "237--244",
  month =        may,
  year =         "1983",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(83)90004-8",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:28:04 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465583900048",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Dietrich:1983:VQF,
  author =       "D. Dietrich",
  title =        "{Verfahren zur L{\"o}sung von Quadratwurzeln f{\"u}r
                 Mikrorechnerprozeduren} \toenglish {Methods for the
                 Solution of Square Roots for Microprocessor
                 Subroutines} \endtoenglish",
  journal =      j-ELEKTRONIKER,
  volume =       "8",
  pages =        "EL-1--EL-6",
  year =         "1983",
  CODEN =        "ELKRBL",
  ISSN =         "0531-9218",
  bibdate =      "Fri Dec 08 13:05:49 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektroniker (Switzerland)",
}

@Article{Dubrulle:1983:CNM,
  author =       "Augustin A. Dubrulle",
  title =        "Class of Numerical Methods for the Computation of
                 {Pythagorean} Sums",
  journal =      j-IBM-JRD,
  volume =       "27",
  number =       "6",
  pages =        "582--589",
  month =        nov,
  year =         "1983",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Moler:1983:RSR} and generalization
                 \cite{Jamieson:1989:RCI}.",
  abstract =     "Moler and Morrison have described an iterative
                 algorithm for the computation of the Pythagorean sum
                 (a**2 plus b**2)** one-half of two real numbers a and
                 b. This algorithm is immune to unwarranted
                 floating-point overflows, has a cubic rate of
                 convergence, and is easily transportable. This paper,
                 which shows that the algorithm is essentially Halley's
                 method applied to the computation of square roots,
                 provides a generalization to any order of convergence.
                 Formulas of orders 2 through 9 are illustrated with
                 numerical examples. The generalization keeps the number
                 of floating-point divisions constant and should be
                 particularly useful for computation in high-precision
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  classcodes =   "C4190 (Other numerical methods); C5230 (Digital
                 arithmetic methods)",
  classification = "723; 921",
  corpsource =   "IBM Sci. Centre, Palo Alto, CA, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  journalabr =   "IBM J Res Dev",
  keywords =     "computer programming; digital arithmetic;
                 floating-point divisions; Halley's method;
                 high-precision floating-point arithmetic; iterative
                 algorithm; iterative methods; mathematical techniques
                 --- Numerical Methods; Pythagorean sums; rate of
                 convergence; square roots",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Ellacott:1983:FTE,
  author =       "S. W. Ellacott",
  title =        "On the {Faber} transform and efficient numerical
                 rational approximation",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "20",
  number =       "5",
  pages =        "989--1000",
  month =        oct,
  year =         "1983",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "41A20 (41A21)",
  MRnumber =     "85f:41010",
  MRreviewer =   "Lee L. Keener",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}

@Article{Fessler:1983:HAA,
  author =       "Theodore Fessler and William F. Ford and David A.
                 Smith",
  title =        "{HURRY}: An Acceleration Algorithm for Scalar
                 Sequences and Series",
  journal =      j-TOMS,
  volume =       "9",
  number =       "3",
  pages =        "346--354",
  month =        sep,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356044.356051",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65B10",
  MRnumber =     "791 970",
  bibdate =      "Sun Sep 04 19:50:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Book{Fox:1968:CPN,
  author =       "L. Fox and I. B. Parker",
  title =        "{Chebyshev} Polynomials in Numerical Analysis",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "ix + 205",
  year =         "1968",
  ISBN =         "0-19-859614-6",
  ISBN-13 =      "978-0-19-859614-1",
  LCCN =         "QA297 .F65",
  MRclass =      "65.10",
  MRnumber =     "228149",
  MRreviewer =   "G. N. Lance",
  bibdate =      "Mon Nov 13 14:02:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Reprinted in 1972 with corrections, but same ISBN.",
  series =       "Oxford mathematical handbooks",
  acknowledgement = ack-nhfb,
  author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
  mynote =       "JRUL: 517",
  series-editor = "John Crank and C. C. Ritchie",
  subject =      "Chebyshev polynomials; Numerical analysis",
  tableofcontents = "TO DO: find this!",
  xxauthor =     "L. (Leslie) Fox and I. B. (Ian Bax) Parker",
}

@Article{Fukushima:1983:OAA,
  author =       "M. Fukushima",
  title =        "An outer approximation algorithm for solving general
                 convex programs",
  journal =      j-OPER-RES,
  volume =       "31",
  number =       "1",
  pages =        "101--113",
  month =        feb,
  year =         "1983",
  CODEN =        "OPREAI",
  ISSN =         "0030-364X (print), 1526-5463 (electronic)",
  ISSN-L =       "0030-364X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2; G.4",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.4 Efficiency",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency",
  fjournal =     "Operations Research",
  genterm =      "algorithms; documentation; performance; reliability;
                 theory",
  guideno =      "09992",
  journal-URL =  "http://pubsonline.informs.org/loi/opre",
  jrldate =      "Jan./Feb. 1983",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.4 MATHEMATICAL
                 SOFTWARE",
}

@Article{Giordano:1983:EAZ,
  author =       "C. Giordano and A. Laforgia",
  title =        "Elementary approximations for zeros of {Bessel}
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "9",
  number =       "3",
  pages =        "221--228",
  month =        sep,
  year =         "1983",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Computational and Applied Mathematics",
  genterm =      "theory",
  guideno =      "08115",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  jrldate =      "Sept. 1983",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Hasson:1983:C,
  author =       "M. Hasson and O. Shisha",
  title =        "On the condition {$ \sum^{\infty }_{n = 1}n^{p -
                 1}E^*_n(f) < \infty $}",
  journal =      j-J-APPROX-THEORY,
  volume =       "39",
  number =       "4",
  pages =        "389--398",
  month =        dec,
  year =         "1983",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  MRclass =      "42A10 (41A10)",
  MRnumber =     "85a:42002",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory",
  guideno =      "07952",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  jrldate =      "Dec. 1983",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Johnson:1983:MGC,
  author =       "Gary M. Johnson",
  title =        "Multiple-grid convergence acceleration of viscous and
                 inviscid flow computations",
  journal =      j-APPL-MATH-COMP,
  volume =       "13",
  number =       "3--4",
  pages =        "375--398",
  month =        nov,
  year =         "1983",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  MRclass =      "76-08",
  MRnumber =     "84m:76010",
  bibdate =      "Thu Feb 27 09:47:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "convergence acceleration",
}

@Article{Kershaw:1983:SEW,
  author =       "D. Kershaw",
  title =        "Some extensions of {W. Gautschi}'s inequalities for
                 the gamma function",
  journal =      j-MATH-COMPUT,
  volume =       "41",
  number =       "164",
  pages =        "607--611",
  month =        oct,
  year =         "1983",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A15 (26D20 65D20)",
  MRnumber =     "84m:33003",
  MRreviewer =   "P. Anandani",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Lehnhoff:1983:NPT,
  author =       "H.-G Lehnhoff",
  title =        "A new proof of {Teljakowskii}'s theorem",
  journal =      j-J-APPROX-THEORY,
  volume =       "38",
  number =       "2",
  pages =        "177--181",
  month =        jun,
  year =         "1983",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory",
  guideno =      "07897",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  jrldate =      "June 1983",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Lehnhoff:1983:SPF,
  author =       "H.-G Lehnhoff",
  title =        "A simple proof of a {A. F. Timan}'s theorem",
  journal =      j-J-APPROX-THEORY,
  volume =       "38",
  number =       "2",
  pages =        "172--176",
  month =        jun,
  year =         "1983",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory",
  guideno =      "07896",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  jrldate =      "June 1983",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@InProceedings{Little:1983:CCS,
  author =       "F. Little",
  editor =       "Robert E. Barnhill and Wolfgang Boehm",
  booktitle =    "Surfaces in computer aided geometric design:
                 proceedings of a conference held at Mathematisches
                 Forschungsinstitut Oberwolfach, {F.R.G.}, April 25--30,
                 1982, organized by Wolfgang Boehm and Josef Hoschek",
  title =        "Convex combination surfaces",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  bookpages =    "xvi + 215",
  pages =        "99--109",
  year =         "1983",
  ISBN =         "0-444-86550-0",
  ISBN-13 =      "978-0-444-86550-2",
  LCCN =         "T385 .S827 1982",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.1; G.1.1; G.1.2",
  CRclass =      "G.1.1 Interpolation; G.1.1 Interpolation formulas;
                 G.1.1 Interpolation; G.1.1 Smoothing; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Interpolation formulas; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Interpolation,
                 Smoothing; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "theory",
  guideno =      "13093",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@TechReport{Lutskii:1983:VFT,
  author =       "G. M. Lutski{\u\i} and O. I. Penchev",
  title =        "{{\cyr Vychislenie {\`e}lementarnykh funktsi{\u\i}
                 metodom tsifra za tsifro{\u\i} v izbytochnykh sistemakh
                 schisleniya}}. ({Russian}) [Calculation of elementary
                 functions by the digit-by-digit method in redundant
                 number systems]",
  type =         "Preprint",
  number =       "83-22",
  institution =  "Akad. Nauk Ukrain. SSR, Inst. Kibernet.",
  address =      "Kiev, USSR",
  pages =        "30",
  year =         "1983",
  MRclass =      "65D20",
  MRnumber =     "719 021",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Mason:1983:CBF,
  author =       "Janet P. Mason",
  title =        "Cylindrical {Bessel} functions for a large range of
                 complex arguments",
  journal =      j-COMP-PHYS-COMM,
  volume =       "30",
  number =       "1",
  pages =        "1--11",
  month =        jul # "\slash " # aug,
  year =         "1983",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(83)90116-9",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:28:05 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465583901169",
  abstract =     "The evaluation of Bessel functions of the first and
                 second kinds, covering a wide range of complex
                 arguments and integer orders, is required in the
                 determination of the intensity of acoustic reflection
                 from absorbing bodies. Numerical problems associated
                 with the calculations are discussed and various means
                 by which these problems have been overcome are
                 explained. The numerical methods used in calculating
                 the Bessel functions of the first, second and third
                 kinds are given, as well as sample results and
                 numerical checks in the form of computer plots and
                 printouts.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{McCabe:1983:ASC,
  author =       "J. H. McCabe",
  title =        "On an asymptotic series and corresponding continued
                 fraction for a gamma function ratio",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "9",
  number =       "2",
  pages =        "125--130",
  month =        jun,
  year =         "1983",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:24 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042783900353",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@TechReport{McCurdy:1983:ACD,
  author =       "A. McCurdy and K. C. Ng and Beresford N. Parlett",
  title =        "Accurate computation of divided differences of the
                 exponential function",
  type =         "Report",
  number =       "PAM-160",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        jun,
  year =         "1983",
  bibdate =      "Fri Nov 11 09:06:19 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Meister:1983:MYF,
  author =       "B. Meister",
  title =        "On {Murphy}'s yield formula",
  journal =      j-IBM-JRD,
  volume =       "27",
  number =       "6",
  pages =        "545--548",
  month =        nov,
  year =         "1983",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "B.7.1; G.1.2",
  CRclass =      "B.7.1 Types and Design Styles; B.7.1 Input/Output
                 circuits; G.1.2 Approximation; G.1.2 Elementary
                 function approximation",
  descriptor =   "Hardware, INTEGRATED CIRCUITS, Types and Design
                 Styles, Input/Output circuits; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  fjournal =     "IBM Journal of Research and Development",
  genterm =      "theory; design; reliability",
  guideno =      "06316",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  jrldate =      "Nov. 1983",
  subject =      "B. Hardware; B.7 INTEGRATED CIRCUITS; G. Mathematics
                 of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Mlodzki:1983:PPC,
  author =       "J. Mlodzki and J. Kuszkowski and M. Suffczynski",
  title =        "A {Pascal} program for calculating the reduced
                 {Coulomb} {Green}'s functions and their partial waves",
  journal =      j-COMP-PHYS-COMM,
  volume =       "29",
  number =       "4",
  pages =        "341--350",
  month =        jun,
  year =         "1983",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(83)90013-9",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Feb 24 18:49:59 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465583900139",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Moler:1983:RSR,
  author =       "Cleve B. Moler and Donald Morrison",
  title =        "Replacing Square Roots by {Pythagorean} Sums",
  journal =      j-IBM-JRD,
  volume =       "27",
  number =       "6",
  pages =        "577--581",
  month =        nov,
  year =         "1983",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Dubrulle:1983:CNM} and generalization
                 \cite{Jamieson:1989:RCI}.",
  URL =          "http://www.research.ibm.com/journal/rd/276/ibmrd2706P.pdf",
  abstract =     "An algorithm is presented for computing a 'Pythagorean
                 sum' a(+)b= square root a/sup 2/+b/sup 2/ directly from
                 a and b without computing their squares or taking a
                 square root. No destructive floating point overflows or
                 underflows are possible. The algorithm can be extended
                 to compute the Euclidean norm of a vector. The
                 resulting subroutine is short, portable, robust, and
                 accurate, but not as efficient as some other
                 possibilities. The algorithm is particularly attractive
                 for computers where space and reliability are more
                 important than speed",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C4190 (Other numerical methods); C5230 (Digital
                 arithmetic methods)",
  corpsource =   "Dept. of Computer Sci., Univ. of New Mexico,
                 Albuquerque, NM, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "algorithms; digital arithmetic; Euclidean norm;
                 floating-point arithmetic; iterative methods;
                 performance; Pythagorean sums; subroutine; vector",
  review =       "ACM CR 8406-0463",
  subject =      "G.1 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Roots of Nonlinear Equations \\ F.2.1 Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials \\ F.2.2 Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations",
  treatment =    "T Theoretical or Mathematical",
}

@PhdThesis{Monk:1983:SFE,
  author =       "P. B. Monk",
  title =        "Some finite element methods for the approximation of
                 the biharmonic equation",
  type =         "{Ph.D} Thesis",
  school =       "Rutgers University, The State University of New
                 Jersey",
  address =      "New Brunswick, NJ, USA",
  pages =        "242",
  year =         "1983",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.8; G.1.2",
  CRclass =      "G.1.8 Partial Differential Equations; G.1.8 Finite
                 element methods; G.1.2 Approximation; G.1.2 Elementary
                 function approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations, Finite element methods;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "design; algorithms; experimentation",
  guideno =      "15929",
  source =       "UMI order no. DA8308441",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Muench:1983:LAF,
  author =       "Donald L. Muench and Gerald Wildenberg",
  title =        "A Logarithm Algorithm for a Five-Function Calculator",
  journal =      j-TWO-YEAR-COLL-MATH-J,
  volume =       "14",
  number =       "4",
  pages =        "324--326",
  month =        sep,
  year =         "1983",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/00494925.1983.11972707",
  ISSN =         "0049-4925 (print), 2325-9116 (electronic)",
  ISSN-L =       "0049-4925",
  bibdate =      "Thu Feb 14 09:49:45 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/collegemathj.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/00494925.1983.11972707",
  acknowledgement = ack-nhfb,
  fjournal =     "Two-Year College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 http://www.jstor.org/journals/00494925.html",
  onlinedate =   "30 Jan 2018",
}

@Article{Nave:1983:ITF,
  author =       "Rafi Nave",
  key =          "Nav83",
  title =        "Implementation of Transcendental Functions on a
                 Numerics Processor",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "11",
  pages =        "221--225",
  year =         "1983",
  CODEN =        "MMICDT",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Math/elefunt.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Microprocessing and Microprogramming",
}

@Article{Prosser:1983:NCS,
  author =       "C. J. Prosser",
  title =        "A note on computing the square root of an integer",
  journal =      j-COMP-J,
  volume =       "26",
  number =       "2",
  pages =        "187--188",
  month =        may,
  year =         "1983",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/187.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/188.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C4190 (Other numerical methods); C7310 (Mathematics
                 computing)",
  corpsource =   "Rutherford and Appleton Lab., Chilton, Didcot, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "binary; computer; fixed-point number; integer;
                 interactive methods; iterative methods; PASCAL; Pascal
                 implementation; square root; subroutines; successive
                 subtraction",
  treatment =    "P Practical",
}

@Article{Salzer:1983:NDG,
  author =       "Herbert E. Salzer",
  title =        "Note on the {Do{\v{c}}ev--Grosswald} asymptotic series
                 for generalized {Bessel} polynomials",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "9",
  number =       "2",
  pages =        "131--135",
  month =        jun,
  year =         "1983",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:24 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  note =         "See errata \cite{Anonymous:1984:EJCb}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042783900365",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Sidi:1983:ZSP,
  author =       "Avram Sidi and Doron S. Lubinsky",
  title =        "On the zeros of some polynomials that arise in
                 numerical quadrature and convergence acceleration",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "20",
  number =       "2",
  pages =        "400--405",
  month =        apr,
  year =         "1983",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0720028",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65H05 (65D30)",
  MRnumber =     "694528 (84f:65046)",
  MRreviewer =   "J. G. Herriot",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  keywords =     "convergence acceleration",
}

@Article{Talman:1983:LSC,
  author =       "James D. Talman",
  title =        "{LSFBTR}: a subroutine for calculating spherical
                 {Bessel} transforms",
  journal =      j-COMP-PHYS-COMM,
  volume =       "30",
  number =       "1",
  pages =        "93--99",
  month =        jul # "\slash " # aug,
  year =         "1983",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(83)90126-1",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:28:05 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465583901261",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Temme:1983:NCC,
  author =       "N. M. Temme",
  title =        "The numerical computation of the confluent
                 hypergeometric function $ {U}(a, \, b, \, z) $",
  journal =      j-NUM-MATH,
  volume =       "41",
  number =       "1",
  pages =        "63--82",
  month =        apr,
  year =         "1983",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65D20 (33A30 65D15)",
  MRnumber =     "84g:65030",
  MRreviewer =   "H. E. Fettis",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "C4120 (Functional analysis); C7310 (Mathematics
                 computing)",
  corpsource =   "Math. Centrum, Amsterdam, Netherlands",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "ALGOL 60 procedures; asymptotic expansions; confluent
                 hypergeometric function; function computation; function
                 evaluation; Miller algorithm; subroutines",
  treatment =    "P Practical; T Theoretical or Mathematical",
}

@TechReport{Temme:1983:TTR,
  author =       "N. M. Temme",
  title =        "Traces to {Tricomi} in recent work on special
                 functions and asymptotics of integrals",
  type =         "Report",
  number =       "TW 239/83",
  institution =  "Stichting mathematisch Centrum",
  address =      "Amsterdam, The Netherlands",
  pages =        "15",
  year =         "1983",
  LCCN =         "A1 M462 TW239/83",
  bibdate =      "Sat Oct 30 18:29:48 2010",
  bibsource =    "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Temme:1983:UAE,
  author =       "Nico M. Temme",
  title =        "Uniform asymptotic expansions of {Laplace} integrals",
  journal =      "Analysis",
  volume =       "3",
  number =       "1--4",
  pages =        "221--249",
  year =         "1983",
  ISSN =         "0174-4747 (print), 2196-6753 (electronic)",
  ISSN-L =       "0174-4747",
  MRclass =      "41A60 (44A10)",
  MRnumber =     "756117",
  MRreviewer =   "F. W. J. Olver",
  bibdate =      "Tue Feb 6 11:39:36 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Analysis. International Journal of Analysis and its
                 Application",
}

@Article{Volz:1983:CAA,
  author =       "H. V{\"o}lz",
  title =        "{CORDIC und {\"a}hnliche Algorithmen der elementaren
                 Funktionen mit besonderer Eignung f{\"u}r Mikrorechner}
                 \toenglish {CORDIC and Similar Algorithms for
                 Elementary Functions with Particular Aptitude for
                 Microcomputers} \endtoenglish",
  journal =      j-NACH-ELEK,
  volume =       "33",
  number =       "12",
  pages =        "506--510",
  month =        "????",
  year =         "1983",
  CODEN =        "NTELAP",
  ISSN =         "0323-4657",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  fjournal =     "Nachrichtentechnik Elektronik",
}

@Article{Wejntrob:1983:ASR,
  author =       "Leon Wejntrob",
  title =        "Approximation of Square Roots",
  journal =      j-TWO-YEAR-COLL-MATH-J,
  volume =       "14",
  number =       "5",
  pages =        "427--431",
  month =        nov,
  year =         "1983",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/00494925.1983.11972733",
  ISSN =         "0049-4925 (print), 2325-9116 (electronic)",
  ISSN-L =       "0049-4925",
  bibdate =      "Thu Feb 14 09:49:48 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/collegemathj.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/00494925.1983.11972733",
  acknowledgement = ack-nhfb,
  fjournal =     "Two-Year College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 http://www.jstor.org/journals/00494925.html",
  keywords =     "rational square roots of rational numbers",
  onlinedate =   "30 Jan 2018",
}

@Article{Xu:1983:HPG,
  author =       "Xian Yu Xu and Jia Kai Li and Gui Jing Xiong and Guo
                 Liang Xu and Chun Qing Lu",
  title =        "High-precision generation of elementary functions.
                 ({Chinese})",
  journal =      "Appl. Math. Math. Comput.",
  volume =       "6",
  pages =        "24--32",
  year =         "1983",
  MRclass =      "65D20",
  MRnumber =     "86e:65031",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Anonymous:1984:EJCb,
  author =       "Anonymous",
  title =        "Errata: {J. Comput. Appl. Math. {\bf 9}: H. E. Salzer,
                 Note on the Do{\v{c}}ev--Grosswald asymptotic series
                 for generalized Bessel polynomials, (1983) 131--135}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "10",
  number =       "1",
  pages =        "133--133",
  month =        feb,
  year =         "1984",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:53 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  note =         "See \cite{Salzer:1983:NDG}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042784900773",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Ardill:1984:ABF,
  author =       "R. W. B. Ardill and K. J. M. Moriarty",
  title =        "Accurate {Bessel} functions {$ J_n(z) $}, {$ Y_n(z)
                 $}, {$ H_n^{(1)}(z) $} and {$ H_n^{(2)}(z) $} of
                 integer order and complex argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-559--C-559",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82734-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:33 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584827344",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Ardill:1984:BFC,
  author =       "W. B. Ardill and K. J. M. Moriarty",
  title =        "The {Bessel} functions {$ J_0 $} and {$ J_1 $} of
                 complex argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  pages =        "C-409--C-409",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82619-3",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Apr 24 10:35:27 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Ardill:1984:SBF,
  author =       "R. W. B. Ardill and K. J. M. Moriarty",
  title =        "Spherical {Bessel} functions $ j_n $ and $ y_n $ of
                 integer order and real argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  pages =        "C-466--C-466",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82666-1",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Apr 24 10:35:27 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  remark =       "No code shown, but uses formulas from
                 \cite{Abramowitz:1964:HMF} for evaluations. Function
                 name is {\tt sphbes}.",
}

@Article{Bardin:1984:CFE,
  author =       "C. Bardin and Y. Dandeu and L. Gauthier and J.
                 Guillermin and T. Lena and J.-M. Pernet and H. H.
                 Wolter and T. Tamura",
  title =        "{Coulomb} functions in entire $ (\eta, \pi) $-plane",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-125--C-126",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82382-6",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:06 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584823826",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Barnett:1984:CCB,
  author =       "A. R. Barnett",
  title =        "{Coulfg}: {Coulomb} and {Bessel} functions and their
                 derivatives, for real arguments, by {Steed}'s method",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-812--C-813",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82930-6",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:49 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584829306",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Barnett:1984:CWF,
  author =       "A. R. Barnett and D. H. Feng and J. W. Steed and L. J.
                 B. Goldfarb",
  title =        "{Coulomb} wave functions for all real $ \eta $ and $
                 \rho $",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-285",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82515-1",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:15 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584825151",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Barnett:1984:KCF,
  author =       "A. R. Barnett",
  title =        "{Klein}: {Coulomb} functions for real $ \lambda $ and
                 positive energy to high accuracy",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-753",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82884-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:49 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584828842",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Barnett:1984:RMR,
  author =       "A. R. Barnett",
  title =        "{RCWFF} --- a modification of the real {Coulomb}
                 wavefunction program {RCWFN}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-370",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82585-0",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:24 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584825850",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Bell:1984:CFN,
  author =       "K. L. Bell and N. S. Scott",
  title =        "{Coulomb} functions (negative energies)",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-648",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82808-8",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:41 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584828088",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@InCollection{Berges:1984:AFE,
  author =       "J. C. Berges",
  booktitle =    "Space mathematics",
  title =        "Arithm{\'e}tique et fonctions {\'e}l{\'e}mentaires sur
                 mini-micro calculateurs. ({French}) [Arithmetic and
                 elementary functions on mini-micro computers]",
  publisher =    "C{\'e}padu{\`e}s",
  address =      "Toulouse, France",
  pages =        "193--229",
  year =         "1984",
  MRclass =      "65-01 (65-04)",
  MRnumber =     "849 200",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@Article{Berndt:1984:APA,
  author =       "Bruce C. Berndt and Larry A. Goldberg",
  title =        "Analytic properties of arithmetic sums arising in the
                 theory of the classical theta functions",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "15",
  number =       "1",
  pages =        "143--150",
  month =        jan,
  year =         "1984",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "11A15 (11A25 11F27)",
  MRnumber =     "85d:11008",
  MRreviewer =   "T. M. Apostol",
  bibdate =      "Sun Nov 28 19:23:19 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/15/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@Article{Black:1984:NIS,
  author =       "Cheryl M. Black and Robert P. Burton and Thomas H.
                 Miller",
  title =        "The Need for an Industry Standard of Accuracy for
                 Elementary-Function Programs",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "361--366",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "792 000",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.0; G.1.2; G.4",
  CRclass =      "G.1.0 General; G.1.0 Numerical algorithms; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.4 Efficiency",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Efficiency",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  genterm =      "theory; algorithms; reliability; standardization",
  guideno =      "02897",
  journal-URL =  "https://dl.acm.org/loi/toms",
  jrldate =      "Dec. 1984",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.4 MATHEMATICAL SOFTWARE",
}

@Article{Borwein:1984:AGM,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic-Geometric Mean and Fast Computation of
                 Elementary Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "26",
  number =       "3",
  pages =        "351--366",
  month =        jul,
  year =         "1984",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1026073",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65D20 (26A09)",
  MRnumber =     "86d:65029",
  MRreviewer =   "S. Conde",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  abstract =     "We produce a self contained account of the
                 relationship between the Gaussian arithmetic-geometric
                 mean iteration and the fast computation of elementary
                 functions. A particularly pleasant algorithm for pi is
                 one of the by-products.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliationaddress = "Dalhousie Univ, Halifax, NS, Can",
  classification = "723; 921",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "AGM (Arithmetic-Geometric Mean); arithmetic-geometric
                 mean; calculation of pi; computational methods;
                 elliptic functions; Iterative Methods; mathematical
                 techniques; numerical mathematics",
}

@Article{Braess:1984:RAE,
  author =       "Dietrich Braess",
  title =        "On rational approximation of the exponential and the
                 square root function",
  journal =      j-LECT-NOTES-MATH,
  volume =       "1105",
  pages =        "89--99",
  year =         "1984",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0072401",
  ISBN =         "3-540-13899-4 (print), 3-540-39113-4 (e-book)",
  ISBN-13 =      "978-3-540-13899-0 (print), 978-3-540-39113-5
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  MRclass =      "41A20 (41A25 65D15)",
  MRnumber =     "783263 (86g:41025)",
  MRreviewer =   "G. Meinardus",
  bibdate =      "Fri May 9 19:07:44 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1980.bib",
  URL =          "http://link.springer.com/chapter/10.1007/BFb0072401/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0072395",
  book-URL =     "http://www.springerlink.com/content/978-3-540-39113-5",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
}

@Article{Campbell:1984:BFRa,
  author =       "J. B. Campbell",
  title =        "{Bessel} Functions {$ J_\nu (x) $} of real order and
                 real argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-583--C-583",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82756-3",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:33 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584827563",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Campbell:1984:BFZ,
  author =       "J. B. Campbell",
  title =        "{Bessel} functions {$ I_\nu (z) $} and {$ K_\nu (z) $}
                 of real order and complex argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-747--C-748",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82880-5",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:49 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584828805",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Coleman:1984:FSB,
  author =       "J. P. Coleman",
  title =        "A {Fortran} subroutine for the {Bessel} function {$
                 J_n(x) $} of order $0$ to $ 10 $",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-654--C-654",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82814-3",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:41 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran2.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584828143",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  remark =       "No code shown, but sums two separate Chebyshev series,
                 one for $x$ in $ [0, 8] $, and a second for $x$ in $
                 (8, \infty) $. Function name is {\tt realjn}.",
}

@Article{Delic:1984:CSS,
  author =       "G. Delic",
  title =        "{Chebyshev} series for the spherical {Bessel} function
                 $ l(r) $",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-577--C-577",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82751-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:33 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584827514",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Demsky:1984:MMC,
  author =       "J. Demsky and M. Schlesinger and R. D. Kent",
  title =        "Micro/mini computer program for calculating the square
                 root of rationals at arbitrary precision",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-877",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82981-1",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:58 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584829811",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Dhanoa:1984:BPE,
  author =       "M. S. Dhanoa and J. France",
  title =        "A {BASIC} program for the evaluation of the gamma
                 functions",
  journal =      j-J-APPL-STAT,
  volume =       "11",
  number =       "2",
  pages =        "225--228",
  year =         "1984",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/02664768400000021",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Tue Sep 6 11:15:50 MDT 2011",
  bibsource =    "http://www.tandf.co.uk/journals/routledge/02664763.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  onlinedate =   "24 May 2006",
}

@Article{Dutka:1984:EHH,
  author =       "Jacques Dutka",
  title =        "The early history of the hypergeometric function",
  journal =      j-ARCH-HIST-EXACT-SCI,
  volume =       "31",
  number =       "1",
  pages =        "15--34",
  month =        mar,
  year =         "1984",
  CODEN =        "AHESAN",
  DOI =          "https://doi.org/10.1007/BF00330241",
  ISSN =         "0003-9519 (print), 1432-0657 (electronic)",
  ISSN-L =       "0003-9519",
  MRclass =      "01A50 (33-03)",
  MRnumber =     "769538 (86d:01010)",
  MRreviewer =   "Willard Parker",
  bibdate =      "Fri Feb 4 21:50:21 MST 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=31&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=31&issue=1&spage=15",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for History of Exact Sciences",
  journal-URL =  "http://link.springer.com/journal/407",
  MRtitle =      "The early history of the hypergeometric function",
}

@Article{Fransen:1984:CMM,
  author =       "Arne Frans{\'e}n and Staffan Wrigge",
  title =        "Calculation of the moments and the moment generating
                 function for the reciprocal gamma distribution",
  journal =      j-MATH-COMPUT,
  volume =       "42",
  number =       "166",
  pages =        "601--616",
  month =        apr,
  year =         "1984",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (60E10 62E15 65U05)",
  MRnumber =     "86f:65042a",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C1210B (Reliability theory); C4130 (Interpolation and
                 function approximation)",
  corpsource =   "Nat. Defence Res. Inst., Stockholm, Sweden",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "kurtosis; moment generating function; moments;
                 polynomials; reciprocal gamma distribution; reliability
                 theory; skewness; variance",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Glaeske:1984:LTS,
  author =       "H.-J. Glaeske and O. I. Mari{\v{c}}ev",
  title =        "The {Laguerre} transform of some elementary
                 functions",
  journal =      j-Z-ANAL-ANWEND,
  volume =       "3",
  number =       "3",
  pages =        "237--244",
  year =         "1984",
  ISSN =         "0232-2064 (print), 1661-4534 (electronic)",
  ISSN-L =       "0232-2064",
  MRclass =      "44A15 (34A10)",
  MRnumber =     "86a:44005",
  MRreviewer =   "Ram Kishore Saxena",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Analysis und ihre Anwendungen}",
}

@Article{Grodd:1984:REN,
  author =       "Laurence W. Grodd and Charles M. Patton",
  title =        "{ROM} extends numerical function set of handheld
                 computer",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "35",
  number =       "7",
  pages =        "25--36",
  month =        jul,
  year =         "1984",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  bibdate =      "Tue Mar 25 14:12:15 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.hpl.hp.com/hpjournal/pdfs/IssuePDFs/1984-07.pdf",
  abstract =     "The plug-in math PAC for HP's new HP-71B Handheld
                 Computer further extends the HP-71B's comprehensive
                 standard numerical function set to provide a
                 mathematical tool of unprecedented capability and power
                 in a personal machine. Full use of complex variables,
                 integration, matrix algebra, and polynomial root
                 finding are some of the capabilities provided by this
                 plug-in module.",
  acknowledgement = ack-nhfb,
  affiliation =  "Hewlett--Packard Co, Corvallis, OR, USA",
  affiliationaddress = "Hewlett--Packard Co, Corvallis, OR, USA",
  classcodes =   "C7310 (Mathematics computing)",
  classification = "723",
  fjournal =     "Hewlett-Packard Journal: technical information from
                 the laboratories of Hewlett-Packard Company",
  journalabr =   "Hewlett Packard J",
  keywords =     "complex; complex variables; computers, miniature; data
                 storage, digital --- Fixed; data type; extended I/O
                 functions; fast Fourier transform; handheld computer;
                 HP-71B hand-held computer; matrix operations; numerical
                 analysis; numerical function set; polynomial; read-only
                 storage; ROM; root finder",
  remark =       "The paper notes: ``Completely support provisions of
                 the proposed IEEE floating-point mathematics standard.
                 \ldots{} an HP-71B REAL variable --- a 12-digit
                 mantissa and a three-digit exponent in the range from $
                 - 499 $ to $ 499 $. Each part of a COMPLEX SHORT
                 variable or array element has the same precision as an
                 HP-71B SHORT variable --- a five-digit mantissa and a
                 three-digit exponent in the range from $ - 499 $ to $
                 499 $. Of course, denormalized numbers, Inf (infinity),
                 and NaNs (not-a-numbers) are also permitted.''",
  treatment =    "P Practical; X Experimental",
}

@Article{Gustafson:1984:SCC,
  author =       "Sven-{\AA}ke Gustafson",
  title =        "On the stability of a class of convergence
                 acceleration methods for power series",
  journal =      j-BIT,
  volume =       "24",
  number =       "4",
  pages =        "510--519",
  month =        dec,
  year =         "1984",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01934909",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65B10",
  MRnumber =     "764823 (86c:65006)",
  MRreviewer =   "D. Levin",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=24&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=24&issue=4&spage=510",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "convergence acceleration",
}

@Article{Karp:1984:ELS,
  author =       "A. H. Karp",
  title =        "Exponential and Logarithm by Sequential Squaring",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-33",
  number =       "5",
  pages =        "462--464",
  month =        may,
  year =         "1984",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1984.1676464",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 09:22:52 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676464",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kolbig:1984:PCL,
  author =       "K. S. K{\"o}lbig",
  title =        "Programs for computing the logarithm of the gamma
                 function, and the digamma function, for complex
                 argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-152",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82404-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:06 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584824042",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Laforgia:1984:FIG,
  author =       "Andrea Laforgia",
  title =        "Further Inequalities for the Gamma Function",
  journal =      j-MATH-COMPUT,
  volume =       "42",
  number =       "166",
  pages =        "597--600",
  month =        apr,
  year =         "1984",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A15",
  MRnumber =     "85i:33001",
  MRreviewer =   "H. E. Fettis",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Dept. of Math., Univ. of Torino, Torino, Italy",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "gamma function; inequalities; polynomials",
  treatment =    "T Theoretical or Mathematical",
}

@Article{McCurley:1984:EE,
  author =       "Kevin S. McCurley",
  title =        "Explicit Estimates for $ \theta (x; 3, l) $ and $ \psi
                 (x; 3, l) $",
  journal =      j-MATH-COMPUT,
  volume =       "42",
  number =       "165",
  pages =        "287--296",
  month =        jan,
  year =         "1984",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11N56",
  MRnumber =     "85g:11085",
  MRreviewer =   "G. J. Rieger",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Dept. of Maths., Michigan State Univ., East Lansing,
                 MI, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "arithmetic progressions; Chebyshev approximation;
                 Chebyshev functions; Dirichlet L-; explicit estimates;
                 functions; prime number; theorem; zeros",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Moon:1984:AFC,
  author =       "Wooil Moon",
  title =        "{Airy} function with complex arguments",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-692",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82842-8",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:41 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584828428",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Nesbet:1984:ARI,
  author =       "R. K. Nesbet",
  title =        "Algorithms for regular and irregular {Coulomb} and
                 {Bessel} functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "32",
  number =       "4",
  pages =        "341--347",
  month =        jul,
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(84)90051-1",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Apr 24 10:35:27 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465584900511",
  abstract =     "Algorithms for computing Coulomb--Bessel functions are
                 considered, with emphasis on obtaining accurate values
                 when the argument $x$ is inside the classical turning
                 point $ x \lambda $. Algorithms of Barnett et al. for
                 the generalized Coulomb functions and their derivatives
                 are discussed in the context of the phase integral
                 formalism. Modified or alternative algorithms are
                 considered that are designed to be valid for all values
                 of argument $x$ and index $ \lambda $ for the functions
                 $ F_\lambda (x) $, $ G_\lambda (x) $. An algorithm for
                 accelerating convergence of a power series by
                 conversion to a continued fraction is presented, and is
                 applied to the evaluation of spherical Bessel
                 functions. An explicit formula for the integrand of the
                 phase integral is presented for spherical Bessel
                 functions. The methods considered need to be augmented
                 by an efficient algorithm for computing the logarithmic
                 derivative of $ G_0 + i F_0 $ for Coulomb functions
                 when $x$ is smaller than the charge parameter $ \eta
                 $.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Newman:1984:ABS,
  author =       "J. N. Newman",
  title =        "Approximations for the {Bessel} and {Struve}
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "43",
  number =       "168",
  pages =        "551--556",
  month =        oct,
  year =         "1984",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1984-0758202-X",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (33A40)",
  MRnumber =     "86c:65021",
  MRreviewer =   "S. Conde",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C1120 (Mathematical analysis); C4130 (Interpolation and
                 function approximation)",
  corpsource =   "Dept. of Ocean Eng., MIT, Cambridge, MA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "accuracy; Bessel functions; function approximation;
                 functions; IBM PC computer; minimax; polynomial
                 approximations; polynomials; rational-fraction
                 approximations; single-precision computations; Struve",
  treatment =    "T Theoretical or Mathematical",
}

@TechReport{Ng:1984:DAA,
  author =       "K. C. Ng",
  title =        "Contributions to the computation of the matrix
                 exponential",
  type =         "Report",
  number =       "PAM-212",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        feb,
  year =         "1984",
  bibdate =      "Fri Nov 11 09:06:19 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Based on the author's Ph.D. thesis.",
  acknowledgement = ack-nhfb,
  keywords =     "$\exp(Bt)$",
}

@Article{Nishimoto:1984:TFD,
  author =       "Katsuyuki Nishimoto",
  title =        "Tables of fractional differintegrations of elementary
                 functions",
  journal =      "J. College Engrg. Nihon Univ. Ser. B",
  volume =       "25",
  pages =        "41--46",
  year =         "1984",
  ISSN =         "0285-6182",
  MRclass =      "30E20 (26A33)",
  MRnumber =     "85f:30065",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Noble:1984:CPE,
  author =       "C. J. Noble and I. J. Thompson",
  title =        "{COULN}, a program for evaluating negative energy
                 {Coulomb} functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "33",
  number =       "4",
  pages =        "413--419",
  month =        oct,
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(84)90146-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Feb 24 13:39:14 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465584901462",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Piessens:1984:ACB,
  author =       "R. Piessens",
  title =        "Automatic computation of {Bessel} function integrals",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-791",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82915-X",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:49 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S001046558482915X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Piessens:1984:CBF,
  author =       "Robert Piessens",
  title =        "The computation of {Bessel} functions on a small
                 computer",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "10",
  number =       "2",
  pages =        "161--166",
  month =        "????",
  year =         "1984",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:00:50 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122184900452",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Piessens:1984:CSA,
  author =       "R. Piessens",
  title =        "{Chebyshev} series approximations for the zeros of the
                 {Bessel} functions",
  journal =      j-J-COMPUT-PHYS,
  volume =       "53",
  number =       "1",
  pages =        "188--192",
  month =        jan,
  year =         "1984",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(84)90060-3",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:18 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999184900603",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Piessens:1984:SEF,
  author =       "R. Piessens",
  title =        "A Series Expansion for the First Positive Zero of the
                 {Bessel} Functions",
  journal =      j-MATH-COMPUT,
  volume =       "42",
  number =       "165",
  pages =        "195--197",
  month =        jan,
  year =         "1984",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A40 (65D20)",
  MRnumber =     "84m:33014",
  MRreviewer =   "M. E. Muldoon",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database; Theory/Comp.Alg.1.bib",
  acknowledgement = ack-nhfb,
  annote =       "Gives explicit series for first positive zero for 4
                 terms, using REDUCE.",
  classcodes =   "B0220 (Mathematical analysis); C1120 (Mathematical
                 analysis)",
  corpsource =   "Dept. of Computer Sci., Univ. of Leuven, Heverlee,
                 Belgium",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; poles and zeros; positive zero;
                 Reduce; series (mathematics); series expansion",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Schmidt:1984:TAI,
  author =       "J. W. Schmidt",
  title =        "Two-Sided Approximations of Inverses, Square Roots and
                 {Cholesky} Factors",
  journal =      "Comput. Math., Banach Center Publ.",
  volume =       "13",
  pages =        "483--497",
  year =         "1984",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-jr,
}

@Article{Seaton:1984:CFA,
  author =       "M. J. Seaton",
  title =        "{Coulomb} functions analytic in the energy",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-771",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82899-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:49 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584828994",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Takemasa:1984:CFC,
  author =       "T. Takemasa and T. Tamura and H. H. Wolter",
  title =        "{Coulomb} functions with complex angular momenta",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-562",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82737-X",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:33 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S001046558482737X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Talman:1984:LSC,
  author =       "James D. Talman",
  title =        "{LSFBTR}: a subroutine for calculating spherical
                 {Bessel} transforms",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-903",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)83002-7",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:58 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584830027",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Tamura:1984:CFC,
  author =       "Taro Tamura and Frank Rybicki",
  title =        "{Coulomb} functions for complex energies",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-5",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82276-6",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:55:58 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584822766",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Trojan:1984:LBF,
  author =       "George M. Trojan",
  title =        "Lower Bounds and Fast Algorithms for Sequence
                 Acceleration",
  journal =      j-J-ACM,
  volume =       "31",
  number =       "2",
  pages =        "329--335",
  month =        apr,
  year =         "1984",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Tight upper and lower bounds are obtained for sequence
                 accelerating. The lower bounds follow from a powerful
                 asymptotic adversary principle. Algorithms are
                 presented and shown to be almost optimal.",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Univ of Western Ontario, Dep of Physics, London,
                 Ont, Can",
  ajournal =     "J. Assoc. Comput. Mach.",
  classification = "723",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
  keywords =     "Algorithms; computer programming; convergence
                 acceleration; lower bounds; sequence acceleration;
                 upper bounds",
}

@Book{vanderLaan:1984:CSF,
  author =       "C. G. van der Laan and N. M. Temme",
  title =        "Calculation of special functions: the gamma function,
                 the exponential integrals and error-like functions",
  volume =       "10",
  publisher =    "Centre for Mathematics and Computer Science",
  address =      "Amsterdam, The Netherlands",
  pages =        "iv + 231",
  year =         "1984",
  ISBN =         "90-6196-277-3",
  ISBN-13 =      "978-90-6196-277-9",
  LCCN =         "QA1 M4591 no. 10",
  bibdate =      "Sat Oct 30 18:43:03 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "CWI tract / Centrum voor Wiskunde en Informatica",
  acknowledgement = ack-nhfb,
}

@Article{vonGudenberg:1984:BMG,
  author =       "J. Wolff {von Gudenberg}",
  title =        "{Berechnung maximal genauer Standardfunktionen mit
                 einfacher Mantissenl{\"a}nge} \toenglish {Computation
                 of Maximally Accurate Elementary Functions Using Simple
                 Mantissa Length} \endtoenglish",
  journal =      j-ELEK-RECHENANLAGEN,
  volume =       "26",
  number =       "5",
  pages =        "230--238",
  month =        oct,
  year =         "1984",
  CODEN =        "ELRAA4",
  ISSN =         "0013-5720",
  bibdate =      "Sun Oct 25 10:29:27 1998",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronische Rechenanlagen",
}

@Article{Walmsley:1984:EEM,
  author =       "John L. Walmsley",
  title =        "On the efficient evaluation of modified {Bessel}
                 functions of zeroth and first orders for arguments of
                 the form $ x \exp (i \pi / 4) $",
  journal =      j-J-COMPUT-PHYS,
  volume =       "56",
  number =       "2",
  pages =        "349--355",
  month =        nov,
  year =         "1984",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(84)90100-1",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:21 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999184901001",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Book{Wawrzynczyk:1984:GRS,
  author =       "Antoni Wawrzy{\'n}czyk and Aleksander Strasburger",
  title =        "Group representations and special functions",
  volume =       "8",
  publisher =    pub-REIDEL,
  address =      pub-REIDEL:adr,
  pages =        "xvi + 688",
  year =         "1984",
  ISBN =         "90-277-1269-7",
  ISBN-13 =      "978-90-277-1269-1",
  LCCN =         "QA171 .W3513 1984; QA1 M4281 v. 8",
  bibdate =      "Sat Oct 30 18:29:38 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Mathematics and its applications. East European
                 series",
  acknowledgement = ack-nhfb,
  remark =       "Translation of Polish title Wsp{\'o}\pm{}czesna teoria
                 funkcji specjalnych.",
  subject =      "Representations of groups; Functions, Special",
}

@Article{Wrigge:1984:NMG,
  author =       "Staffan Wrigge",
  title =        "A note on the moment generating function for the
                 reciprocal gamma distribution",
  journal =      j-MATH-COMPUT,
  volume =       "42",
  number =       "166",
  pages =        "617--621",
  month =        apr,
  year =         "1984",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (60E10 62E15 65U05)",
  MRnumber =     "86f:65042b",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Nat. Defence Res. Inst., Stockholm, Sweden",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Euler--Maclaurin expansion; moment generating
                 function; polynomials; reciprocal gamma distribution",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Akrivis:1985:ENC,
  author =       "G. Akrivis",
  title =        "The error norm of certain {Gaussian} quadrature
                 formulae",
  journal =      j-MATH-COMPUT,
  volume =       "45",
  number =       "172",
  pages =        "513--519",
  month =        oct,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D32",
  MRnumber =     "87a:65051",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290B (Error analysis in numerical methods); B0290F
                 (Interpolation and function approximation); C4110
                 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation)",
  corpsource =   "Math. Inst., Munchen Univ., West Germany",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "error analysis; error functional; error norm; function
                 approximation; Gaussian quadrature formulae;
                 integration; weight functions; wide class",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Arfken:1985:MMP,
  author =       "George B. (George Brown) Arfken",
  title =        "Mathematical methods for physicists",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  edition =      "Third",
  pages =        "xxii + 985",
  year =         "1985",
  ISBN =         "0-12-059820-5",
  ISBN-13 =      "978-0-12-059820-5",
  LCCN =         "QA37.2 .A74 1985",
  bibdate =      "Wed Mar 15 06:50:49 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/book/9780120598205",
  abstract =     "Mathematical Methods for Physicists, Third Edition
                 provides an advanced undergraduate and beginning
                 graduate study in physical science, focusing on the
                 mathematics of theoretical physics. This edition
                 includes sections on the non-Cartesian tensors,
                 dispersion theory, first-order differential equations,
                 numerical application of Chebyshev polynomials, the
                 fast Fourier transform, and transfer functions. Many of
                 the physical examples provided in this book, which are
                 used to illustrate the applications of mathematics, are
                 taken from the fields of electromagnetic theory and
                 quantum mechanics. The Hermitian operators, Hilbert
                 space, and concept of completeness are also
                 deliberated. This book is beneficial to students
                 studying graduate level physics, particularly
                 theoretical physics.",
  acknowledgement = ack-nhfb,
  author-dates = "1922--",
  subject =      "Mathematics; Mathematical physics; Math{\'e}matiques;
                 Physique math{\'e}matique; Mathematical physics.;
                 Mathematics.; Wiskundige methoden.; Reactoren.;
                 Groepentheorie.; Kwantummechanica.; Elektromechanica.;
                 Vectoren (wiskunde); Elektrodynamica.;
                 Math{\'e}matiques.; Physique math{\'e}matique.;
                 Math{\'e}matiques de l'ing{\'e}nieur.",
  tableofcontents = "Vector Analysis \\
                 Rotation of the Coordinate Axes \\
                 Scalar or Dot Product \\
                 Vector or Cross Product \\
                 Triple Scalar Product, Triple Vector Product \\
                 Gradient, [down triangle, open] \\
                 Divergence, [down triangle, open] \\
                 Curl, [down triangle, open] x \\
                 Successive Applications of [down triangle, open] \\
                 Vector Integration \\
                 Gauss's Theorem \\
                 Stokes's Theorem \\
                 Potential Theory \\
                 Gauss's Law, Poisson's Equation \\
                 Dirac Delta Function \\
                 Helmholtz's Theorem \\
                 Curved Coordinates, Tensors \\
                 Orthogonal Coordinates \\
                 Differential Vector Operators \\
                 Special Coordinate Systems: Introduction \\
                 Circular Cylindrical Coordinates \\
                 Spherical Polar Coordinates \\
                 Tensor Analysis \\
                 Contraction, Direct Product \\
                 Quotient Rule \\
                 Pseudotensors, Dual Tensors \\
                 Non-Cartesian Tensors \\
                 Tensor Derivative Operators \\
                 Determinants and Matrices \\
                 Determinants \\
                 Matrices \\
                 Orthogonal Matrices \\
                 Hermitian Matrices, Unitary Matrices \\
                 Diagonalization of Matrices \\
                 Normal Matrices \\
                 Group Theory \\
                 Introduction to Group Theory \\
                 Generators of Continuous Groups \\
                 Orbital Angular Momentum \\
                 Angular Momentum Coupling \\
                 Homogeneous Lorentz Group \\
                 Lorentz Covariance of Maxwell's Equations \\
                 Discrete Groups \\
                 Infinite Series \\
                 Convergence Tests \\
                 Alternating Series \\
                 Algebra of Series \\
                 Series of Functions \\
                 Taylor's Expansion \\
                 Power Series \\
                 Elliptic Integrals \\
                 Bernoulli Numbers, Euler-Maclaurin Formula \\
                 Asymptotic Series \\
                 Infinite Products \\
                 Functions of a Complex Variable I \\
                 Complex Algebra",
}

@Article{Bank:1985:SEM,
  author =       "Randolph E. Bank and Craig C. Douglas",
  title =        "Sharp estimates for multigrid rates of convergence
                 with general smoothing and acceleration",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "22",
  number =       "4",
  pages =        "617--633",
  month =        aug,
  year =         "1985",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65F10 (65N20)",
  MRnumber =     "86j:65037",
  MRreviewer =   "L. W. Ehrlich",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  keywords =     "convergence acceleration",
}

@InProceedings{Bannur:1985:VIS,
  author =       "J. Bannur and A. Varma",
  title =        "The {VLSI} Implementation of a Square Root Algorithm",
  crossref =     "Hwang:1985:PSC",
  pages =        "159--165",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Bannur_Varma.pdf",
  abstract =     "VLSI implementation of a square root algorithm is
                 studied. Two possible implementations of the basic
                 nonrestoring algorithm are presented --- the second is
                 more area-efficient and modular than the first. The
                 implementations are simple and easy to control, but, at
                 the same time, are more area-time efficient than many
                 existing designs. A hardware algorithm suited to
                 microprogram implementation is also given. Extension of
                 the algorithms to achieve $ 1 / 2 $-bit precision is
                 discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Borodin:1985:DND,
  author =       "Allan Borodin and Ronald Fagin and John E. Hopcroft
                 and Martin Tompa",
  title =        "Decreasing the Nesting Depth of Expressions Involving
                 Square Roots",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "1",
  number =       "2",
  pages =        "169--188",
  month =        jun,
  year =         "1985",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  MRclass =      "68Q40 (12F05)",
  MRnumber =     "87a:68087",
  bibdate =      "Sat May 10 15:54:09 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
  keywords =     "Simplification",
}

@Article{Brezinski:1985:CAM,
  author =       "Claude Brezinski",
  title =        "Convergence acceleration methods: the past decade",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "12--13",
  number =       "??",
  pages =        "19--36",
  month =        may,
  year =         "1985",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(85)90005-6",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65Bxx (65J05)",
  MRnumber =     "793942 (86f:65019)",
  bibdate =      "Thu Dec 01 10:11:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "convergence acceleration",
  remark =       "Proceedings of the international conference on
                 computational and applied mathematics (Leuven, 1984).",
}

@Article{Carlson:1985:AEF,
  author =       "B. C. Carlson and John L. Gustafson",
  title =        "Asymptotic expansion of the first elliptic integral",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "16",
  number =       "5",
  pages =        "1072--1092",
  month =        sep,
  year =         "1985",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33A25 (41A60)",
  MRnumber =     "87d:33002",
  MRreviewer =   "Kusum Soni",
  bibdate =      "Sat Dec 5 18:14:13 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@Article{Cathey:1985:ISR,
  author =       "James Cathey",
  title =        "68000 Integer square root routine in {16BST}",
  journal =      j-DDJ,
  volume =       "10",
  number =       "5",
  pages =        "118--??",
  month =        may,
  year =         "1985",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@InProceedings{Conover:1985:AHS,
  author =       "B. Conover and D. L. Gustafson",
  title =        "An Algorithm for High Speed Square Roots",
  crossref =     "IEEE:1985:ERC",
  pages =        "19--21",
  year =         "1985",
  bibdate =      "Fri Jun 11 18:04:41 1999",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Frenzen:1985:NAE,
  author =       "C. L. Frenzen and R. Wong",
  title =        "A note on asymptotic evaluation of some {Hankel}
                 transforms",
  journal =      j-MATH-COMPUT,
  volume =       "45",
  number =       "172",
  pages =        "537--548",
  month =        oct,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "41A60 (44A15 65R10)",
  MRnumber =     "87c:41024",
  MRreviewer =   "F. W. J. Olver",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0230 (Integral transforms); B0290Z (Other numerical
                 methods)C1130 (Integral transforms); C4190 (Other
                 numerical methods)",
  corpsource =   "Dept. of Math., British Columbia Univ., Vancouver, BC,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "asymptotic expansion; Bessel function; Bessel
                 functions; growth condition; Hankel transforms;
                 meromorphic function; transforms",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Gal:1985:CEF,
  author =       "Shmuel Gal",
  title =        "Computing Elementary Functions: a New Approach for
                 Achieving High Accuracy and Good Performance",
  crossref =     "Miranker:1985:ASC",
  pages =        "1--16",
  year =         "1985",
  DOI =          "https://doi.org/10.1007/3-540-16798-6_1",
  bibdate =      "Thu Sep 01 12:27:23 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Gustafson:1985:SCA,
  author =       "Sven-{\AA}ke Gustafson",
  title =        "Stable convergence acceleration using {Laplace}
                 transforms",
  journal =      j-NUM-MATH,
  volume =       "47",
  number =       "3",
  pages =        "387--394",
  month =        nov,
  year =         "1985",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65B10 (65D30)",
  MRnumber =     "86m:65009",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "B0230 (Integral transforms); C1130 (Integral
                 transforms)",
  corpsource =   "Dept. of Numerical Anal. and Comput. Sci., R. Inst. of
                 Technol., Stockholm, Sweden",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "convergence acceleration; Laplace transforms; power
                 series; quadrature schemes; series (mathematics);
                 stable convergence acceleration",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Hill:1985:RCS,
  author =       "I. D. Hill and M. C. Pike",
  title =        "Remark on ``{Algorithm 299: Chi-Squared Integral}''",
  journal =      j-TOMS,
  volume =       "11",
  number =       "2",
  pages =        "185--185",
  month =        jun,
  year =         "1985",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Feb 06 05:28:22 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See
                 \cite{Hill:1967:ACS,elLozy:1976:RAC,elLozy:1979:RAS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hull:1985:PRV,
  author =       "T. E. Hull and A. Abrham",
  title =        "Properly Rounded Variable Precision Square Root",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "229--237",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214408.214413",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15 (65G05)",
  MRnumber =     "87a:65041",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p229-hull/;
                 http://www.acm.org/pubs/toc/Abstracts/toms/214413.html",
  abstract =     "The square root function presented here returns a
                 properly rounded approximation to the square root of
                 its argument, or it raises an error condition if the
                 argument is negative. {\em Properly rounded} means
                 rounded to the nearest, or to nearest even in case of a
                 tie. It is {\em variable precision} in that it is
                 designed to return a $p$-digit approximation to a
                 $p$-digit argument, for any $ p > 0 $. (Precision $p$
                 means $p$ decimal digits.) The program and the analysis
                 are valid for all $ p > 0 $, but current
                 implementations place some restrictions on $p$.",
  acknowledgement = ack-nhfb,
  catcode =      "G.4; G.4; G.1.0; G.1.2; G.4; G.1.0",
  CRclass =      "G.4 Algorithm analysis; G.4 Verification; G.1.0
                 General; G.1.0 Numerical algorithms; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.4 Certification and testing; G.1.0 General; G.1.0
                 Error analysis",
  descriptor =   "Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis; Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Verification; Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing; Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Error
                 analysis",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  genterm =      "algorithms; verification",
  guideno =      "02789",
  journal-URL =  "https://dl.acm.org/loi/toms",
  jrldate =      "Sept. 1985",
  keywords =     "algorithms; decimal floating-point arithmetic;
                 verification",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Verification. {\bf
                 G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Error analysis. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms.",
}

@Article{Humblet:1985:BFE,
  author =       "J. Humblet",
  title =        "{Bessel} function expansions of {Coulomb} wave
                 functions",
  journal =      j-J-MATH-PHYS,
  volume =       "26",
  number =       "4",
  pages =        "656--659",
  month =        apr,
  year =         "1985",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.526602",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "81C05 (33A40 81G45)",
  MRnumber =     "87c:81034",
  bibdate =      "Mon Oct 31 11:57:19 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v26/i4/p656_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "4",
}

@Article{Jones:1985:CIG,
  author =       "William B. Jones and W. J. Thron",
  title =        "On the computation of incomplete gamma functions in
                 the complex domain",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "12--13",
  number =       "??",
  pages =        "401--417",
  month =        may,
  year =         "1985",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:27:12 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042785900342",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Kravchuk:1985:ACE,
  author =       "V. R. Kravchuk",
  title =        "Approximation of certain elementary functions by
                 rational functions of order $ (n, 2) $. ({Russian})",
  journal =      "Akad. Nauk Ukrain. SSR Inst. Mat. Preprint",
  volume =       "18",
  pages =        "7--40",
  year =         "1985",
  MRclass =      "41A25 (41A10)",
  MRnumber =     "87b:41017",
  MRreviewer =   "R. Smarzewski",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Kravchuk:1985:EAE,
  author =       "V. R. Kravchuk",
  title =        "Effective approximation of elementary functions by
                 rational polynomials of order $ (n, 1) $. ({Russian})",
  journal =      j-UKR-MAT-Z,
  volume =       "37",
  number =       "2",
  pages =        "175--180, 270",
  year =         "1985",
  CODEN =        "UMZHAA",
  ISSN =         "0041-6053",
  MRclass =      "41A20 (41A25)",
  MRnumber =     "86h:41013",
  MRreviewer =   "Miguel A. Jim{\'e}nez Pozo",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Ukrainskii matematicheskii zhurnal",
  language =     "Russian",
}

@Article{Lazard:1985:PFD,
  author =       "Daniel Lazard",
  title =        "Primitives des fonctions {\'e}l{\'e}mentaires
                 (d'apr{\`e}s {Risch} et {Davenport}). ({French})
                 [Primitives of elementary functions (following {Risch}
                 and {Davenport})] {Seminar Bourbaki, Vol. 1983/84, No.
                 121-122}",
  journal =      "Ast{\'e}risque",
  volume =       "121--122",
  pages =        "295--308",
  year =         "1985",
  MRclass =      "12H05 (12-04)",
  MRnumber =     "86k:12010",
  MRreviewer =   "J. H. Davenport",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@Article{Lewanowicz:1985:RRH,
  author =       "Stanis{\l}aw Lewanowicz",
  title =        "Recurrence relations for hypergeometric functions of
                 unit argument",
  journal =      j-MATH-COMPUT,
  volume =       "45",
  number =       "172",
  pages =        "521--535",
  month =        oct,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A35 (65Q05)",
  MRnumber =     "86m:33004",
  MRreviewer =   "S. Conde",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290 (Numerical analysis); C4100 (Numerical
                 analysis)",
  corpsource =   "Inst. of Comput. Sci., Wroclaw Univ., Poland",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "(mathematics); convergence of numerical methods;
                 hypergeometric function; numerical analysis; recurrence
                 relation; series; unit argument",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Lo:1985:GPB,
  author =       "Hao-Yung Lo and Y. Aoki",
  title =        "Generation of a Precise Binary Logarithm with
                 Difference Grouping Programmable Logic Array",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "8",
  pages =        "681--691",
  month =        aug,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676614",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:33:17 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676614",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Majerski:1985:SRA,
  author =       "S. Majerski",
  title =        "Square-Rooting Algorithms for High-Speed Digital
                 Circuits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "8",
  pages =        "724--733",
  month =        aug,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676618",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:33:17 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676618",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Martin:1985:FAB,
  author =       "Pablo Mart{\'\i}n and Antonio L. Guerrero",
  title =        "Fractional approximations to the {Bessel} function {$
                 J_0 (x) $}",
  journal =      j-J-MATH-PHYS,
  volume =       "26",
  number =       "4",
  pages =        "705--707",
  month =        apr,
  year =         "1985",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.526610",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "41A21 (33A40)",
  MRnumber =     "86g:41031",
  MRreviewer =   "Hans-J{\"u}rgen Albrand",
  bibdate =      "Mon Oct 31 11:57:19 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v26/i4/p705_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "3",
}

@Article{Milgram:1985:GIE,
  author =       "M. S. Milgram",
  title =        "The Generalized Integro-Exponential Function",
  journal =      j-MATH-COMPUT,
  volume =       "44",
  number =       "170",
  pages =        "443--458",
  month =        apr,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A70 (65D15)",
  MRnumber =     "86c:33024",
  MRreviewer =   "S. Conde",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290D (Functional analysis); B0290F (Interpolation
                 and function approximation); C4120 (Functional
                 analysis); C4130 (Interpolation and function
                 approximation)",
  corpsource =   "AECL, Chalk River, Ont., Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "exponential function; exponential integral;
                 first-order functions; function; function
                 approximation; function evaluation; generalized
                 integro-; incomplete gamma; minimax; rational minimax
                 approximations; techniques",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Muller:1985:DBC,
  author =       "Jean-Michel Muller",
  title =        "Discrete basis and computation of elementary
                 functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "9",
  pages =        "857--862",
  month =        sep,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676643",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65D20 (65V05)",
  MRnumber =     "87e:65016",
  MRreviewer =   "D. Zwick",
  bibdate =      "Sun Jul 10 08:33:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676643",
  abstract =     "We give necessary and sufficient conditions in order
                 that the infinite product or sum of the terms of a
                 positive decreasing sequence generates the reals in a
                 given interval.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InCollection{Muller:1985:RNR,
  author =       "Jean-Michel Muller",
  booktitle =    "Seminar on number theory, 1984--1985 (Talence,
                 1984/1985)",
  title =        "Repr{\'e}sentation des nombres r{\'e}els et calcul des
                 fonctions {\'e}l{\'e}mentaires. ({French})
                 [Representation of real numbers and calculation of
                 elementary functions]",
  volume =       "12",
  publisher =    "Univ. Bordeaux {I}",
  address =      "Talence, France",
  pages =        "22",
  year =         "1985",
  MRclass =      "26-04 (11B13 11B34 26A09)",
  MRnumber =     "87k:26001",
  MRreviewer =   "S. L. Segal",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "French",
  remark =       "From the MRreview: ``About one third of the paper is
                 devoted to algorithms for calculating quantities like
                 square root, exponential, logarithm, or trigonometric
                 funtions, using discrete bases. Indeed, the major
                 motivation for the present paper is obtaining simple
                 algorithms which can easily be realized by
                 hardware.''",
}

@TechReport{Parlett:1985:DAA,
  author =       "Beresford N. Parlett and K. C. Ng",
  title =        "Development of an accurate algorithm for {$ \exp (B t)
                 $}",
  type =         "Technical Report",
  number =       "PAM-294",
  institution =  inst-CPAM-UCB,
  address =      inst-CPAM-UCB:adr,
  month =        aug,
  year =         "1985",
  bibdate =      "Fri Nov 11 09:06:19 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Peralta:1985:TRN,
  author =       "Rene Caupolican Peralta",
  title =        "Three results in number theory and cryptography: a new
                 algorithm to compute square roots modulo a prime
                 number; On the bit complexity of the discrete
                 logarithm; a framework for the study of
                 cryptoprotocols",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "52",
  month =        dec,
  year =         "1985",
  LCCN =         "????",
  bibdate =      "Sat Oct 17 16:25:07 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "dissertations; dissertations, academic --- UCB ---
                 computer science --- 1981--1990; University of
                 California, Berkeley. computer science division --",
}

@Article{Pereira:1985:ECF,
  author =       "N. Costa Pereira",
  title =        "Estimates for the {Chebyshev} function $ \psi (x) -
                 \theta (x) $",
  journal =      j-MATH-COMPUT,
  volume =       "44",
  number =       "169",
  pages =        "211--221",
  month =        jan,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11A25 (11N45 11Y35 33A70)",
  MRnumber =     "86k:11005",
  bibdate =      "Thu Jun 15 07:26:46 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  note =         "See corrigendum \cite{Pereira:1987:CEC}.",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Chebyshev approximation; Chebyshev function",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Schoof:1985:ECF,
  author =       "Ren{\'e} Schoof",
  title =        "Elliptic Curves Over Finite Fields and the Computation
                 of Square Roots $ \operatorname {mod} p $",
  journal =      j-MATH-COMPUT,
  volume =       "44",
  number =       "170",
  pages =        "483--494",
  month =        apr,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y16 (11G20 14G15)",
  MRnumber =     "86e:11122",
  MRreviewer =   "Karl Rubin",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0250 (Combinatorial mathematics); B0290D (Functional
                 analysis); C1160 (Combinatorial mathematics); C4120
                 (Functional analysis); C4240 (Programming and algorithm
                 theory)",
  corpsource =   "Amsterdam Univ., Netherlands",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computational complexity; deterministic algorithm;
                 elliptic curve; F/sub q/-points; finite fields;
                 function evaluation; number theory; square roots mod p;
                 Weierstrass equation",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Shah:1985:SAA,
  author =       "Arvind K. Shah",
  title =        "A Simpler Approximation for Areas Under the Standard
                 Normal Curve",
  journal =      j-AMER-STAT,
  volume =       "39",
  number =       "1",
  pages =        "80--80",
  month =        feb,
  year =         "1985",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Jan 27 12:40:28 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326426;
                 https://www.math.utah.edu/pub/tex/bib/amstat1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2683918",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Spijker:1985:SRS,
  author =       "M. N. Spijker",
  title =        "Stepsize restrictions for stability of one-step
                 methods in the numerical solution of initial value
                 problems",
  journal =      j-MATH-COMPUT,
  volume =       "45",
  number =       "172",
  pages =        "377--392",
  month =        oct,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65L20 (65M10)",
  MRnumber =     "86j:65106",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "A0260 (Numerical approximation and analysis); A0560
                 (Transport processes: theory); B0290F (Interpolation
                 and function approximation); B0290P (Differential
                 equations); C4130 (Interpolation and function
                 approximation); C4170 (Differential equations); C7320
                 (Physics and chemistry computing)",
  corpsource =   "Inst. of Appl. Math. and Comput. Sci., Leiden Univ.,
                 Netherlands",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "convection; convergence of numerical methods;
                 differential equations; diffusion;
                 diffusion-convection; error growth; initial value
                 problems; iterative methods; numerical solution;
                 partial; problem; stability of one-step methods;
                 stepsize restrictions",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Sreedharan:1985:ASS,
  author =       "J. Sreedharan and A. Dhurkadas",
  title =        "8086 algorithm solves square roots",
  journal =      j-EDN,
  volume =       "30",
  number =       "7",
  pages =        "272",
  month =        apr,
  year =         "1985",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@Article{Temme:1985:LTI,
  author =       "N. M. Temme",
  title =        "{Laplace} type integrals: transformation to standard
                 form and uniform asymptotic expansions",
  journal =      j-QUART-APPL-MATH,
  volume =       "43",
  number =       "1",
  pages =        "103--123",
  year =         "1985",
  CODEN =        "QAMAAY",
  DOI =          "https://doi.org/10.1090/qam/782260",
  ISSN =         "0033-569x (print), 1552-4485 (electronic)",
  ISSN-L =       "0033-569X",
  MRclass =      "44A10 (41A60)",
  MRnumber =     "782260",
  MRreviewer =   "I. Feny{\H{o}}",
  bibdate =      "Tue Feb 6 11:42:02 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Quarterly of Applied Mathematics",
  journal-URL =  "http://dl.acm.org/citation.cfm?id=J641;
                 http://www.ams.org/journals/qam",
}

@Article{Agarwal:1986:NSV,
  author =       "Ramesh C. Agarwal and James W. Cooley and Fred G.
                 Gustavson and James B. Shearer and Gordon Slishman and
                 Bryant Tuckerman",
  title =        "New Scalar and Vector Elementary Functions for the
                 {IBM System\slash 370}",
  journal =      j-IBM-JRD,
  volume =       "30",
  number =       "2",
  pages =        "126--144",
  month =        mar,
  year =         "1986",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "76W05",
  MRnumber =     "840 341",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See clarification \cite{Agarwal:1987:CNS}.",
  abstract =     "Algorithms have been developed to compute short-and
                 long-precision elementary functions: SIN, COS, TAN,
                 COTAN, LOG, LOG10, EXP, POWER, SQRT, ATAN, ASIN, ACOS,
                 ATAN2, and CABS, in scalar (28 functions) and vector
                 (22 functions) mode. They have been implemented as part
                 of the new VS FORTRAN library recently announced along
                 with the IBM 3090 Vector Facility. These algorithms are
                 essentially table-based algorithms. An important
                 feature of these algorithms is that they produce
                 bitwise-identical results on scalar and vector
                 System\slash 370 machines. Of these, for five functions
                 the computed value result is always the correctly
                 rounded value of the infinite-precision result. For the
                 rest of the functions, the value returned is one of the
                 two floating-point neighbors bordering the
                 infinite-precision result, which implies exact results
                 if they are machine-representable. For the five
                 correctly rounded elementary functions, scalar and
                 vector algorithms are designed independently to
                 optimize performance in each case.",
  acknowledgement = ack-nhfb,
  classification = "723",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  journalabr =   "IBM J Res Dev",
  keywords =     "algorithms; Algorithms; computer metatheory; computer
                 programming; computer programming languages ---
                 fortran; design; elementary functions; fortran library;
                 IBM System/370; infinite-precision result; measurement;
                 performance; table-based algorithms",
  subject =      "C.4 Computer Systems Organization, PERFORMANCE OF
                 SYSTEMS \\ I.1.2 Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms \\ F.3.3 Theory of
                 Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies
                 of Program Constructs, Functional constructs \\ C.1.2
                 Computer Systems Organization, PROCESSOR ARCHITECTURES,
                 Multiple Data Stream Architectures (Multiprocessors),
                 Array and vector processors",
}

@Article{Amos:1986:APP,
  author =       "D. E. Amos",
  title =        "{Algorithm 644}: a Portable Package for {Bessel}
                 Functions of a Complex Argument and Nonnegative Order",
  journal =      j-TOMS,
  volume =       "12",
  number =       "3",
  pages =        "265--273",
  month =        sep,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/7921.214331",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "889 069",
  bibdate =      "Tue Mar 09 10:26:27 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also
                 \cite{Amos:1990:RPP,Amos:1995:RAP,Kodama:2007:RA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p265-amos/",
  abstract =     "This algorithm is a package of subroutines for
                 Computing Bessel functions $ H_v^{(1)}(z) $, $
                 H_v^{(2)}(z) $, $ I_v(z) $, $ J_v(z) $, $ K_v(z) $, $
                 Y_v(z) $ and Airy functions $ \mbox {Ai}(z) $, $ \mbox
                 {Ai}'(z) $, $ \mbox {Bi}(z) $, $ \mbox {Bi}'(z) $ for
                 orders $ v \geq 0 $ and complex $z$ in $ - \pi < \mbox
                 {arg} z \leq \pi $. Eight callable subroutines and
                 their double-precision counterparts are provided.
                 Exponential scaling and sequence generation are
                 auxiliary options.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.m}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Miscellaneous. {\bf G.m}: Mathematics of Computing,
                 MISCELLANEOUS.",
}

@Article{Andrews:1986:SCA,
  author =       "George E. Andrews and Ian P. Goulden and David M.
                 Jackson",
  title =        "{Shanks}' convergence acceleration transform,
                 {Pad{\'e}} approximants and partitions",
  journal =      j-J-COMB-THEORY-A,
  volume =       "43",
  number =       "1",
  pages =        "70--84",
  year =         "1986",
  CODEN =        "JCBTA7",
  DOI =          "https://doi.org/10.1016/0097-3165(86)90024-5",
  ISSN =         "0097-3165 (print), 1096-0899 (electronic)",
  ISSN-L =       "0097-3165",
  MRclass =      "65B99 (11N99 11Y35)",
  MRnumber =     "859298 (88c:65005)",
  MRreviewer =   "Kenneth A. Jukes",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Combinatorial Theory (Series A)",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00973165",
  keywords =     "convergence acceleration",
}

@Article{Bustoz:1986:GFI,
  author =       "Joaquin Bustoz and Mourad E. H. Ismail",
  title =        "On Gamma Function Inequalities",
  journal =      j-MATH-COMPUT,
  volume =       "47",
  number =       "176",
  pages =        "659--667",
  month =        oct,
  year =         "1986",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A15 (26D20)",
  MRnumber =     "87m:33002",
  MRreviewer =   "G. Gasper",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1130 (Integral transforms); C1140Z (Other and
                 miscellaneous)",
  corpsource =   "Dept. of Math., Arizona State Univ., Tempe, AZ, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "gamma function inequalities; infinite divisibility;
                 Laplace; Laplace transforms; monotonic functions;
                 probability; probability distributions; quotients;
                 transforms",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Campbell:1986:NSR,
  author =       "R. A. Campbell",
  title =        "{NS32000} Square Roots",
  journal =      j-DDJ,
  volume =       "11",
  number =       "3",
  pages =        "122--123, 106",
  month =        mar,
  year =         "1986",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Fri Dec 08 13:05:56 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Article{Cathey:1986:LEI,
  author =       "J. Cathey",
  title =        "Letter to the editor [Integer Square Root]",
  journal =      j-DDJ,
  volume =       "11",
  number =       "8",
  pages =        "14, 82--85",
  month =        aug,
  year =         "1986",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Thu Sep 08 07:59:25 1994",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Article{Clenshaw:1986:GEL,
  author =       "C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olver
                 and P. R. Turner",
  title =        "Generalized Exponential and Logarithmic Functions",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "12",
  number =       "5--6",
  pages =        "1091--1101",
  month =        sep # "\slash " # dec,
  year =         "1986",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(86)90233-6",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "33A70 (39B10 65G05)",
  MRnumber =     "MR0871348 (88a:33027)",
  bibdate =      "Fri Jul 09 06:27:26 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Generalizations of the exponential and logarithmic
                 functions are defined and an investigation is made of
                 two possible versions of these functions. Some
                 applications are described, including computer
                 arithmetic, properties of very large and very small
                 numbers, and the determination of functional roots.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Clenshaw:1986:UAR,
  author =       "C. W. Clenshaw and F. W. J. Olver",
  title =        "Unrestricted algorithms for reciprocals and square
                 roots",
  journal =      j-BIT,
  volume =       "26",
  number =       "4",
  pages =        "475--492",
  month =        dec,
  year =         "1986",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01935054",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65D20",
  MRnumber =     "87k:65019",
  MRreviewer =   "Luciano Biasini",
  bibdate =      "Wed Jan 4 18:52:19 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=26&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=26&issue=4&spage=475",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  xxpages =      "476--492??",
}

@Article{DiDonato:1986:CIG,
  author =       "Armido R. DiDonato and Alfred H. {Morris, Jr.}",
  title =        "Computation of the Incomplete Gamma Function Ratios
                 and Their Inverse",
  journal =      j-TOMS,
  volume =       "12",
  number =       "4",
  pages =        "377--393",
  month =        dec,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/22721.23109",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:31:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-4/p377-didonato/",
  abstract =     "An algorithm is given for computing the incomplete
                 gamma function ratios $ P(a, x) $ and $ Q(a, x) $ for $
                 a \geq 0 $, $ x \geq 0 $, $ a + x \neq 0 $. Temme's
                 uniform asymptotic expansions are used. The algorithm
                 is robust; results accurate to 14 significant digits
                 can be obtained. An extensive set of coefficients for
                 the Temme expansions is included.\par

                 An algorithm, employing third-order Schr{\"o}der
                 iteration supported by Newton-Raphson iteration, is
                 provided for computing $x$ when $a$, $ P(a, x) $, and $
                 Q(a, x) $ are given. Three iterations at most are
                 required to obtain 10 significant digit accuracy for
                 $x$.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  review =       "ACM CR 8709-0775",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation.",
}

@Article{DiMarzio:1986:IPA,
  author =       "F. {Di Marzio}",
  title =        "An improved procedure for the accurate evaluation of
                 polygamma functions with integer and half-integer
                 argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "39",
  number =       "3",
  pages =        "343--345",
  month =        apr,
  year =         "1986",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(86)90095-0",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:28:13 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465586900950",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Dutka:1986:SRT,
  author =       "Jacques Dutka",
  title =        "On square roots and their representations",
  journal =      j-ARCH-HIST-EXACT-SCI,
  volume =       "36",
  number =       "1",
  pages =        "21--39",
  month =        mar,
  year =         "1986",
  CODEN =        "AHESAN",
  DOI =          "https://doi.org/10.1007/BF00357439",
  ISSN =         "0003-9519 (print), 1432-0657 (electronic)",
  ISSN-L =       "0003-9519",
  MRclass =      "01A05 (11-03 11A63)",
  MRnumber =     "863340 (87m:01003)",
  MRreviewer =   "Donald Cook",
  bibdate =      "Fri Feb 4 21:50:24 MST 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=36&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=36&issue=1&spage=21",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for History of Exact Sciences",
  journal-URL =  "http://link.springer.com/journal/407",
  MRtitle =      "On square roots and their representations",
}

@Article{Evans:1986:RIU,
  author =       "D. J. Evans and G. M. Megson",
  title =        "{Romberg} integration using systolic arrays",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "3",
  number =       "4",
  pages =        "289--304",
  month =        oct,
  year =         "1986",
  CODEN =        "PACOEJ",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "11019",
  catcode =      "G.1.1; G.1.2",
  CRclass =      "G.1.1 Interpolation; G.1.1 Extrapolation; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Extrapolation; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Parallel Computing",
  genterm =      "theory; design; algorithms",
  guideno =      "1986-10554",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191",
  journalabbrev = "Parallel Comput.",
  jrldate =      "Oct. 1986",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{FernandezVelicia:1986:HPA,
  author =       "F. J. {Fern{\'a}ndez Velicia}",
  title =        "High-precision analytic approximations for the
                 {Fermi--Dirac} functions by means of elementary
                 functions",
  journal =      j-PHYS-REV-A-3,
  volume =       "34",
  number =       "5",
  pages =        "4387--4395",
  year =         "1986",
  CODEN =        "PLRAAN",
  ISSN =         "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519",
  MRclass =      "33A70 (82A05)",
  MRnumber =     "MR869021 (88b:33024)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review. A. Third Series",
  journal-URL =  "http://pra.aps.org/browse",
}

@Article{Froman:1986:PIF,
  author =       "Per Olof Fr{\"o}man and Finn Karlsson and Staffan
                 Yngve",
  title =        "Phase-integral formulas for {Bessel} functions and
                 their relation to already existing asymptotic
                 formulas",
  journal =      j-J-MATH-PHYS,
  volume =       "27",
  number =       "11",
  pages =        "2738--2747",
  month =        nov,
  year =         "1986",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.527296",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "41A60 (33A40 81C12)",
  MRnumber =     "87j:41073",
  bibdate =      "Mon Oct 31 11:57:50 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v27/i11/p2738_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "10",
}

@InProceedings{Gal:1986:CEF,
  author =       "Shmuel Gal",
  title =        "Computing elementary functions: a new approach for
                 achieving high accuracy and good performance",
  crossref =     "Miranker:1986:ASC",
  pages =        "1--16",
  year =         "1986",
  MRclass =      "65D20",
  MRnumber =     "868 283",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Math/elefunt.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gustavson:1986:FEF,
  author =       "F. G. Gustavson",
  title =        "Fast Elementary Function Algorithms for 370 Machines",
  crossref =     "Miranker:1986:ASC",
  pages =        "17--17",
  year =         "1986",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Misc/MPG/lncs235.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Book{Hochstadt:1986:FMP,
  author =       "Harry Hochstadt",
  title =        "The Functions of Mathematical Physics",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xi + 322",
  year =         "1986",
  ISBN =         "0-486-65214-9 (paperback), 0-486-16878-6 (e-book)",
  ISBN-13 =      "978-0-486-65214-6 (paperback), 978-0-486-16878-4
                 (e-book)",
  LCCN =         "QA351 .H68 1986",
  bibdate =      "Tue Dec 5 10:51:16 MST 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "1: Orthogonal Polynomials \\
                 1 Linear Spaces / 1 \\
                 2 Orthogonal Polynomials / 6 \\
                 3 The Recurrence Formula / 8 \\
                 4 The Christoffel--Darboux Formula / 9 \\
                 5 The Weierstrass Approximation Theorem / 11 \\
                 6 The Zeros of the Orthogonal Polynomials / 14 \\
                 7 Approximation Theory / 16 \\
                 8 More about the Zeros of the Orthonormal Polynomials /
                 23 \\
                 9 The completeness of the Orthonormal Polynomials in
                 the Space of Square-Integrable Functions / 27 \\
                 10 Generalizations and an Application to Conformal
                 Mappings / 32 \\
                 \\
                 2: The Classical Orthogonal Polynomials 1 Rodrigues'
                 Formula and the Classical Orthogonal Polynomials / 39
                 \\
                 2 The Differential Equations Satisfied by the Classical
                 Orthogonal Polynomials / 43 \\
                 3 On the Zeros of the Jacobi Polynomials / 45 \\
                 4 An Alternative Approach to the Tchebicheff
                 Polynomials / 46 \\
                 5 An Application of the Hermite Polynomials to Quantum
                 Mechanics / 49 \\
                 6 The Completeness of the Hermite and Laguerre
                 Polynomials / 53 \\
                 7 Generating Functions / 57 \\
                 \\
                 3: The Gamma Function 1 Definitions and Basic
                 Properties / 61 \\
                 2 Analytic Continuation and Integral Representations /
                 65 \\
                 3 Asymptotic Expansions / 69 \\
                 4 Beta Functions / 75 \\
                 5 The Logarithmic Derivative of the Gamma Function / 77
                 \\
                 6 Mellin--Barnes Integrals / 78 \\
                 7 Mellin Transforms / 80 \\
                 8 Applications to Algebraic Equations / 81 \\
                 \\
                 4: Hypergeometric Functions 1 Review of Linear
                 Differential Equations with Regular Singular Points /
                 88 \\
                 2 The Hypergeometric Differential Equation / 90 \\
                 3 The Hypergeometric Function / 93 \\
                 4 A General Method for Finding Integral Representations
                 / 100 \\
                 5 Integral Representations for the Hypergeometric
                 Function / 105 \\
                 6 The Twenty-four Solutions of the Hypergeometric /
                 Equation106 \\
                 7 The Schwarz--Christoffel Transformation / 112 \\
                 8 Mappings of Curvilinear Triangles / 119 \\
                 9 Group Theoretic Discussion of the Case $ \pi(\alpha_1
                 + \alpha_2 + \alpha_3) > \pi$ / 130 \\
                 10 Nonlinear Transformations of Hypergeometric
                 Functions / 132 \\
                 \\
                 5: The Legendre Functions 1 Laplace's Differential
                 Equation / 138 \\
                 2 Maxwell's Theory of Poles / 140 \\
                 3 Relationship to the Hypergeometric Functions / 141
                 \\
                 4 Expansion Formulas / 147 \\
                 5 The Addition Theorem / 149 \\
                 6 Green's Functions / 153 \\
                 7 The Complete Solution of Legendre's Differential
                 Equation / 156 \\
                 8 Asymptotic Formulas / 161 \\
                 \\
                 6: Spherical Harmonics in $p$ Dimensions 1 Homogeneous
                 Polynomials / 168 \\
                 2 Orthogonality of Spherical Harmonics / 171 \\
                 3 Legendre Polynomials / 175 \\
                 4 Applications to Boundary Value Problems / 183 \\
                 \\
                 7: Confluent Hypergeometric Functions 1 Relationship to
                 the Hypergeometric Functions / 189 \\
                 2 Applications of These Functions in Mathematical
                 Physics / 191 \\
                 3 Integral Representations / 195 \\
                 4 Asymptotic Representations / 198 \\
                 \\
                 8: Bessel Functions 1 Basic Definitions / 200 \\
                 2 Integral Representations / 203 \\
                 3 Relationship to the Legendre Functions / 205 \\
                 4 The Generating Function of the Bessel Function / 207
                 \\
                 5 More Integral Representations / 210 \\
                 6 Addition Theorems / 216 \\
                 7 The Complete Solution of Bessel's Equation / 223 \\
                 8 Asymptotic Expansions for Large Argument / 225 \\
                 9 Airy Functions / 230 \\
                 10 Asymptotic Expansions for Large Indices and Large
                 Arguments / 235 \\
                 11 Some Applications of Bessel Functions in Physical
                 Optics / 241 \\
                 12 The Zeros of Bessel Functions / 249 \\
                 13 Fourier--Bessel Expansions / 257 \\
                 14 Applications in Mathematical Physics / 266 \\
                 15 Discontinuous Integrals / 269 \\
                 \\
                 9: Hill's Equation 1 Mathieu's Equation / 281 \\
                 2 Hill's Equation / 282 \\
                 3 The Discriminant / 287 \\
                 4 Expansion Theorems / 299 \\
                 5 Inverse Problems / 305 \\
                 6 Hill's Equations with Even Coefficients / 309 \\
                 7 Mathieu's Equation Revisited / 310 \\
                 8 Energy Bands in Crystals / 313 \\
                 Appendix / 314 \\
                 \\
                 Bibliography / 318 \\
                 \\
                 Index / 321",
}

@Article{Hull:1986:VPE,
  author =       "T. E. Hull and A. Abrham",
  title =        "Variable Precision Exponential Function",
  journal =      j-TOMS,
  volume =       "12",
  number =       "2",
  pages =        "79--91",
  month =        jun,
  year =         "1986",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15 (65D20)",
  MRnumber =     "863 786",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p79-hull/;
                 http://www.acm.org/pubs/toc/Abstracts/toms/6498.html",
  acknowledgement = ack-nhfb,
  bibno =        "91",
  content =      "algorithms; verification; THEORY",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.4 Algorithm analysis; G.4
                 Certification and testing; G.4 Verification",
  CRnumber =     "1986-02428",
  descriptor =   "mathematics of computing, numerical analysis,
                 approximation, elementary function approximation;
                 mathematics of computing, mathematical software,
                 algorithm analysis; mathematics of computing,
                 mathematical software, certification and testing;
                 mathematics of computing, mathematical software,
                 verification",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  fortitle =     "ACM Trans. Math. Softw.",
  genterm =      "June 1986",
  guideno =      "2",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory; verification",
  review =       "ACM CR 8702-0091",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Verification.",
}

@Article{Jacobsen:1986:FRC,
  author =       "Lisa Jacobsen and William B. Jones and Haakon
                 Waadeland",
  title =        "Further results on the computation of incomplete gamma
                 functions",
  journal =      j-LECT-NOTES-MATH,
  volume =       "1199",
  pages =        "67--89",
  year =         "1986",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0075936",
  ISBN =         "3-540-16768-4 (print), 3-540-38817-6 (e-book)",
  ISBN-13 =      "978-3-540-16768-6 (print), 978-3-540-38817-3
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  MRclass =      "40A15 (33A10 33A15)",
  MRnumber =     "870245 (88f:40004)",
  MRreviewer =   "Marietta J. Tretter",
  bibdate =      "Thu May 15 18:46:23 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1985.bib",
  URL =          "http://link.springer.com/chapter/10.1007/BFb0075936/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0075930",
  book-URL =     "http://www.springerlink.com/content/978-3-540-38817-3",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
}

@Article{Kushner:1986:ECC,
  author =       "Ed Kushner and Rick Broussard",
  title =        "Efficient computation of the cylindrical {Bessel}
                 functions of complex argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "42",
  number =       "3",
  pages =        "345--349",
  month =        nov,
  year =         "1986",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(86)90004-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:28:16 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465586900044",
  abstract =     "An algorithm that generates the cylindrical Bessel
                 function very accurately for a wide range of complex
                 arguments has been developed by Mason. The Mason
                 algorithm consists of four different methods that apply
                 to different portions of the complex plane. Experience
                 with the Floating Point Systems FPS-364
                 minisupercomputer indicates several ways by which these
                 methods can be made more efficient. Specific
                 improvements relate to: (1) the method for
                 determination of the point where backward recursion is
                 initiated for the Bessel functions of the first kind;
                 (2) the way that the Bessel functions of the first and
                 second kind are normalized when $ |y| < 5 $ and $ |x|
                 \leq 20 $; and (3) the extent that asymptotic
                 expansions are used when $ |x| > 20 $ and $ |y| < 5 $.
                 The first and third modifications will result in
                 increased efficiency for all architectures. The second
                 modification will be of value for many, but probably
                 not all, architectures.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Laforgia:1986:IBF,
  author =       "Andrea Laforgia",
  title =        "Inequalities for {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "15",
  number =       "1",
  pages =        "75--81",
  month =        may,
  year =         "1986",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:55 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042786902396",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Lavoie:1986:SEG,
  author =       "J. L. Lavoie",
  title =        "Some evaluations for the generalized hypergeometric
                 series",
  journal =      j-MATH-COMPUT,
  volume =       "46",
  number =       "173",
  pages =        "215--218",
  month =        jan,
  year =         "1986",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A35 (65D20)",
  MRnumber =     "87c:33007",
  MRreviewer =   "S. D. Bajpai",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0200 (Engineering mathematics and mathematical
                 techniques); B0290Z (Other numerical methods); C1100
                 (Mathematical techniques); C4190 (Other numerical
                 methods)",
  corpsource =   "Laval Univ., Que., Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "evaluation formulae; generalized hypergeometric
                 series; series (mathematics); summation formulae; unit
                 argument; Whipple's theorem",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Marsaglia:1986:CIG,
  author =       "John C. W. Marsaglia",
  title =        "{C249}. {The} incomplete gamma function and
                 {Ramanujan}'s rational approximation to $ e^x $",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "24",
  number =       "2",
  pages =        "163--168",
  year =         "1986",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949658608810899",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Tue Apr 22 09:11:07 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
}

@Article{Muller:1986:MDC,
  author =       "Jean-Michel Muller",
  title =        "Une m{\'e}thodologie du calcul hardware des fonctions
                 {\'e}l{\'e}mentaires. ({French}) [{A} methodology for
                 the hardware computation of elementary functions]",
  journal =      j-MATH-MODEL-NUM-ANA,
  volume =       "20",
  number =       "4",
  pages =        "667--695",
  year =         "1986",
  CODEN =        "RMMAEV",
  ISSN =         "0764-583X (print), 1290-3841 (electronic)",
  ISSN-L =       "0764-583X",
  MRclass =      "65D20 (41-04)",
  MRnumber =     "88h:65043",
  MRreviewer =   "E. W. Cheney",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical modelling and numerical analysis =
                 Modelisation math{\'e}matique et analyse num{\'e}rique:
                 $M^2AN$",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=MZA",
  language =     "Russian",
}

@Article{Petkovic:1986:SIS,
  author =       "M. S. Petkovi{\'c} and L. V. Stefanovi{\'c}",
  title =        "On some improvements of square root iteration for
                 polynomial complex zeros",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "15",
  number =       "1",
  pages =        "13--25",
  month =        may,
  year =         "1986",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(86)90235-9",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:55 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042786902359",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "polynomial root finding",
}

@Article{Piessens:1986:ATP,
  author =       "Robert Piessens and Shafique Ahmed",
  title =        "Approximation for the turning points of {Bessel}
                 functions",
  journal =      j-J-COMPUT-PHYS,
  volume =       "64",
  number =       "1",
  pages =        "253--257",
  month =        may,
  year =         "1986",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(86)90029-X",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:29 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/002199918690029X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Book{Prudnikov:1986:ISE,
  author =       "Anatolij P. Prudnikov and Jurij A. Bry{\v{c}}kov and
                 Oleg I. Mari{\v{c}}ev",
  title =        "Integrals and series. {Elementary} functions",
  volume =       "1",
  publisher =    "Gordon and Breach Science Publishers",
  address =      "New York, NY, USA",
  pages =        "798",
  year =         "1986",
  ISBN =         "2-88124-089-5",
  ISBN-13 =      "978-2-88124-089-8",
  LCCN =         "QA308.P7813 1986",
  bibdate =      "Thu Nov 2 15:40:35 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1927--",
  remark =       "Translated from the Russian by N. M. Queen.",
  seriestableofcontents = "v. 1. Elementary functions \\
                 v. 2. Special functions \\
                 v. 3. More special functions \\
                 v. 4. Direct Laplace transforms \\
                 v. 5. Inverse Laplace transforms",
  subject =      "Integrals; Series",
}

@Book{Prudnikov:1986:ISS,
  author =       "Anatolij P. Prudnikov and Jurij A. Bry{\v{c}}kov and
                 Oleg I. Mari{\v{c}}ev",
  title =        "Integrals and series. {Special} functions",
  volume =       "2",
  publisher =    "Gordon and Breach Science Publishers",
  address =      "New York, NY, USA",
  pages =        "750",
  year =         "1986",
  ISBN =         "2-88124-090-9",
  ISBN-13 =      "978-2-88124-090-4",
  LCCN =         "QA308.P7813 1986",
  MRclass =      "26A33, 26A36, 26A39, 26A42, 26B15, 26B20, 26B25",
  bibdate =      "Thu Nov 2 15:43:13 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "Translated from the Russian by N. M. Queen.",
  seriestableofcontents = "v. 1. Elementary functions \\
                 v. 2. Special functions \\
                 v. 3. More special functions \\
                 v. 4. Direct Laplace transforms \\
                 v. 5. Inverse Laplace transforms",
  subject =      "Integrals; Series",
}

@Article{Reichel:1986:PAU,
  author =       "L. Reichel",
  title =        "On polynomial approximation in the uniform norm by the
                 discrete least squares method",
  journal =      j-BIT,
  volume =       "26",
  number =       "3",
  pages =        "350--368",
  month =        jan,
  year =         "1986",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "12404",
  catcode =      "G.1.2; G.1.2; G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Least squares
                 approximation; G.1.2 Approximation; G.1.2 Spline and
                 piecewise polynomial approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Least squares approximation; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Approximation, Spline
                 and piecewise polynomial approximation",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  genterm =      "algorithms",
  guideno =      "1986-03278",
  journal-URL =  "http://link.springer.com/journal/10543",
  jrldate =      "Jan. 1986",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Ronning:1986:CTF,
  author =       "Gerd Ronning",
  title =        "On the curvature of the trigamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "15",
  number =       "3",
  pages =        "397--399",
  month =        jul,
  year =         "1986",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:56 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042786902311",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{S:1986:CEF,
  author =       "A. S. Kuz'menko and K. I. Rogozin",
  title =        "Calculation of elementary functions in a number system
                 with arbitrary basis on the basis of order-differential
                 transformations. ({Russian})",
  journal =      "Prace Nauk. Inst. Cybernet. Tech. Politech.
                 Wroc{\l}aw. Ser. Konfer.",
  volume =       "74",
  number =       "31",
  pages =        "259--262",
  year =         "1986",
  MRclass =      "65G99 (65D20)",
  MRnumber =     "894 691",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Shore:1986:AID,
  author =       "Haim Shore",
  title =        "An approximation for the inverse distribution function
                 of a combination of random variables, with an
                 application to operating theatres",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "23",
  number =       "3",
  pages =        "157--181",
  year =         "1986",
  CODEN =        "JSCSAJ",
  ISSN =         "0094-9655 (print), 1563-5163 (electronic)",
  ISSN-L =       "0094-9655",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Ban-llan University, Israel",
  bibno =        "5358",
  catcode =      "G.3; G.m; G.1.2; G.2.1; J.3; G.3",
  content =      "The author worked on a project to predict the
                 percentage of time that operations are carried out
                 relative to the time that the operating theater is
                 available. The numerator of the percentage is a
                 weighted sum of the times required to carry out
                 different kinds of operations, where the weights are
                 the numbers of operations of each kind to be performed.
                 Since different kinds of operations have different mean
                 times, this sum has a skewed distribution.\par

                 Based on the Central Limit Theorem, the normal
                 distribution is the most widely used approximation to
                 the distribution of a weighted sum of random variables.
                 However, this approximation is not very good if the sum
                 has a skewed distribution.\par

                 In a separate paper [1], the author derived an
                 alternative approximation based on the first four
                 moments of the sum. In the present paper, he applies
                 this approximation to the operating theater problem by
                 estimating the moments of the times of the different
                 kinds of operations. The paper also contains a Monte
                 Carlo comparison of the normal approximation with the
                 proposed approximation for four underlying
                 distributions of the sum.",
  CRclass =      "G.3 Statistical computing; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.2.1 Combinatorics;
                 G.2.1 Generating functions; J.3 Health; G.3
                 Probabilistic algorithms (including Monte Carlo)",
  CRnumber =     "8612-1109",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing; Mathematics of Computing,
                 MISCELLANEOUS; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, DISCRETE
                 MATHEMATICS, Combinatorics, Generating functions;
                 Computer Applications, LIFE AND MEDICAL SCIENCES,
                 Health; Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Probabilistic algorithms (including Monte
                 Carlo)",
  fjournal =     "Journal of Statistical Computation and Simulation",
  genterm =      "algorithms; measurement",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
  journalabbrev = "J. Stat. Comput. Simul.",
  jrldate =      "1986",
  reviewer =     "M. Snyder",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.m
                 MISCELLANEOUS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2
                 DISCRETE MATHEMATICS; J. Computer Applications; J.3
                 LIFE AND MEDICAL SCIENCES; G. Mathematics of Computing;
                 G.3 PROBABILITY AND STATISTICS",
}

@Article{Skeel:1986:CVS,
  author =       "Robert D. Skeel",
  title =        "Construction of Variable-Stepsize Multistep Formulas",
  journal =      j-MATH-COMPUT,
  volume =       "47",
  number =       "176",
  pages =        "503--510, S45--S52",
  month =        oct,
  year =         "1986",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65L05",
  MRnumber =     "87j:65080",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4110 (Error analysis in numerical methods); C4170
                 (Differential equations)",
  corpsource =   "Dept. of Comput. Sci., Illnois Univ., Urbana, IL,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Adams formula; adaptable multistep methods;
                 backward-differentiation; differential equations; error
                 analysis; estimation; first Dahlquist barrier; fixed
                 leading coefficient method; fixed-coefficient methods;
                 fixed-stepsize; formula; formula changing; initial
                 value; interpolatory methods; local error; minimum
                 storage variable-stepsize; multistep formula; Nordsieck
                 stepsize changing technique; problems; step methods;
                 variable; variable coefficient methods; variable-order
                 family of variable-coefficient formulas",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Skeel:1986:SCV,
  author =       "Robert D. Skeel",
  title =        "Supplement to Construction of Variable-Stepsize
                 Multistep Formulas",
  journal =      j-MATH-COMPUT,
  volume =       "47",
  number =       "176",
  pages =        "S45--S52",
  month =        oct,
  year =         "1986",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Temme:1986:DIC,
  author =       "N. M. Temme",
  title =        "A double integral containing the modified {Bessel}
                 function: asymptotics and computation",
  journal =      j-MATH-COMPUT,
  volume =       "47",
  number =       "176",
  pages =        "683--691",
  month =        oct,
  year =         "1986",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A40 (41A60 65D30)",
  MRnumber =     "87m:33006",
  MRreviewer =   "S. D. Bajpai",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4110 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation); C4160
                 (Numerical integration and differentiation)",
  corpsource =   "Centre for Math. and Comput. Sci., Amsterdam,
                 Netherlands",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "distribution function; double integral; error
                 analysis; error function; integral; integration;
                 modified Bessel function; normal; polynomials;
                 probability; series (mathematics); series expansions;
                 two-dimensional",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Thompson:1986:CBF,
  author =       "I. J. Thompson and A. R. Barnett",
  title =        "{Coulomb} and {Bessel} functions of complex arguments
                 and order",
  journal =      j-J-COMPUT-PHYS,
  volume =       "64",
  number =       "2",
  pages =        "490--509",
  month =        jun,
  year =         "1986",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(86)90046-X",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:30 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/002199918690046X",
  abstract =     "The Coulomb wavefunctions, originally constructed for
                 real $ \varrho > 0 $, real $ \eta $ and integer $
                 \lambda \geq 0 $ are defined for $ \varrho $, $ \eta $,
                 and $ \lambda $ all complex. We examine the complex
                 continuation of a variety of series and
                 continued-fraction expansions for the Coulomb functions
                 and their logarithmic derivatives, and then see how
                 these expansions may be selectively combined to
                 calculate both the regular and irregular functions and
                 their derivatives. The resulting algorithm [46] is a
                 complex generalisation of Steed's method [6, 7] as it
                 appears in the real procedure COULFG [10]. Complex
                 Whittaker, confluent hypergeometric and Bessel
                 functions can also be calculated.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Zaritskaya:1986:ACE,
  author =       "Z. V. Zaritskaya and A. I. Shva{\u\i} and P. {\=E}.
                 Antonyuk",
  title =        "Approximation of certain elementary functions in the
                 metric $ {L} $. ({Russian})",
  journal =      "Vestnik L'vov. Politekhn. Inst.",
  volume =       "202",
  pages =        "38--40",
  year =         "1986",
  MRclass =      "149.41A10 (33A10)",
  MRnumber =     "87j:41030",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Agarwal:1987:CNS,
  author =       "Ramesh C. Agarwal and James W. Cooley and Fred G.
                 Gustavson and James B. Shearer and Gordon Slishman and
                 Bryant Tuckerman",
  title =        "Clarification: {``New scalar and vector elementary
                 functions for the IBM System/370''} [{IBM J. Res.
                 Develop. {\bf 30} (1986), no. 2, 126--144}]",
  journal =      j-IBM-JRD,
  volume =       "31",
  number =       "2",
  pages =        "274--274",
  year =         "1987",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "76W05",
  MRnumber =     "MR894626",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Agarwal:1986:NSV}.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Business Machines Corporation. Journal
                 of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@PhdThesis{Braune:1987:HSF,
  author =       "K. Braune",
  title =        "{Hochgenaue Standardfunktionen f{\"u}r reelle und
                 komplexe Punkte und Intervalle in beliebigen
                 Gleitpunktrastern} \toenglish {High-Accuracy Elementary
                 Functions for Real and Complex Points and Intervals in
                 Arbitrary Floating-Point Systems} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  year =         "1987",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}

@Article{Buhring:1987:BUA,
  author =       "Wolfgang B{\"u}hring",
  title =        "The behavior at unit argument of the hypergeometric
                 function {${}_3 F_2$}",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "18",
  number =       "5",
  pages =        "1227--1234",
  month =        sep,
  year =         "1987",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33A30",
  MRnumber =     "88j:33004",
  MRreviewer =   "K. M. Saksena",
  bibdate =      "Sun Nov 28 19:24:11 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/18/5;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@Article{Carlson:1987:TEI,
  author =       "B. C. Carlson",
  title =        "A Table of Elliptic Integrals of the Second Kind",
  journal =      j-MATH-COMPUT,
  volume =       "49",
  number =       "180",
  pages =        "595--606, S13--S17",
  month =        oct,
  year =         "1987",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05 (33A25 65V05)",
  MRnumber =     "89b:65013",
  MRreviewer =   "F. W. J. Olver",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4160 (Numerical integration and differentiation);
                 C7310 (Mathematics)",
  corpsource =   "Dept. of Math., Iowa State Univ., Ames, IA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "elliptic integrals of the second kind; FORTRAN
                 listings; integration; mathematics computing; standard
                 R-functions",
  treatment =    "P Practical; T Theoretical or Mathematical; X
                 Experimental",
}

@Article{Crandall:1987:EFE,
  author =       "R. E. Crandall and J. P. Buhler",
  title =        "Elementary function expansions for {Madelung}
                 constants",
  journal =      j-J-PHYS-A,
  volume =       "20",
  number =       "16",
  pages =        "5497--5510",
  year =         "1987",
  CODEN =        "JPHAC5",
  ISSN =         "0305-4470 (print), 1361-6447 (electronic)",
  ISSN-L =       "0305-4470",
  MRclass =      "82A60 (82-08)",
  MRnumber =     "MR924725 (88m:82034)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Physics. A. Mathematical and General",
  journal-URL =  "http://iopscience.iop.org/0305-4470",
}

@Article{DiDonato:1987:AFS,
  author =       "Armido R. {DiDonato} and Alfred H. {Morris Jr.}",
  title =        "{Algorithm 654}: {FORTRAN} Subroutines for Computing
                 the Incomplete Gamma Function Ratios and their
                 Inverse",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "318--319",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.214348",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 4 21:43:08 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran2.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/pdf/10.1145/29380.214348",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation. {\bf G.m}: Mathematics of
                 Computing, MISCELLANEOUS.",
}

@Article{Dunham:1987:PMAa,
  author =       "Charles B. Dunham",
  title =        "Provably monotone approximations",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "2",
  pages =        "6--11",
  month =        apr,
  year =         "1987",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/24936.24938",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:15 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "theory; verification",
  subject =      "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation",
}

@Article{Dunham:1987:PMAb,
  author =       "Charles B. Dunham",
  title =        "Provably monotone approximations, {II}",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "3",
  pages =        "30--31",
  month =        jul,
  year =         "1987",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/36318.36323",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:15 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "theory",
  subject =      "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation",
}

@Article{Gervais:1987:RAF,
  author =       "R. Gervais and Q. I. Rahman and G. Schmeisser",
  title =        "Representation and approximation of functions via $
                 (0, 2) $-interpolation",
  journal =      j-J-APPROX-THEORY,
  volume =       "50",
  number =       "2",
  pages =        "89--110",
  month =        jun,
  year =         "1987",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "30719",
  catcode =      "G.1.2; G.1.1",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.1 Interpolation; G.1.1 Spline and
                 piecewise polynomial interpolation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Spline and piecewise polynomial
                 interpolation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory; verification",
  guideno =      "1987-09238",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "June 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Ifantis:1987:UBF,
  author =       "E. K. Ifantis and P. D. Siafarikas and C. B. Kouris",
  title =        "Upper bounds for the first zeros of {Bessel}
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "17",
  number =       "3",
  pages =        "355--358",
  month =        mar,
  year =         "1987",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:57 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042787901117",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Johnson:1987:AES,
  author =       "Kenneth C. Johnson",
  title =        "{Algorithm 650}: Efficient Square Root Implementation
                 on the 68000",
  journal =      j-TOMS,
  volume =       "13",
  number =       "2",
  pages =        "138--151",
  month =        jun,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/328512.328520",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15",
  MRnumber =     "898 489",
  bibdate =      "Sun Sep 4 21:36:32 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Johnson:1987:CES}.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Johnson:1987:CES,
  author =       "Kenneth C. Johnson",
  title =        "Corrigendum: {``Algorithm 650: efficient square root
                 implementation on the 68000'' [ACM Trans. Math.
                 Software {\bf 13} (1987), no. 2, 138--151]}",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "320--320",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.356210",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "320. 65D15",
  MRnumber =     "918 582",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Johnson:1987:AES}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Kahan:1987:BCC,
  author =       "W. Kahan",
  title =        "Branch Cuts for Complex Elementary Functions or Much
                 Ado About Nothing's Sign Bit",
  crossref =     "Iserles:1987:SAN",
  volume =       "9",
  pages =        "165--211",
  year =         "1987",
  MRclass =      "65E05",
  MRnumber =     "88k:65027",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Inst. Math. Appl. Conf. Ser. New Ser.",
  acknowledgement = ack-nhfb,
}

@Article{Kolbig:1987:BRC,
  author =       "K. S. K{\"o}lbig",
  title =        "Book Review: {{\booktitle{Calculation of Special
                 Functions, the Gamma Function, the Exponential
                 Integrals and Error-Like Functions}} (C. G. van der
                 Laan and N. M. Temme)}",
  journal =      j-SIAM-REVIEW,
  volume =       "29",
  number =       "4",
  pages =        "660--661",
  month =        "????",
  year =         "1987",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1029138",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:54:19 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/29/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "December 1987",
}

@PhdThesis{Kramer:1987:ISR,
  author =       "W. Kr{\"a}mer",
  title =        "Inverse Standardfunktionen f{\"u}r reelle und komplexe
                 Intervallargumente mit a priori Fehlerabsch{\"a}tzungen
                 f{\"u}r beliebige Datenformate \toenglish {Inverse
                 Elementary Functions for Real and Complex Interval
                 Arguments with A-Priori Error Estimates for Arbitrary
                 Data Formats} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  year =         "1987",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  author-dates = "1952--2014 (WK)",
}

@Article{Lewanowicz:1987:CRR,
  author =       "Stanis{\l}aw Lewanowicz",
  title =        "Corrigendum: {``Recurrence relations for
                 hypergeometric functions of unit argument''} {[Math.
                 Comp. {\bf 45} (1985), no. 172, 521--535, MR
                 86m:33004]}",
  journal =      j-MATH-COMPUT,
  volume =       "48",
  number =       "178",
  pages =        "853--853",
  month =        apr,
  year =         "1987",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A35 (65Q05)",
  MRnumber =     "88a:33013",
  bibdate =      "Wed Jan 15 09:19:34 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@MastersThesis{Liu:1987:BEF,
  author =       "Z. A. Liu",
  title =        "{Berkeley} Elementary Function Test Suite",
  type =         "{M.S.} thesis",
  school =       "Computer Science Division, Department of Electrical
                 Engineering and Computer Science, Univerity of
                 California at Berkeley",
  address =      "Berkeley, CA, USA",
  month =        dec,
  year =         "1987",
  bibdate =      "Mon Sep 12 23:52:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
}

@Article{Lo:1987:HGA,
  author =       "Hao-Yung Lo and Jau-Ling Chen",
  title =        "A Hardwired Generalized Algorithm for Generating the
                 Logarithm Base-$k$ by Iteration",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "11",
  pages =        "1363--1367",
  month =        nov,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.5009477",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009477",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Mathis:1987:EFP,
  author =       "Robert F. Mathis",
  title =        "Elementary Functions Package for {Ada}",
  crossref =     "ACM:1987:UAA",
  pages =        "95--100",
  month =        dec,
  year =         "1987",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/ada.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Moricz:1987:ACF,
  author =       "Ferenc Moricz and Xianliang Shi",
  title =        "Approximation to continuous functions by {Cesaro}
                 means of double {Fourier} series and conjugate series",
  journal =      j-J-APPROX-THEORY,
  volume =       "49",
  number =       "4",
  pages =        "346--377",
  month =        apr,
  year =         "1987",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "30744",
  catcode =      "G.1.2; G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Least squares
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Least squares approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory; verification",
  guideno =      "1987-09224",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "April 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Musielak:1987:AEG,
  author =       "J. Musielak",
  title =        "Approximation of elements of a generalized {Orlicz}
                 sequence space by nonlinear, singular kernels",
  journal =      j-J-APPROX-THEORY,
  volume =       "50",
  number =       "4",
  pages =        "366--372",
  month =        aug,
  year =         "1987",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "30716",
  catcode =      "G.2.1; G.1.5; G.1.2",
  CRclass =      "G.2.1 Combinatorics; G.2.1 Generating functions; G.1.5
                 Roots of Nonlinear Equations; G.1.5 Convergence; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, DISCRETE MATHEMATICS,
                 Combinatorics, Generating functions; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
                 Equations, Convergence; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory; verification",
  guideno =      "1987-09257",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Aug. 1987",
  subject =      "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Pereira:1987:CEC,
  author =       "N. Costa Pereira",
  title =        "Corrigendum: {``Estimates for the Chebyshev function $
                 \psi (x) - \theta (x) $''} {[Math. Comp. {\bf 44}
                 (1985), no. 169, 211--221, MR 86k:11005]}",
  journal =      j-MATH-COMPUT,
  volume =       "48",
  number =       "177",
  pages =        "447--447",
  month =        jan,
  year =         "1987",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11A25 (11N45 11Y35 33A70)",
  MRnumber =     "87k:11006",
  bibdate =      "Thu Jun 15 07:27:03 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Pereira:1985:ECF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Proinov:1987:NIA,
  author =       "Petko D. Proinov",
  title =        "Numerical integration and approximation of
                 differentiable functions, {II}",
  journal =      j-J-APPROX-THEORY,
  volume =       "50",
  number =       "4",
  pages =        "373--393",
  month =        aug,
  year =         "1987",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "30717",
  catcode =      "G.1.4; G.1.2",
  CRclass =      "G.1.4 Quadrature and Numerical Differentiation; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Quadrature and Numerical Differentiation; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory; verification",
  guideno =      "1987-09258",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Aug. 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Rolfe:1987:FIS,
  author =       "Timothy J. Rolfe",
  title =        "On a Fast Integer Square Root Algorithm",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "4",
  pages =        "6--11",
  month =        oct,
  year =         "1987",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:16 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/signum.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "algorithms; performance; theory",
  subject =      "F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Number-theoretic computations",
}

@Article{Smith:1987:BAM,
  author =       "P. W. Smith and J. J. Swetits",
  title =        "Best approximation by monotone functions",
  journal =      j-J-APPROX-THEORY,
  volume =       "49",
  number =       "4",
  pages =        "398--403",
  month =        apr,
  year =         "1987",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "30747",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory; verification",
  guideno =      "1987-09227",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "April 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Book{Spanier:1987:AF,
  author =       "Jerome Spanier and Keith B. Oldham",
  title =        "An Atlas of Functions",
  publisher =    pub-HEMISPHERE,
  address =      pub-HEMISPHERE:adr,
  pages =        "ix + 700",
  year =         "1987",
  ISBN =         "0-89116-573-8, 3-540-17395-1",
  ISBN-13 =      "978-0-89116-573-6, 978-3-540-17395-3",
  LCCN =         "QA331 .S685 1987",
  bibdate =      "Fri Aug 31 16:20:13 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/canjstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "See also the second edition \cite{Oldham:2009:AF}.",
  acknowledgement = ack-nhfb,
  subject =      "elementary functions; special functions; cognate
                 functions; complementary incomplete gamma function;
                 complementary modulus; complete beta function; complex
                 argument when; cosecant functions; cotangent functions;
                 digamma function; economized polynomial; error function
                 complement; eta numbers; function and its reciprocal;
                 hypergeometric algorithm; important definite integrals;
                 incomplete elliptic integrals; inverse gudermannian
                 function; inverse hyperbolic functions; negative
                 integer order; other definite integrals; parabolic
                 cylinder function; polygamma functions; purely
                 imaginary argument; reciprocal linear function;
                 reflection formula",
  tableofcontents = "Preface / ix \\
                 0 General Considerations / 1 \\
                 1 The Constant Function $c$ / 11 \\
                 2 The Factorial Function $n!$ and Its Reciprocal / 19
                 \\
                 3 The Zeta Numbers and Related Functions / 25 \\
                 4 The Bernoulli Numbers, $B_n$ / 35 \\
                 5 The Euler Numbers, $E_n$ / 39 \\
                 6 The Binomial Coefficients $\binom{\nu}{m}$ / 43 \\
                 7 The Linear Function $b x + c$ and Its Reciprocal / 53
                 \\
                 8 The Unit-Step $u(x - a)$ and Related Functions / 63
                 \\
                 9 The Integer-Value ${\tt Int}(x)$ and Fractional-Value
                 ${\tt frac}(x)$ Functions / 71 \\
                 10 The Dirac Delta Function $\delta(x - a)$ / 79 \\
                 11 The Integer Powers $(bx + c)^n$ and $x^n$ / 83 \\
                 12 The Square-Root Function $\sqrt{b x + c}$ and Its
                 Reciprocal / 91 \\
                 13 The Noninteger Powers $x^\nu$ / 99 \\
                 14 The $b \sqrt{a^2 - x^2}$ Function and Its Reciprocal
                 / 107 \\
                 15 The $b \sqrt{x^2 + a}$ Function and Its Reciprocal /
                 115 \\
                 16 The Quadratic Function $a x^2 + b x + c$ and Its
                 Reciprocal / 123 \\
                 17 The Cubic Function $x^3 + a x^2 + b x + c$ and
                 Higher Polynomials / 131 \\
                 18 The Pochhammer Polynomials $(x)_n$ / 149 \\
                 19 The Bernoulli Polynomials $B_n(x)$ / 167 \\
                 20 The Euler Polynomials $E_n(x)$ / 175 \\
                 21 The Legendre Polynomials $P_n(x)$ / 183 \\
                 22 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ /
                 193 \\
                 23 The Laguerre Polynomials $L_n(x)$ / 209 \\
                 24 The Hermite Polynomials $H_n(x)$ / 217 \\
                 25 The Logarithmic Function $\ln(x)$ / 225 \\
                 26 The Exponential Function $\exp(b x + c)$ / 233 \\
                 27 Exponentials of Powers $\exp(-a x^\nu)$ / 253 \\
                 28 The Hyperbolic Sine $\sinh(x)$ and Cosine $\cosh(x)$
                 Functions / 263 \\
                 29 The Hyperbolic Secant $\sech(x)$ and Cosecant
                 $\csch(x)$ Functions / 273 \\
                 30 The Hyperbolic Tangent $\tanh(x)$ and Cotangent
                 $\coth(x)$ Functions / 279 \\
                 31 The Inverse Hyperbolic Functions / 285 \\
                 32 The Sine $\sin(x)$ and Cosine $\cos(x)$ Functions /
                 295 \\
                 33 The Secant $\sec(x)$ and Cosecant $\csc(x)$
                 Functions / 311 \\
                 34 The Tangent $\tan(x)$ and Cotangent $\cot(x)$
                 Functions / 319 \\
                 35 The Inverse Trigonometric Functions / 331 \\
                 36 Periodic Functions / 343 \\
                 37 The Exponential Integral $\Ei(x)$ and Related
                 Functions / 351 \\
                 38 Sine and Cosine Integrals / 361 \\
                 39 The Fresnel Integrals $S(x)$ and $C(x)$ / 373 \\
                 40 The Error Function $\erf(x)$ and Its Complement
                 $\erfc(x)$ / 385 \\
                 41 The $\exp(x) \erfc(\sqrt{x})$ and Related Functions
                 / 395 \\
                 42 Dawson's Integral / 405 \\
                 43 The Gamma Function $\Gamma(x)$ / 411 \\
                 44 The Digamma Function $\psi(x)$ / 423 \\
                 45 The Incomplete Gamma $\gamma(\nu,x)$ and Related
                 Functions / 435 \\
                 46 The Parabolic Cylinder Function $D_\nu(x)$ / 445 \\
                 47 The Kummer Function $M(a; c; x)$ / 459 \\
                 48 The Tricomi Function $U(a; c; x)$ 471 \\
                 49 The Hyperbolic Bessel Functions $I_0(x)$ and
                 $I_1(x)$ / 479 \\
                 50 The General Hyperbolic Bessel Function $I_\nu(x)$ /
                 489 \\
                 51 The Basset Function $K_\nu(x)$ / 499 \\
                 52 The Bessel Coefficients $J_0(x)$ and $J_1(x)$ / 509
                 \\
                 53 The Bessel Function $J_\nu(x)$ / 521 \\
                 54 The Neumann Function $Y_\nu(x)$ / 533 \\
                 55 The Kelvin Functions / 543 \\
                 56 The Airy Functions $\Ai(x)$ and $\Bi(x)$ / 555 \\
                 57 The Struve Function / 563 \\
                 58 The Incomplete Beta Function $B(\nu; \mu; x)$ / 573
                 \\
                 59 The Legendre Functions $P_\nu(x)$ and $Q_\nu(x)$ /
                 581 \\
                 60 The Gauss Function $F(a, b; c; x)$ / 599 \\
                 61 The Complete Elliptic Integrals $K(p)$ and $E(p)$ /
                 609 \\
                 62 The Incomplete Elliptic Integrals $F(p; \phi)$ and
                 $E(p; \phi)$ / 621 \\
                 63 The Jacobian Elliptic Functions / 635 \\
                 64 The Hurwitz Function $\zeta(\nu; u)$ / 653 \\
                 Appendix A Utility Algorithms / 665 \\
                 Appendix B Some Useful Data / 673 \\
                 References and Bibliography / 679 \\
                 Subject Index / 681 \\
                 Symbol Index / 691",
}

@Article{Stoyanov:1987:AE,
  author =       "Basil J. Stoyanov and Richard A. Farrell",
  title =        "On the Asymptotic Evaluation of $ \int^{\pi / 2}_0
                 {J}^2_0 (\gamma \sin x) d x $",
  journal =      j-MATH-COMPUT,
  volume =       "49",
  number =       "179",
  pages =        "275--279",
  month =        jul,
  year =         "1987",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "41A60 (65D30)",
  MRnumber =     "88e:41067",
  MRreviewer =   "Roderick Wong",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1120 (Analysis); C4180 (Integral equations)",
  corpsource =   "Appl. Phys. Lab., Johns Hopkins Univ., Laurel, MD,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "analytical expression; asymptotic behavior; asymptotic
                 evaluation; Bessel functions; first kind; integral;
                 integral equations; order Bessel function; positive
                 parameter; zeroth-",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Tanese:1987:PGA,
  author =       "Reiko Tanese",
  editor =       "John J. Grefenstette",
  booktitle =    "Genetic algorithms and their applications: proceedings
                 of the second International Conference on Genetic
                 Algorithms: July 28--31, 1987 at the Massachusetts
                 Institute of Technology, Cambridge, {MA}",
  title =        "Parallel genetic algorithms for a hypercube",
  publisher =    pub-ERLBAUM,
  address =      pub-ERLBAUM:adr,
  bookpages =    "260",
  pages =        "177--183",
  year =         "1987",
  ISBN =         "0-8058-0158-8, 0-8058-0159-6 (paperback)",
  ISBN-13 =      "978-0-8058-0158-3, 978-0-8058-0159-0 (paperback)",
  LCCN =         "Q334 .I5561 1987",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  price =        "US\$39.95",
  acknowledgement = ack-nhfb,
  bibno =        "42536",
  catcode =      "I.2.6; G.1.0; G.1.2; C.1.2",
  CRclass =      "I.2.6 Learning; I.2.6 Analogies; G.1.0 General; G.1.0
                 Parallel algorithms; G.1.2 Approximation; G.1.2
                 Elementary function approximation; C.1.2 Multiple Data
                 Stream Architectures (Multiprocessors); C.1.2 Parallel
                 processors",
  descriptor =   "Computing Methodologies, ARTIFICIAL INTELLIGENCE,
                 Learning, Analogies; Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Parallel algorithms;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Computer Systems Organization, PROCESSOR ARCHITECTURES,
                 Multiple Data Stream Architectures (Multiprocessors),
                 Parallel processors",
  genterm =      "algorithms; performance; experimentation",
  guideno =      "1988-16888",
  procdate =     "Sponsored by Amer. Assoc. for AI, Naval Res. Lab. and
                 Bolt Beranek & Newman, July 28-31, 1987",
  procloc =      "Cambridge, MA",
  subject =      "I. Computing Methodologies; I.2 ARTIFICIAL
                 INTELLIGENCE; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; C. Computer Systems Organization;
                 C.1 PROCESSOR ARCHITECTURES",
}

@Article{Thompson:1987:IEF,
  author =       "Peter Thompson",
  title =        "Implementing an Elementary Function Library",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "2",
  pages =        "2--5",
  month =        apr,
  year =         "1987",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  bibno =        "24937",
  catcode =      "G.m; D.3.2",
  CRclass =      "D.3.2 Language Classifications; D.3.2 OCCAM",
  descriptor =   "Mathematics of Computing, MISCELLANEOUS; Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 OCCAM",
  fjournal =     "ACM SIGNUM Newsletter",
  genterm =      "theory; languages",
  guideno =      "1987-03363",
  journal-URL =  "https://dl.acm.org/loi/signum",
  journalabbrev = "SIGNUM Newsl.",
  jrldate =      "April 1987",
  subject =      "G. Mathematics of Computing; G.m MISCELLANEOUS; D.
                 Software; D.3 PROGRAMMING LANGUAGES",
}

@Article{Thompson:1987:MBF,
  author =       "I. J. Thompson and A. R. Barnett",
  title =        "Modified {Bessel} functions {$ I_\nu (z) $} and {$
                 K_\nu (z) $} of real order and complex argument, to
                 selected accuracy",
  journal =      j-COMP-PHYS-COMM,
  volume =       "47",
  number =       "2--3",
  pages =        "245--257",
  month =        nov # "\slash " # dec,
  year =         "1987",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(87)90111-1",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:28:21 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See erratum \cite{Thompson:2004:EBB}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465587901111",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Timan:1987:DFP,
  author =       "A. F. Timan",
  title =        "Distribution of fractional parts and approximation of
                 functions with singularities by {Bernstein}
                 polynomials",
  journal =      j-J-APPROX-THEORY,
  volume =       "50",
  number =       "2",
  pages =        "167--174",
  month =        jun,
  year =         "1987",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "30725",
  catcode =      "G.1.5; G.1.2",
  CRclass =      "G.1.5 Roots of Nonlinear Equations; G.1.5 Polynomials,
                 methods for; G.1.2 Approximation; G.1.2 Elementary
                 function approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations, Polynomials, methods for;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory; verification",
  guideno =      "1987-09244",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "June 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Visentin:1987:FAE,
  author =       "Kley Visentin and Pablo Mart{\'\i}n",
  title =        "Fractional approximation to elliptic functions",
  journal =      j-J-MATH-PHYS,
  volume =       "28",
  number =       "2",
  pages =        "330--333",
  month =        feb,
  year =         "1987",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.527661",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "41A10 (33A65)",
  MRnumber =     "87m:41009",
  bibdate =      "Mon Oct 31 11:57:55 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v28/i2/p330_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "4",
}

@Article{Zurawski:1987:DHS,
  author =       "J. H. P. Zurawski and J. B. Gosling",
  title =        "Design of a High-Speed Square Root Multiply and Divide
                 Unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "1",
  pages =        "13--23",
  month =        jan,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.5009445",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009445",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Zwick:1987:BAC,
  author =       "D. Zwick",
  title =        "Best approximation by convex functions",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "94",
  number =       "6",
  pages =        "528--534",
  month =        jul,
  year =         "1987",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "University of Vermont, Vermont, NY",
  bibno =        "43727",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "American Mathematical Monthly",
  genterm =      "theory; verification",
  guideno =      "1988-04405",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  journalabbrev = "Am. Math. Monthly",
  jrldate =      "June/July 1987",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Book{Aberth:1988:PNA,
  author =       "Oliver Aberth",
  title =        "Precise Numerical Analysis",
  publisher =    pub-WCB,
  address =      pub-WCB:adr,
  pages =        "x + 225",
  year =         "1988",
  ISBN =         "0-697-06760-2",
  ISBN-13 =      "978-0-697-06760-9",
  LCCN =         "QA297 .A28 1988",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "file://sunrise/u/sy/beebe/tex/bib/all_brec.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Aberth addresses elementary issues of precise floating
                 point computations using variable precision range
                 arithmetic. Numbers are represented as a variable
                 precision number $ \pm $ a range. Rational arithmetic
                 is also considered. Chapters are devoted to
                 \begin{enumerate} \item rootfinding, \item polynomial
                 rootfinding, \item numerical linear algebra, \item
                 differentiation and integration, and \item ordinary
                 differential equations.\end{enumerate} Differentiation
                 is handled by a codelist approach like [Rall81a], and
                 applications to Taylor series are given. Interval
                 techniques for ordinary differential equations are
                 based on using an {\it a priori\/} bound to capture
                 remainder terms. Several methods are illustrated,
                 including Taylor series methods.",
  acknowledgement = ack-nj,
  comment =      "Text for a one semester, junior level course in
                 numerical analysis. Includes PC disk with software
                 written in PBASIC. Sound introductory level discussion
                 of code lists and error capture techniques.",
  keywords =     "differentiation; differentiation arithmetic; general
                 numerical analysis; integration; interval techniques;
                 linear algebra; ordinary differential equations.;
                 variable precision arithmetic",
}

@Article{Alonso:1988:SCN,
  author =       "Javier Alonso and Carlos Benitez",
  title =        "Some characteristic and non-characteristic properties
                 of inner product spaces",
  journal =      j-J-APPROX-THEORY,
  volume =       "55",
  number =       "3",
  pages =        "318--325",
  month =        dec,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "56052",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "theory; verification",
  guideno =      "1988-10198",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Dec. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Bailey:1988:CDD,
  author =       "David H. Bailey",
  title =        "The computation of $ \pi $ to $ 29, 360, 000 $ decimal
                 digits using {Borweins}' quartically convergent
                 algorithm",
  journal =      j-MATH-COMPUT,
  volume =       "50",
  number =       "181",
  pages =        "283--296",
  month =        jan,
  year =         "1988",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y60 (11-04 11K16 65-04)",
  MRnumber =     "88m:11114",
  MRreviewer =   "A. J. van der Poorten",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1140Z (Other and miscellaneous); C1160 (Combinatorial
                 mathematics); C4130 (Interpolation and function
                 approximation); C5470 (Performance evaluation and
                 testing); C7310 (Mathematics)",
  corpsource =   "NASA Ames Res. Centre, Moffet Field, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Borwein quartically convergent algorithm; computation
                 of pi; computer testing; Cray 2 computer test; decimal
                 expansion; elliptic integrals; iterative methods;
                 mathematics computing; multiprecision arithmetic;
                 number theory; prime modulus; series (mathematics);
                 statistical analyses; statistical analysis; transform",
  treatment =    "X Experimental",
}

@Article{Bloom:1988:LCL,
  author =       "Thomas Bloom",
  title =        "The {Lebesgue} constant for {Lagrange} interpolation
                 in the simplex",
  journal =      j-J-APPROX-THEORY,
  volume =       "54",
  number =       "3",
  pages =        "338--353",
  month =        sep,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "56887",
  catcode =      "G.1.1; G.1.2; G.1.2; G.1.7; G.1.7",
  CRclass =      "G.1.1 Interpolation; G.1.1 Interpolation formulas;
                 G.1.2 Approximation; G.1.2 Minimax approximation and
                 algorithms; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; G.1.7 Ordinary Differential
                 Equations; G.1.7 Convergence and stability; G.1.7
                 Ordinary Differential Equations; G.1.7 Boundary value
                 problems",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Interpolation formulas; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Minimax
                 approximation and algorithms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Convergence
                 and stability; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Boundary
                 value problems",
  fjournal =     "Journal of Approximation Theory",
  guideno =      "1988-10170",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Sept. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Borwein:1988:CFF,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "On the Complexity of Familiar Functions and Numbers",
  journal =      j-SIAM-REVIEW,
  volume =       "30",
  number =       "4",
  pages =        "589--601",
  month =        dec,
  year =         "1988",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1030134",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "68Q25 (03D15 11Y16)",
  MRnumber =     "967961; 89k:68061",
  MRreviewer =   "Klaus W. Wagner",
  bibdate =      "Sat Mar 29 09:54:29 MDT 2014",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 Compendex database;
                 http://epubs.siam.org/toc/siread/30/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  abstract =     "This paper examines low-complexity approximations to
                 familiar functions and numbers. The intent is to
                 suggest that it is possible to base a taxonomy of such
                 functions and numbers on their computational
                 complexity. A central theme is that traditional methods
                 of approximation are often very far from optimal, while
                 good or optimal methods are often very far from
                 obvious. For most functions, provably optimal methods
                 are not known; however the gap between what is known
                 and what is possible is often small. A considerable
                 number of open problems are posed and a number of
                 related examples are presented.",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Halifax, NS, Can",
  bibno =        "58008",
  catcode =      "G.1.2; F.2.1; F.1.3",
  classification = "921",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; F.2.1 Numerical Algorithms and Problems;
                 F.1.3 Complexity Classes",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems;
                 Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Complexity Classes",
  fjournal =     "SIAM Review",
  genterm =      "algorithms; theory; performance",
  guideno =      "1988-13907",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabbrev = "SIAM Rev.",
  journalabr =   "SIAM Rev",
  jrldate =      "Dec. 1988",
  keywords =     "Algebraic Approximation; Approximation Theory;
                 Computation of Digits; Familiar Functions; Low
                 Complexity Approximation; Mathematical Techniques;
                 Rational Approximation; Reduced Complexity
                 Approximation",
  onlinedate =   "December 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; F. Theory of Computation; F.1
                 COMPUTATION BY ABSTRACT DEVICES",
}

@Article{Borwein:1988:PAE,
  author =       "Peter B. Borwein",
  title =        "{Pad{\'e}} approximants for the $q$-elementary
                 functions",
  journal =      j-CONST-APPROX,
  volume =       "4",
  number =       "4",
  pages =        "391--402",
  year =         "1988",
  ISSN =         "0176-4276 (print), 1432-0940 (electronic)",
  ISSN-L =       "0176-4276",
  MRclass =      "41A21 (33A10 41A20)",
  MRnumber =     "89f:41022",
  MRreviewer =   "Annie A. M. Cuyt",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Constructive Approximation",
  journal-URL =  "http://link.springer.com/journal/365",
}

@InCollection{Brezinski:1988:NAC,
  author =       "Claude Brezinski",
  booktitle =    "{Nonlinear numerical methods and rational
                 approximation (Wilrijk, 1987)}",
  title =        "A new approach to convergence acceleration methods",
  volume =       "43",
  publisher =    "Reidel",
  address =      "Dordrecht",
  pages =        "373--405",
  year =         "1988",
  MRclass =      "65Bxx (40A25)",
  MRnumber =     "1005369 (90m:65010)",
  MRreviewer =   "John P. Coleman",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Math. Appl.",
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
}

@Article{Carlson:1988:TEI,
  author =       "B. C. Carlson",
  title =        "A Table of Elliptic Integrals of the Third Kind",
  journal =      j-MATH-COMPUT,
  volume =       "51",
  number =       "183",
  pages =        "267--280, S1--S5",
  month =        jul,
  year =         "1988",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33A25 (65A05)",
  MRnumber =     "89k:33003",
  MRreviewer =   "F. W. J. Olver",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290R (Integral equations); B0220 (Analysis); B0290D
                 (Functional analysis); B0290M (Numerical integration
                 and differentiation); C4180 (Integral equations); C1120
                 (Analysis); C4120 (Functional analysis); C4160
                 (Numerical integration and differentiation)",
  corpsource =   "Iowa State Univ., Ames, IA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Cauchy principal values; elliptic integrals; FORTRAN
                 listings; function evaluation; integral equations;
                 integration; points; real singular; recurrence
                 relations; standard R-functions",
  treatment =    "P Practical; T Theoretical or Mathematical",
}

@Article{Cartwright:1988:JTC,
  author =       "Donald I. Cartwright and Krzysztof Kucharski",
  title =        "{Jackson's Theorem} for compact connect {Lie} groups",
  journal =      j-J-APPROX-THEORY,
  volume =       "55",
  number =       "3",
  pages =        "352--359",
  month =        dec,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "56056",
  catcode =      "G.2.m; G.1.2",
  CRclass =      "G.2.m Miscellaneous; G.1.2 Approximation; G.1.2
                 Elementary function approximation",
  descriptor =   "Mathematics of Computing, DISCRETE MATHEMATICS,
                 Miscellaneous; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "verification; theory",
  guideno =      "1988-10202",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Dec. 1988",
  subject =      "G. Mathematics of Computing; G.2 DISCRETE MATHEMATICS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Chellali:1988:ACN,
  author =       "Mustapha Chellali",
  title =        "Acc{\'e}l{\'e}ration de calcul de nombres de
                 {Bernoulli}. ({French}) [{Bernoulli} number calculation
                 acceleration]",
  journal =      j-J-NUMBER-THEORY,
  volume =       "28",
  number =       "3",
  pages =        "347--362",
  month =        mar,
  year =         "1988",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/0022-314X(88)90047-9",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Wed Jul 15 08:46:57 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0022314X88900479",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
  language =     "French",
}

@Article{Chiccoli:1988:EGE,
  author =       "C. Chiccoli and S. Lorenzutta and G. Maino",
  title =        "On the evaluation of generalized exponential integrals
                 {$ E_\nu (x) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "78",
  number =       "2",
  pages =        "278--287",
  month =        oct,
  year =         "1988",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(88)90050-2",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:42 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999188900502",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Cover:1988:DII,
  author =       "Thomas M. Cover and Joy A. Thomas",
  title =        "Determinant inequalities via information theory",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "9",
  number =       "3",
  pages =        "384--392",
  month =        jul,
  year =         "1988",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "58040",
  catcode =      "H.1.1; G.1.3; F.2.1; G.1.2",
  CRclass =      "H.1.1 Systems and Information Theory; H.1.1
                 Information theory; G.1.3 Numerical Linear Algebra;
                 G.1.3 Determinants; F.2.1 Numerical Algorithms and
                 Problems; F.2.1 Computations on matrices; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Information Systems, MODELS AND PRINCIPLES, Systems
                 and Information Theory, Information theory; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Determinants; Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  genterm =      "algorithms; theory; performance",
  guideno =      "1988-13777",
  journal-URL =  "http://epubs.siam.org/simax",
  journalabbrev = "SIAM J. Matrix Anal. Appl.",
  jrldate =      "July 1988",
  subject =      "H. Information Systems; H.1 MODELS AND PRINCIPLES; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}

@InProceedings{Davenport:1988:ICF,
  author =       "J. H. Davenport",
  editor =       "N. M. Stephens and M. P. Thorne",
  booktitle =    "Computers in mathematical research: based on the
                 proceedings of a conference organized by the Institute
                 of Mathematics and its Applications on computers in
                 mathematical research, held at University College,
                 Cardiff in September 1986",
  title =        "Integration in closed form",
  volume =       "14",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  bookpages =    "235",
  year =         "1988",
  ISBN =         "0-19-853620-8",
  ISBN-13 =      "978-0-19-853620-8",
  LCCN =         "QA11.A1 C618 1986",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  price =        "US\$57.50",
  series =       "Institute of Mathematics and its applications
                 conference series, new series",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Bath",
  bibno =        "52474",
  catcode =      "J.2; F.2.1; G.1.2; G.1.2; I.2.9; F.2.1",
  CRclass =      "J.2 Mathematics and statistics; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Number-theoretic
                 computations; G.1.2 Approximation; G.1.2 Rational
                 approximation; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; I.2.9 Robotics; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computations in finite
                 fields",
  descriptor =   "Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Mathematics and statistics; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Number-theoretic computations; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Rational
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Computing Methodologies, ARTIFICIAL
                 INTELLIGENCE, Robotics; Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations in finite
                 fields",
  genterm =      "algorithms; theory",
  guideno =      "1988-16247",
  page =         "119--134",
  procdate =     "Sept. 1986",
  procloc =      "Cardiff, Wales",
  subject =      "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; F. Theory of Computation; F.2 ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS; I. Computing
                 Methodologies; I.2 ARTIFICIAL INTELLIGENCE; F. Theory
                 of Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY",
  waffil =       "Univ. College, Cardiff, Wales; Univ. College, Cardiff,
                 Wales",
}

@TechReport{DiDonato:1988:SDC,
  author =       "Armido I. DiDonato and Alfred H. {Morris, Jr.}",
  title =        "Significant Digit Computation of the Incomplete Beta
                 Function Ratios",
  type =         "Technical Report",
  number =       "NSWC TR 88-365",
  institution =  "Naval Surface Warfare Center (K33)",
  address =      "Dahlgren, VA 22448-5000, USA",
  month =        nov,
  year =         "1988",
  bibdate =      "Sat Nov 15 10:30:20 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.dtic.mil/dtic/tr/fulltext/u2/a210118.pdf",
  abstract =     "An algorithm is given for evaluating the incomplete
                 beta function ratio $ I_x(a, b) $ and its complement $
                 1 - I_x(a, b) $. Two new procedures are used with
                 classical results. A listing of a transportable Fortran
                 subroutine using this algorithm is given. The
                 subroutine is accurate to 14 significant digits when
                 the precision is not restricted by inherent error.",
  acknowledgement = ack-nhfb,
  keywords =     "bratio; continued fraction; expm1; gamma; incomplete
                 gamma function; ln; log1p; r1mach; spmpar",
}

@Article{Dunham:1988:PMA,
  author =       "Charles B. Dunham",
  title =        "Provably monotone approximations, {III}",
  journal =      j-SIGNUM,
  volume =       "23",
  number =       "1",
  pages =        "10--10",
  month =        jan,
  year =         "1988",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/43931.43934",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:16 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "theory",
  subject =      "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation",
}

@TechReport{Duprat:1988:EPE,
  author =       "J. Duprat and J. M. Muller",
  title =        "Evaluation of Polynomials and elementary Functions by
                 integrated Circuits",
  number =       "RR698-I",
  institution =  "IMAG",
  address =      "Grenoble, France",
  month =        jan,
  year =         "1988",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/eureca.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Duprat:1988:HPE,
  author =       "Jean Duprat and Jean-Michel Muller",
  title =        "Hardwired polynomial evaluation",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "3",
  pages =        "291--309",
  month =        jun,
  year =         "1988",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "CNRS, Grenoble, Fr",
  classification = "721; 722; 723; 921; C4130 (Interpolation and
                 function approximation); C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Inst. Nat. Polytech. de Grenoble, France",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "computer architecture; computers, digital ---
                 Circuits; digital arithmetic; elementary functions;
                 hardwired polynomial evaluation; mathematical
                 functions; mathematical techniques; Polynomials;
                 polynomials; special-purpose circuits; VLSI
                 implementation",
  treatment =    "P Practical",
}

@Article{Feng:1988:AIN,
  author =       "Y. Y. Feng and J. Kozak",
  title =        "An approach to the interpolation of nonuniformly
                 spaced data",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "23",
  number =       "2",
  pages =        "169--178",
  month =        aug,
  year =         "1988",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "56475",
  catcode =      "G.1.1; G.1.2; G.1.7; G.1.1; G.1.4",
  CRclass =      "G.1.1 Interpolation; G.1.1 Spline and piecewise
                 polynomial interpolation; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.1.7 Ordinary
                 Differential Equations; G.1.7 Boundary value problems;
                 G.1.1 Interpolation; G.1.1 Smoothing; G.1.4 Quadrature
                 and Numerical Differentiation; G.1.4 Error analysis",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Spline and piecewise polynomial
                 interpolation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Boundary
                 value problems; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Smoothing; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation, Error analysis",
  fjournal =     "Journal of Computational and Applied Mathematics",
  genterm =      "algorithms; theory",
  guideno =      "1988-10490",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  journalabbrev = "J. Comput. Appl. Math.",
  jrldate =      "August 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Gawronski:1988:ZLT,
  author =       "Wolfgang Gawronski and Ulrich Stadtm{\"u}ller",
  title =        "On the zeros of {Lerch}'s transcendental function of
                 real parameters",
  journal =      j-J-APPROX-THEORY,
  volume =       "53",
  number =       "3",
  pages =        "354--364",
  month =        jun,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Trier, Trier, FRG; Univ. of Ulm, Ulm, FRG",
  bibno =        "49727",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "verification; theory",
  guideno =      "1988-10146",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "June 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Gillman:1988:ARG,
  author =       "E. Gillman and H. R. Fiebig",
  title =        "Accurate recursive generation of spherical {Bessel}
                 and {Neumann} functions for a large range of indices",
  journal =      j-COMPUT-PHYS,
  volume =       "2",
  number =       "1",
  pages =        "62--??",
  month =        jan,
  year =         "1988",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168296",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:45:10 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168296",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}

@Article{Guerrero:1988:HOT,
  author =       "Antonio L. Guerrero and Pablo Martin",
  title =        "Higher order two-point quasi-fractional approximations
                 to the {Bessel} functions {$ J_0 (x) $} and {$ J_1 (x)
                 $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "77",
  number =       "1",
  pages =        "276--281",
  month =        jul,
  year =         "1988",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(88)90168-4",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:41 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999188901684",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
  remark =       "This work produces only 3D approximations.",
}

@Article{Hautot:1988:CAC,
  author =       "A. Hautot",
  title =        "Convergence acceleration of continued fractions of
                 {Poincar{\'e}} type",
  journal =      j-APPL-NUM-MATH,
  volume =       "4",
  number =       "2--4",
  pages =        "309--322",
  month =        jun,
  year =         "1988",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65B05 (40A15)",
  MRnumber =     "90b:65005",
  MRreviewer =   "Gh. Adam",
  bibdate =      "Sat Feb 8 10:09:54 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}

@Article{Heilmann:1988:SSM,
  author =       "Margareta Heilmann",
  title =        "{$ L_p $}-saturation of some modified {Bernstein}
                 operators",
  journal =      j-J-APPROX-THEORY,
  volume =       "54",
  number =       "3",
  pages =        "260--273",
  month =        sep,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "56880",
  catcode =      "G.1.2; G.1.9; G.1.7; G.1.7",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.9 Integral Equations; G.1.9
                 Integro-differential equations; G.1.7 Ordinary
                 Differential Equations; G.1.7 Boundary value problems;
                 G.1.7 Ordinary Differential Equations; G.1.7
                 Convergence and stability",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Integral
                 Equations, Integro-differential equations; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations, Boundary value problems; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations, Convergence and stability",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "algorithms; theory",
  guideno =      "1988-10163",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Sept. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Horwitz:1988:TPF,
  author =       "Alan L. Horwitz and Lee A. Rubel",
  title =        "Totally positive functions and totally bounded
                 functions on $ [ - 1, 1] $",
  journal =      j-J-APPROX-THEORY,
  volume =       "52",
  number =       "2",
  pages =        "204--216",
  month =        feb,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Pennsylvania State Univ., University Park; Univ. of
                 Illinois, Urbana",
  bibno =        "49653",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "verification; theory",
  guideno =      "1988-10106",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "February 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Ifantis:1988:BFP,
  author =       "E. K. Ifantis and P. D. Siafarikas",
  title =        "Bounds for the first positive zero of a mixed {Bessel}
                 function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "21",
  number =       "2",
  pages =        "245--249",
  month =        feb,
  year =         "1988",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:38 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042788902737",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Jacobsen:1988:CAL,
  author =       "Lisa Jacobsen and Haakon Waadeland",
  title =        "Convergence acceleration of limit periodic continued
                 fractions under asymptotic side conditions",
  journal =      j-NUM-MATH,
  volume =       "53",
  number =       "3",
  pages =        "285--298",
  month =        jul,
  year =         "1988",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65B99 (30B70 40A15)",
  MRnumber =     "89h:65010",
  MRreviewer =   "Claude Brezinski",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290 (Numerical analysis); C4100 (Numerical
                 analysis)",
  corpsource =   "Dept. of Math. and Stat., Trondheim Univ., Dragvoll,
                 Norway",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "asymptotic side conditions; convergence acceleration;
                 convergence of numerical methods; hypergeometric
                 functions; limit periodic continued fractions; regular
                 C-fraction expansions",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Johnsson:1988:DPP,
  author =       "S. L. Johnsson",
  editor =       "J. R. Rice",
  booktitle =    "Mathematical aspects of scientific software",
  title =        "Data parallel programming and basic linear algebra
                 subroutines",
  volume =       "14",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "vi + 208",
  pages =        "183--196",
  year =         "1988",
  ISBN =         "0-387-96706-0",
  ISBN-13 =      "978-0-387-96706-6",
  LCCN =         "QA76.76.D47 M366 1988",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "The IMS volumes in mathematics and its applications",
  acknowledgement = ack-nhfb,
  bibno =        "42725",
  catcode =      "G.1.2; D.1.m; G.4",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; D.1.m Miscellaneous",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Software, PROGRAMMING TECHNIQUES, Miscellaneous;
                 Mathematics of Computing, MATHEMATICAL SOFTWARE",
  genterm =      "theory; algorithms; design; languages",
  guideno =      "1988-02324",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 D. Software; D.1 PROGRAMMING TECHNIQUES; G. Mathematics
                 of Computing; G.4 MATHEMATICAL SOFTWARE",
  waffil =       "Purdue Univ., West Lafayette, IN",
}

@Article{Kirby:1988:ELA,
  author =       "James C. Kirby",
  title =        "An Efficient Logarithm Algorithm for Calculators",
  journal =      j-COLLEGE-MATH-J,
  volume =       "19",
  number =       "3",
  pages =        "257--260",
  month =        may,
  year =         "1988",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/07468342.1988.11973125",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:50:43 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/collegemathj.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/07468342.1988.11973125",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  onlinedate =   "30 Jan 2018",
}

@Article{Kowalski:1988:ASP,
  author =       "Marek Kowalski and Waldemar Sielski",
  title =        "Approximation of smooth periodic functions in several
                 variables",
  journal =      j-J-COMPLEXITY,
  volume =       "4",
  number =       "4",
  pages =        "356--372",
  month =        dec,
  year =         "1988",
  CODEN =        "JOCOEH",
  ISSN =         "0885-064X (print), 1090-2708 (electronic)",
  ISSN-L =       "0885-064X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "56811",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of complexity",
  genterm =      "algorithms; verification; theory",
  guideno =      "1988-10411",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0885064X",
  journalabbrev = "J. Complexity",
  jrldate =      "Dec. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Kramer:1988:ISF,
  author =       "W. Kr{\"a}mer",
  title =        "Inverse standard functions for real and complex point
                 and interval arguments with dynamic accuracy",
  journal =      j-COMPUTING-SUPPLEMENTUM,
  pages =        "185--212",
  year =         "1988",
  CODEN =        "COSPDM",
  ISSN =         "0344-8029",
  bibdate =      "Thu Dec 14 17:19:38 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Computer Arithmetic and Scientific Computation.",
  abstract =     "Algorithms to compute inverse standard functions to
                 arbitrary accuracy with safe error bounds are given.
                 Not only approximation errors but also all possible
                 rounding errors are considered. The desired accuracy of
                 the function as well as the base of the number system
                 used are parameters of the error formula. For
                 implementation it is only assumed that the four
                 elementary arithmetic operations are performed with a
                 certain number of correct digits of the function value.
                 The interval routines are constructed out of the point
                 routines considering the monotonicity behaviour of the
                 functions. The ambiguity of the complex functions is
                 briefly discussed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Karlsruhe Univ., West Germany",
  author-dates = "1952--2014 (WK)",
  classification = "B0290B (Error analysis in numerical methods); B0290F
                 (Interpolation and function approximation); C4110
                 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation)",
  confdate =     "30 Sept.-2 Oct. 1987",
  conflocation = "Karlsruhe, West Germany",
  confsponsor =  "Karlsruhe Univ.; GAMM Committee",
  fjournal =     "Computing. Supplementum",
  issue =        "no.6 p. 185-212",
  keywords =     "Approximation errors; Dynamic accuracy; Error formula;
                 Interval arguments; Inverse standard functions;
                 Monotonicity behaviour; Rounding errors",
  pubcountry =   "Austria",
  thesaurus =    "Error analysis; Function approximation",
}

@Article{Laforgia:1988:MRI,
  author =       "Andrea Laforgia and Silvana Sismondi",
  title =        "Monotonicity results and inequalities for the gamma
                 and error functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "23",
  number =       "1",
  pages =        "25--33",
  month =        jul,
  year =         "1988",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:39 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042788903287",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Lembarki:1988:CAL,
  author =       "Alami Lembarki",
  title =        "Convergence acceleration of limit $k$-periodic
                 continued fractions",
  journal =      j-APPL-NUM-MATH,
  volume =       "4",
  number =       "2--4",
  pages =        "337--349",
  month =        jun,
  year =         "1988",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65B05 (40A15)",
  MRnumber =     "89j:65012",
  MRreviewer =   "Thomas A. Atchison",
  bibdate =      "Sat Feb 8 10:09:54 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}

@InCollection{Levrie:1988:CAM,
  author =       "Paul Levrie and Robert Piessens",
  booktitle =    "{Nonlinear numerical methods and rational
                 approximation (Wilrijk, 1987)}",
  title =        "Convergence acceleration for {Miller}'s algorithm",
  volume =       "43",
  publisher =    "Reidel",
  address =      "Dordrecht, The Netherlands",
  pages =        "349--370",
  year =         "1988",
  MRclass =      "65B10 (26C15 39A10)",
  MRnumber =     "1005368 (90m:65012)",
  MRreviewer =   "Pierre Hillion",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Math. Appl.",
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
}

@Article{Lou:1988:ETR,
  author =       "Lou van den Dries",
  title =        "On the elementary theory of restricted elementary
                 functions",
  journal =      j-J-SYMBOLIC-LOGIC,
  volume =       "53",
  number =       "3",
  pages =        "796--808",
  year =         "1988",
  CODEN =        "JSYLA6",
  ISSN =         "0022-4812 (print), 1943-5886 (electronic)",
  ISSN-L =       "0022-4812",
  MRclass =      "03C65 (03C40 03C68 12L12)",
  MRnumber =     "89i:03074",
  MRreviewer =   "M. Yasuhara",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Logic",
  journal-URL =  "http://projecteuclid.org/euclid.jsl;
                 http://www.jstor.org/journal/jsymboliclogic",
}

@PhdThesis{Marsaglia:1988:CES,
  author =       "John Christopher Winston Marsaglia",
  title =        "Computer Evaluation of the special functions of
                 probability and statistics",
  type =         "{Ph.D.} Dissertation",
  school =       "Department of Computer Science, Washington State
                 University",
  address =      "Pullman, WA, USA",
  pages =        "vii + 79",
  month =        aug,
  year =         "1988",
  bibdate =      "Wed Jun 22 07:17:49 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "$\exp(x)$; $\Phi(x)$; Bernoulli numbers; chi-square
                 distribution; continued fraction; continuous Poisson
                 distribution; Erlang distribution; exponential
                 distribution; Gamma function; incomplete Gamma
                 function; normal distribution; normal probability
                 distribution; Poisson distribution; Stirling's
                 approximation",
}


@Article{Milone:1988:EDF,
  author =       "L. A. Milone and A. A. E. Milone",
  title =        "Evaluation of {Dawson}'s function",
  journal =      j-ASTROPHYS-SPACE-SCI,
  volume =       "147",
  number =       "1",
  pages =        "189--191",
  year =         "1988",
  CODEN =        "APSSBE",
  DOI =          "https://doi.org/10.1007/bf00656618",
  ISSN =         "0004-640X (print), 1572-946X (electronic)",
  ISSN-L =       "0004-640X",
  bibdate =      "Sat Feb 17 11:54:06 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =      "Astrophys. Space Sci.",
  fjournal =     "Astrophysics and Space Science",
  journal-URL =  "http://link.springer.com/journal/10509",
}

@Article{Mimachi:1988:PRI,
  author =       "Katsuhisa Mimachi",
  title =        "A proof of {Ramanujan}'s identity by use of loop
                 integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "19",
  number =       "6",
  pages =        "1490--1493",
  month =        nov,
  year =         "1988",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "58904",
  catcode =      "G.1.9; G.1.2; F.2.2",
  CRclass =      "G.1.9 Integral Equations; G.1.9 Integro-differential
                 equations; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; F.2.2 Nonnumerical Algorithms
                 and Problems; F.2.2 Geometrical problems and
                 computations",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Integral
                 Equations, Integro-differential equations; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations",
  fjournal =     "SIAM Journal on Mathematical Analysis",
  genterm =      "algorithms; theory",
  guideno =      "1988-13744",
  journal-URL =  "http://epubs.siam.org/sima",
  journalabbrev = "SIAM J. Math. Anal.",
  jrldate =      "Nov. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY",
}

@Article{Muroi:1988:ECR,
  author =       "Kazuo Muroi",
  title =        "Extraction of Cube Roots in {Babylonian} Mathematics",
  journal =      j-CENTAURUS,
  volume =       "31",
  number =       "3",
  pages =        "181--188",
  month =        oct,
  year =         "1988",
  CODEN =        "CENTA4",
  DOI =          "https://doi.org/10.1111/j.1600-0498.1988.tb00736.x",
  ISSN =         "0008-8994 (print), 1600-0498 (electronic)",
  ISSN-L =       "0008-8994",
  bibdate =      "Sat Jul 27 18:43:36 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/centaurus.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Centaurus: An International Journal of the History of
                 Science and its Cultural Aspects",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1600-0498/",
  onlinedate =   "26 Jul 2007",
}

@Book{Nikiforov:1988:SFM,
  author =       "Arnol'd F. Nikiforov and Vasilij B. Uvarov",
  title =        "Special functions of mathematical physics: a unified
                 introduction with applications",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "xviii + 427",
  year =         "1988",
  ISBN =         "3-7643-3183-6, 0-8176-3183-6",
  ISBN-13 =      "978-3-7643-3183-2, 978-0-8176-3183-3",
  LCCN =         "QC20.7.F87 N692e",
  bibdate =      "Sat Oct 30 18:34:41 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.gbv.de:20011/gvk",
  note =         "Translated from the Russian by Ralph P. Boas.",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht002696178",
  acknowledgement = ack-nhfb,
}

@Article{Olver:1988:EBL,
  author =       "F. W. J. Olver",
  title =        "Error Bounds for Linear Recurrence Relations",
  journal =      j-MATH-COMPUT,
  volume =       "50",
  number =       "182",
  pages =        "481--499",
  month =        apr,
  year =         "1988",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65Q05 (39A10 65G05)",
  MRnumber =     "89e:65146",
  MRreviewer =   "B. Choczewski",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290B (Error analysis in numerical methods); C4110
                 (Error analysis in numerical methods)",
  corpsource =   "Maryland Univ., College Park, MD, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "a posteriori methods; analysis; Bessel function;
                 bounds; computational complexity; difference equations;
                 error; homogeneous second order; Legendre function;
                 linear recurrence relations; monotonic systems;
                 numerical examples; O(r) arithmetic operations;
                 oscillatory systems; realistic error; relations;
                 rounded interval arithmetic",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Polyak:1988:SOM,
  author =       "R. A. Polyak",
  title =        "Smooth optimization methods for minimax problems",
  journal =      j-SIAM-J-CONTROL-OPTIM,
  volume =       "26",
  number =       "6",
  pages =        "1274--1286",
  month =        nov,
  year =         "1988",
  CODEN =        "SJCODC",
  ISSN =         "0363-0129 (print), 1095-7138 (electronic)",
  ISSN-L =       "0363-0129",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "57989",
  catcode =      "G.1.6; G.1.2; F.2.1; G.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Nonlinear programming; G.1.2
                 Approximation; G.1.2 Minimax approximation and
                 algorithms; F.2.1 Numerical Algorithms and Problems;
                 F.2.1 Computation of transforms; G.1.2 Approximation;
                 G.1.2 Elementary function approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Nonlinear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Minimax
                 approximation and algorithms; Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computation of
                 transforms; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "SIAM Journal on Control and Optimization",
  genterm =      "algorithms; theory; performance",
  guideno =      "1988-13621",
  journal-URL =  "http://epubs.siam.org/sicon",
  journalabbrev = "SIAM J. Control Optim.",
  jrldate =      "Nov. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}

@InCollection{Powell:1988:RBF,
  author =       "J. D. Powell",
  editor =       "D. F. (David Francis) Griffiths and G. A. Watson",
  booktitle =    "Numerical analysis 1987",
  title =        "Radial basis function approximations to polynomials",
  volume =       "170",
  publisher =    "Longman, Inc.",
  address =      "New York, NY, USA",
  bookpages =    "300",
  pages =        "223--241",
  year =         "1988",
  ISBN =         "0-582-02157-X",
  ISBN-13 =      "978-0-582-02157-0",
  LCCN =         "QA297.N828 1988",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  price =        "US\$54.95",
  series =       "Pitman research notes in mathematics series",
  acknowledgement = ack-nhfb,
  bibno =        "54996",
  catcode =      "G.1.2; G.1.2; G.1.9; G.1.1; G.3; G.1.7",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Spline and
                 piecewise polynomial approximation; G.1.9 Integral
                 Equations; G.1.9 Integro-differential equations; G.1.1
                 Interpolation; G.1.1 Spline and piecewise polynomial
                 interpolation; G.3 Statistical computing; G.1.7
                 Ordinary Differential Equations; G.1.7 Convergence and
                 stability",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Spline and piecewise polynomial
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Integral Equations, Integro-differential
                 equations; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Spline and piecewise
                 polynomial interpolation; Mathematics of Computing,
                 PROBABILITY AND STATISTICS, Statistical computing;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Convergence and stability",
  genterm =      "algorithms; performance",
  guideno =      "1988-01246",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G.3 PROBABILITY AND STATISTICS",
  waffil =       "Univ. of Dundee; Univ. of Dundee",
}

@Article{Proinov:1988:ISF,
  author =       "Petko D. Proinov",
  title =        "Integration of smooth functions and $ \phi
                 $-discrepancy",
  journal =      j-J-APPROX-THEORY,
  volume =       "52",
  number =       "3",
  pages =        "284--292",
  month =        mar,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Plovdiv, Plovdiv, Bulgaria",
  bibno =        "49659",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "verification; theory",
  guideno =      "1988-10111",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "March 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Puoskari:1988:MCB,
  author =       "M. Puoskari",
  title =        "A method for computing {Bessel} function integrals",
  journal =      j-J-COMPUT-PHYS,
  volume =       "75",
  number =       "2",
  pages =        "334--344",
  month =        apr,
  year =         "1988",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(88)90116-7",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:40 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999188901167",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Richardson:1988:NMT,
  author =       "Daniel Richardson",
  title =        "Nonstandard models of the theory of elementary
                 functions of a real variable",
  journal =      j-Z-MATH-LOGIK-GRUNDL-MATH,
  volume =       "34",
  number =       "4",
  pages =        "355--372",
  year =         "1988",
  CODEN =        "ZMLGAQ",
  ISBN =         "0044-3050",
  ISBN-13 =      "0044-3050",
  ISSN =         "0044-3050",
  MRclass =      "03B30 (03C62 03H15 26E35)",
  MRnumber =     "90a:03009",
  MRreviewer =   "Reuven H. Gurevi{\v{c}}",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r mathematische Logik und
                 Grundlagen der Mathematik}",
}

@Article{Ruscheweyh:1988:EST,
  author =       "Stephan Ruscheweyh",
  title =        "Extension of {Szeg{\H{o}}}'s theorem on the sections
                 of univalent functions",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "19",
  number =       "6",
  pages =        "1442--1449",
  month =        nov,
  year =         "1988",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "58899",
  catcode =      "G.1.2; G.1.9; F.2.2; F.2.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.9 Integral Equations; G.1.9
                 Integro-differential equations; F.2.2 Nonnumerical
                 Algorithms and Problems; F.2.2 Computations on discrete
                 structures; F.2.2 Nonnumerical Algorithms and Problems;
                 F.2.2 Geometrical problems and computations",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Integral
                 Equations, Integro-differential equations; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Computations on discrete structures; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations",
  fjournal =     "SIAM Journal on Mathematical Analysis",
  genterm =      "algorithms; theory",
  guideno =      "1988-13739",
  journal-URL =  "http://epubs.siam.org/sima",
  journalabbrev = "SIAM J. Math. Anal.",
  jrldate =      "Nov. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY",
}

@Article{Schappacher:1988:EIG,
  author =       "Norbert Schappacher",
  title =        "Elliptic integrals and the gamma function",
  journal =      j-LECT-NOTES-MATH,
  volume =       "1301",
  pages =        "117--127",
  year =         "1988",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0082098",
  ISBN =         "3-540-18915-7 (print), 3-540-38842-7 (e-book)",
  ISBN-13 =      "978-3-540-18915-2 (print), 978-3-540-38842-5
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  bibdate =      "Fri May 9 19:07:24 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1985.bib",
  URL =          "http://link.springer.com/chapter/10.1007/BFb0082098/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0082094",
  book-URL =     "http://www.springerlink.com/content/978-3-540-38842-5",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
}

@InProceedings{Schwarz:1988:CLI,
  author =       "Jerry Schwarz",
  title =        "A {C++} Library for Infinite Precision Floating
                 Point",
  crossref =     "USENIX:1988:UPC",
  bookpages =    "362",
  pages =        "271--281",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "ftp://ftp.uu.net/library/bibliography;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The Real library supports infinite precision floating
                 point computation in C++. Arbitrary precision rational
                 arithmetic and transcendental functions are
                 supported.",
  acknowledgement = ack-nhfb,
  affiliation =  "AT\&T Bell Laboratories, Murray Hill",
  classification = "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques)",
  confdate =     "17--21 Oct. 1988",
  conflocation = "Denver, CO, USA",
  keywords =     "C++ library; Infinite precision floating point;
                 Rational arithmetic; Real library; Transcendental
                 functions",
  pubcountry =   "USA",
  thesaurus =    "C language; Digital arithmetic; Object-oriented
                 programming; Subroutines",
}

@InProceedings{Sobczyk:1988:SMA,
  author =       "Kazimierz Sobczyk",
  editor =       "W. Schiehlen and W. Wedig",
  booktitle =    "Analysis and estimation of stochastic mechanical
                 systems",
  title =        "Stochastic modelling and analysis of fatigue",
  volume =       "303",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "350",
  pages =        "269--313",
  year =         "1988",
  ISBN =         "0-387-82058-2",
  ISBN-13 =      "978-0-387-82058-3",
  LCCN =         "TA350.3.I5 no.303; TJ173 .A531 1988",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Courses and lectures",
  acknowledgement = ack-nhfb,
  bibno =        "58064",
  catcode =      "J.2; I.6.3; G.1.8; G.3; G.1.2; G.1.9",
  CRclass =      "J.2 Engineering; I.6.3 Applications; G.1.8 Partial
                 Differential Equations; G.1.8 Difference methods; G.3
                 Probabilistic algorithms (including Monte Carlo); G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.9 Integral Equations; G.1.9 Integro-differential
                 equations",
  descriptor =   "Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Engineering; Computing Methodologies,
                 SIMULATION AND MODELING, Applications; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Partial Differential
                 Equations, Difference methods; Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Probabilistic
                 algorithms (including Monte Carlo); Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Integral Equations,
                 Integro-differential equations",
  genterm =      "algorithms; theory; design; measurement; reliability",
  guideno =      "1988-17476",
  procdate =     "1987",
  procloc =      "International Centre for Mechanical Sciences in
                 Udine",
  subject =      "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; I. Computing Methodologies; I.6 SIMULATION
                 AND MODELING; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.3
                 PROBABILITY AND STATISTICS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS",
  waffil =       "Univ. of Stuttgart; Univ. of Karlsruhe",
}

@Article{Stephens:1988:SCR,
  author =       "A. J. Stephens and H. C. Williams",
  title =        "Some computational results on a problem concerning
                 powerful numbers",
  journal =      j-MATH-COMPUT,
  volume =       "50",
  number =       "182",
  pages =        "619--632",
  month =        apr,
  year =         "1988",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11R11 (11A51 11R27 11Y16 11Y40)",
  MRnumber =     "89d:11091",
  MRreviewer =   "H. J. Godwin",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0210 (Algebra); B0250 (Combinatorial mathematics);
                 C1110 (Algebra); C1160 (Combinatorial mathematics)",
  corpsource =   "Dept. of Comput. Sci., Manitoba Univ., Winnipeg, Man.,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computational complexity; continued; fractions; free
                 integer; fundamental unit; number theory; positive
                 square-; real quadratic number fields; regulator
                 algorithm Amdahl 5850; step algorithm; time complexity
                 $O(D^{1/4+\epsilon})$",
  treatment =    "T Theoretical or Mathematical; X Experimental",
}

@InProceedings{Stillinger:1988:CPS,
  author =       "Frank H. Stillinger",
  editor =       "Donald G. Truhlar",
  booktitle =    "Mathematical frontiers in computational chemical
                 physics",
  title =        "Collective phenomena in statistical mechanics and the
                 geometry of potential energy hypersurfaces",
  volume =       "15",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "xii + 349",
  pages =        "157--173",
  year =         "1988",
  ISBN =         "0-387-96782-6",
  ISBN-13 =      "978-0-387-96782-0",
  LCCN =         "QD455.3.M3 M38 1988",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the Workshop on Atomic and Molecular
                 Structure and Dynamics, held June 15--July 24, 1987, at
                 the Institute for Mathematics and Its Applications,
                 University of Minnesota.",
  price =        "US\$36.80",
  series =       "The IMA volumes in mathematics and its applications",
  acknowledgement = ack-nhfb,
  bibno =        "58051",
  catcode =      "J.2; J.2; J.2; F.2.2; G.3; G.1.2",
  CRclass =      "J.2 Physics; J.2 Chemistry; J.2 Engineering; F.2.2
                 Nonnumerical Algorithms and Problems; F.2.2 Geometrical
                 problems and computations; G.3 Statistical computing;
                 G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Physics; Computer Applications, PHYSICAL
                 SCIENCES AND ENGINEERING, Chemistry; Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Engineering; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations; Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Statistical computing; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  genterm =      "algorithms; theory",
  guideno =      "1988-17776",
  procdate =     "1982",
  procloc =      "Univ. of Minnesota, Minneapolis",
  subject =      "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; J. Computer Applications; J.2 PHYSICAL
                 SCIENCES AND ENGINEERING; J. Computer Applications; J.2
                 PHYSICAL SCIENCES AND ENGINEERING; F. Theory of
                 Computation; F.2 ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY; G. Mathematics of Computing; G.3
                 PROBABILITY AND STATISTICS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS",
  waffil =       "Univ. of Minnesota, Minneapolis",
}

@Article{Sun:1988:SAF,
  author =       "Xiehua Sun",
  title =        "On the simultaneous approximation of functions and
                 their derivatives by the {Szasz--Mirakyan} operator",
  journal =      j-J-APPROX-THEORY,
  volume =       "55",
  number =       "3",
  pages =        "279--288",
  month =        dec,
  year =         "1988",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "56048",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "verification; theory",
  guideno =      "1988-10194",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Dec. 1988",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@TechReport{Tang:1988:PIG,
  author =       "Ping Tak Peter Tang",
  title =        "Portable Implementation of a Generic Exponential
                 Function",
  type =         "Technical report",
  number =       "ANL-88-3",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  year =         "1988",
  bibdate =      "Fri Dec 28 11:27:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Book{vanRijckevorsek:1988:CCA,
  editor =       "Jan L. A. van Rijckevorsek and Jan de Leeus",
  title =        "Component and correspondence analysis: dimension
                 reduction by functional approximation",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiii + 146",
  year =         "1988",
  ISBN =         "0-471-91847-4",
  ISBN-13 =      "978-0-471-91847-9",
  LCCN =         "QA278.5 .C6571 1988",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  price =        "US\$40",
  series =       "Wiley series in probability and mathematical
                 statistics",
  acknowledgement = ack-nhfb,
  bibno =        "59092",
  catcode =      "G.1.2; G.3",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.3 Statistical computing",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing",
  genterm =      "theory; algorithms",
  guideno =      "1988-03042",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS",
}

@Book{Vilenkin:1988:SFT,
  author =       "N. Ja. (Naum Jakovlevich) Vilenkin",
  title =        "Special functions and the theory of group
                 representations",
  volume =       "22",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "x + 613",
  year =         "1988",
  ISBN =         "0-8218-1572-5",
  ISBN-13 =      "978-0-8218-1572-4",
  LCCN =         "QA3 .A5 v.22 1988",
  bibdate =      "Sat Oct 30 17:01:56 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  note =         "Reprint of 1968 edition.",
  series =       "Translations of mathematical monographs",
  acknowledgement = ack-nhfb,
  subject =      "Representations of groups; Functions, Special",
}

@Article{Wong:1988:AE,
  author =       "R. Wong",
  title =        "Asymptotic Expansion of $ \int^{\pi / 2}_0 {J}^2_\nu
                 (\lambda \cos \theta) d \theta $",
  journal =      j-MATH-COMPUT,
  volume =       "50",
  number =       "181",
  pages =        "229--234",
  month =        jan,
  year =         "1988",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "41A60 (33A40)",
  MRnumber =     "89g:41022",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "A0260 (Numerical approximation and analysis); A0270
                 (Computational techniques); C4130 (Interpolation and
                 function approximation); C4160 (Numerical integration
                 and differentiation)",
  corpsource =   "Dept. of Appl. Math., Manitoba Univ., Winnipeg, Man.,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "asymptotic expansion; Bessel function; Bessel
                 functions; crystallography; diffraction theory;
                 function approximation; integral; integration",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Ahmed:1989:EEF,
  author =       "H. M. Ahmed",
  title =        "Efficient Elementary Function Generation with
                 Multipliers",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "52--59",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
}

@Article{Armbruster:1989:KSD,
  author =       "Dieter Armbruster and John Guckenheimer and Philip
                 Holmes",
  title =        "{Kuramoto--Sivashinsky} dynamics on the
                 center-unstable manifold",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "49",
  number =       "3",
  pages =        "676--691",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Cornell Univ., Ithaca, NY; Cornell Univ., Ithaca, NY;
                 Cornell Univ., Ithaca, NY",
  bibno =        "64938",
  catcode =      "G.1.7; G.1.7; G.1.0; J.2; G.1.2; G.1.8",
  CRclass =      "G.1.7 Ordinary Differential Equations; G.1.7
                 Convergence and stability; G.1.7 Ordinary Differential
                 Equations; G.1.7 Boundary value problems; G.1.0
                 General; G.1.0 Numerical algorithms; J.2 Physics; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.8 Partial Differential Equations",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Convergence and stability;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Boundary value problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms; Computer Applications, PHYSICAL
                 SCIENCES AND ENGINEERING, Physics; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Partial Differential
                 Equations",
  fjournal =     "SIAM Journal on Applied Mathematics",
  genterm =      "algorithms; theory; experimentation",
  guideno =      "1989-09707",
  journal-URL =  "http://epubs.siam.org/siap",
  journalabbrev = "SIAM J. Appl. Math.",
  jrldate =      "June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J.
                 Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}

@Article{Avellaneda:1989:OBE,
  author =       "Marco Avellaneda and Graeme W. Milton",
  title =        "Optimal bounds on the effective bulk modulus of
                 polycrystals",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "49",
  number =       "3",
  pages =        "824--837",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "64947",
  catcode =      "G.1.8; J.2; G.1.2; G.1.6",
  CRclass =      "G.1.8 Partial Differential Equations; G.1.8 Difference
                 methods; J.2 Physics; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.1.6 Optimization;
                 G.1.6 Constrained optimization",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations, Difference methods; Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Physics; Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Constrained optimization",
  fjournal =     "SIAM Journal on Applied Mathematics",
  genterm =      "algorithms; theory; experimentation",
  guideno =      "1989-09716",
  journal-URL =  "http://epubs.siam.org/siap",
  journalabbrev = "SIAM J. Appl. Math.",
  jrldate =      "June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}

@Article{Bauer:1989:BKR,
  author =       "Friedrich L. Bauer",
  title =        "{Eine Bemerkung zu Koechers Reihen f{\"u}r die
                 Eulersche Konstante}. ({German}) [{A} remark on
                 {Koecher}'s series for the {Euler}'s constant]",
  journal =      "Bayer. Akad. Wiss. Math.-Natur. Kl. Sitzungsber.",
  pages =        "27--33 (1990)",
  year =         "1989",
  ISSN =         "0340-7586",
  MRclass =      "11Y60 (65D20) 26A06 11Y60 65D20",
  MRnumber =     "1086008",
  MRreviewer =   "F. Beukers",
  bibdate =      "Thu Aug 20 18:22:34 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "0777.26004",
  acknowledgement = ack-nhfb,
  author-dates = "Friedrich (``Fritz'') Ludwig Bauer (10 June 1924--26
                 March 2015)",
  fjournal =     "Bayerische Akademie der Wissenschaften.
                 Mathematisch-Naturwissenschaftliche Klasse.
                 Sitzungsberichte",
  keywords =     "asymptotic expansion; Euler's constant; series
                 representation",
  language =     "German",
  zmid =         "00005959",
}

@Article{Belaga:1989:TMM,
  author =       "E. G. Belaga",
  title =        "Through the mincing machine with a {Boolean} layer
                 cake: nonstandard computations over {Boolean} circuits
                 in the lower-bounds-to-circuit-size complexity
                 proving",
  journal =      j-ACTA-INFO,
  volume =       "26",
  number =       "4",
  pages =        "381--407",
  month =        feb,
  year =         "1989",
  CODEN =        "AINFA2",
  ISSN =         "0001-5903 (print), 1432-0525 (electronic)",
  ISSN-L =       "0001-5903",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. Louis Pasteur, Strasbourg Cedex, France and
                 Univ. su Pisa, Pisa, Italy",
  bibno =        "69310",
  catcode =      "F.4.1; B.6.1; F.1.1; F.1.3; F.2.2; F.1.2; G.1.2;
                 F.2.2",
  CRclass =      "F.4.1 Mathematical Logic; F.4.1 Computational logic;
                 B.6.1 Design Styles; B.6.1 Combinational logic; F.1.1
                 Models of Computation; F.1.1 Unbounded-action devices;
                 F.1.3 Complexity Classes; F.2.2 Nonnumerical Algorithms
                 and Problems; F.2.2 Complexity of proof procedures;
                 F.1.2 Modes of Computation; F.1.2 Alternation and
                 nondeterminism; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; F.2.2 Nonnumerical Algorithms
                 and Problems; F.2.2 Computations on discrete
                 structures",
  descriptor =   "Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
                 LANGUAGES, Mathematical Logic, Computational logic;
                 Hardware, LOGIC DESIGN, Design Styles, Combinational
                 logic; Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Models of Computation, Unbounded-action
                 devices; Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Complexity Classes; Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Nonnumerical Algorithms and Problems, Complexity of
                 proof procedures; Theory of Computation, COMPUTATION BY
                 ABSTRACT DEVICES, Modes of Computation, Alternation and
                 nondeterminism; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Computations on discrete
                 structures",
  fjournal =     "Acta Informatica",
  genterm =      "algorithms; theory",
  guideno =      "1989-03239",
  journal-URL =  "http://www.springerlink.com/content/0001-5903",
  journalabbrev = "Acta Inf.",
  jrldate =      "Feb. 1989",
  subject =      "F. Theory of Computation; F.4 MATHEMATICAL LOGIC AND
                 FORMAL LANGUAGES; B. Hardware; B.6 LOGIC DESIGN; F.
                 Theory of Computation; F.1 COMPUTATION BY ABSTRACT
                 DEVICES; F. Theory of Computation; F.1 COMPUTATION BY
                 ABSTRACT DEVICES; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F.
                 Theory of Computation; F.1 COMPUTATION BY ABSTRACT
                 DEVICES; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY",
}

@Article{Birge:1989:SUB,
  author =       "John R. Birge and Roger J. Wets",
  title =        "Sublinear upper bounds for stochastic programs with
                 recourse",
  journal =      j-MATH-PROG,
  volume =       "43",
  number =       "2",
  pages =        "131--149",
  month =        feb,
  year =         "1989",
  CODEN =        "MHPGA4",
  ISSN =         "0025-5610",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Michigan, Ann Arbor; Univ. of California,
                 Davis",
  bibno =        "65226",
  catcode =      "G.1.6; G.1.7; G.3; G.1.6; G.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.7
                 Ordinary Differential Equations; G.1.7 Convergence and
                 stability; G.3 Probabilistic algorithms (including
                 Monte Carlo); G.1.6 Optimization; G.1.6 Gradient
                 methods; G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations, Convergence and stability; Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Probabilistic
                 algorithms (including Monte Carlo); Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization, Gradient
                 methods; Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Mathematical Programming",
  genterm =      "algorithms; theory; performance",
  guideno =      "1989-09042",
  journal-URL =  "http://link.springer.com/journal/10107",
  journalabbrev = "Math. Program.",
  jrldate =      "February 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}

@Article{Borwein:1989:MI,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "On the Mean Iteration $ (a, b) \leftarrow \big (\frac
                 {a + 3b}{4}, \frac {\sqrt {ab} + b}{2} \big) $",
  journal =      j-MATH-COMPUT,
  volume =       "53",
  number =       "187",
  pages =        "311--326",
  month =        jul,
  year =         "1989",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2008364",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "30D05 (33A25)",
  MRnumber =     "968148, 90a:30075",
  MRreviewer =   "Carl C. Cowen",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  URL =          "http://docserver.carma.newcastle.edu.au/1586/",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Dept. of Math. Stat. and Comput. Sci., Dalhousie
                 Univ., Halifax, NS, Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computation; convergence of numerical methods;
                 converging process; iterative methods; iterative
                 process; limit; mean iteration; nontrivial
                 identifications; quadratically; symbolic; uniformizing
                 parameters",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Borwein:1989:RME,
  author =       "J. M. Borwein and P. B. Borwein and D. H. Bailey",
  title =        "{Ramanujan}, modular equations, and approximations to
                 $ \pi $ or how to compute one billion digits of $ \pi
                 $",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "96",
  number =       "3",
  pages =        "201--219",
  month =        mar,
  year =         "1989",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Dalhousie Univ., Halifax; Dalhousie Univ., Halifax",
  bibno =        "65243",
  catcode =      "I.1.2; G.1.2; G.1.8; G.1.4; I.1.3; F.2.1; F.2.1",
  CRclass =      "I.1.2 Algorithms; I.1.2 Algebraic algorithms; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.8 Partial Differential Equations; G.1.8 Elliptic
                 equations; G.1.4 Quadrature and Numerical
                 Differentiation; G.1.4 Multiple quadrature; I.1.3
                 Languages and Systems; F.2.1 Numerical Algorithms and
                 Problems; F.2.1 Computation of transforms; F.2.1
                 Numerical Algorithms and Problems; F.2.1
                 Number-theoretic computations",
  descriptor =   "Computing Methodologies, ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Partial Differential
                 Equations, Elliptic equations; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation, Multiple quadrature; Computing
                 Methodologies, ALGEBRAIC MANIPULATION, Languages and
                 Systems; Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computation of transforms; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Number-theoretic computations",
  fjournal =     "American Mathematical Monthly",
  genterm =      "algorithms; theory",
  guideno =      "1989-03459",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  journalabbrev = "Am. Math. Monthly",
  jrldate =      "March 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION",
}

@Article{Bos:1989:CPR,
  author =       "L. Bos",
  title =        "A characteristic of points in {$ R^2 $} having
                 {Lebesgue} function of polynomial growth",
  journal =      j-J-APPROX-THEORY,
  volume =       "56",
  number =       "3",
  pages =        "316--329",
  month =        mar,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72254",
  catcode =      "F.2.1; G.1.1; G.1.2; F.2.2; G.1.2; G.1.3",
  CRclass =      "F.2.1 Numerical Algorithms and Problems; F.2.1
                 Computations on matrices; G.1.1 Interpolation; G.1.1
                 Interpolation formulas; G.1.2 Approximation; G.1.2
                 Elementary function approximation; F.2.2 Nonnumerical
                 Algorithms and Problems; F.2.2 Geometrical problems and
                 computations; G.1.2 Approximation; G.1.2 Chebyshev
                 approximation and theory; G.1.3 Numerical Linear
                 Algebra; G.1.3 Sparse and very large systems",
  descriptor =   "Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Interpolation, Interpolation
                 formulas; Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Geometrical problems and computations;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Chebyshev approximation and theory;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Sparse and very large systems",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "algorithms; theory",
  guideno =      "1989-07812",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Mar. 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Book{Boyd:1989:CFS,
  author =       "John Philip Boyd",
  title =        "{Chebyshev} and {Fourier} spectral methods",
  volume =       "49",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 798",
  year =         "1989",
  ISBN =         "0-387-51487-2, 3-540-51487-2",
  ISBN-13 =      "978-0-387-51487-1, 978-3-540-51487-9",
  LCCN =         "QA404.5 .B69 1989",
  bibdate =      "Sat Feb 17 14:00:30 MST 2024",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Lecture notes in engineering",
  acknowledgement = ack-nhfb,
  subject =      "Chebyshev polynomials; Fourier analysis; Spectral
                 theory (Mathematics); Polyn{\'y}omes de Tchebychev;
                 Analyse de Fourier; Spectre (Math{\'y}ematiques);
                 Chebyshev polynomials; Fourier analysis; Spectral
                 theory (Mathematics)",
}

@Article{Bronstein:1989:AIE,
  author =       "Manuel Bronstein",
  title =        "An algorithm for the integration of elementary
                 functions",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "378",
  pages =        "491--497",
  year =         "1989",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  MRclass =      "65D30",
  MRnumber =     "91a:65050",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "EUROCAL '87 (Leipzig, 1987).",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Bronstein:1989:SRE,
  author =       "M. Bronstein",
  title =        "Simplification of real elementary functions",
  crossref =     "ACM:1989:PAI",
  pages =        "207--211",
  year =         "1989",
  bibdate =      "Tue Sep 17 06:46:18 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/issac.bib",
  abstract =     "The author describes an algorithm, based on Risch's
                 real structure theorem, that determines explicitly all
                 the algebraic relations among a given set of real
                 elementary functions. He provides examples from its
                 implementation in the Scratchpad computer algebra
                 system that illustrate the advantages over the use of
                 complex logarithms and exponentials.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Res. Div., T. J. Watson Res. Center, Yorktown
                 Heights, NY, USA",
  classification = "C1110 (Algebra); C7310 (Mathematics)",
  keywords =     "Computer algebra system; Real elementary functions;
                 Real structure theorem; Scratchpad",
  thesaurus =    "Functions; Mathematics computing; Symbol
                 manipulation",
}

@Article{Cao:1989:ABS,
  author =       "J.-D. Cao and H. H. Gonska",
  title =        "Approximation by {Boolean} sums of positive linear
                 operators. {II}. {Gopengauz}-type estimates",
  journal =      j-J-APPROX-THEORY,
  volume =       "57",
  number =       "1",
  pages =        "77--89",
  month =        apr,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72266",
  catcode =      "G.1.2; G.1.2; G.3; G.2.1",
  CRclass =      "G.1.2 Approximation; G.1.2 Nonlinear approximation;
                 G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.3 Statistical computing; G.2.1
                 Combinatorics; G.2.1 Generating functions",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Nonlinear approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Statistical
                 computing; Mathematics of Computing, DISCRETE
                 MATHEMATICS, Combinatorics, Generating functions",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-07823",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "April 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.2 DISCRETE
                 MATHEMATICS",
}

@Article{Carlson:1989:TEI,
  author =       "B. C. Carlson",
  title =        "A Table of Elliptic Integrals: Cubic Cases",
  journal =      j-MATH-COMPUT,
  volume =       "53",
  number =       "187",
  pages =        "327--333",
  month =        jul,
  year =         "1989",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65A05 (33A25 65D20)",
  MRnumber =     "89m:65009",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4180 (Integral equations); C1120 (Analysis)",
  corpsource =   "Dept. of Math., Iowa State Univ., Ames, IA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "cubic polynomial; elliptic; elliptic integral; first
                 kind; Fortran codes; functions; integral equations;
                 integrals; integration interval; R-; rational
                 integrands; real zeros; second kind; square root;
                 table; third kind",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Chen:1989:EMB,
  author =       "X. R. Chen and P. R. Krishnaiah and W. W. Liang",
  title =        "Estimation of multivariate binary density using
                 orthogonal functions",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "31",
  number =       "2",
  pages =        "178--186",
  month =        nov,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259x (print), 1095-7243 (electronic)",
  ISSN-L =       "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Pittsburgh, Pittsburgh, PA; Univ. of
                 Pittsburgh, Pittsburgh, PA; Univ. of Pittsburgh,
                 Pittsburgh, PA",
  bibno =        "69313",
  catcode =      "D.3.3; G.3; G.1.3; G.1.2",
  CRclass =      "D.3.3 Language Constructs; D.3.3 Procedures,
                 functions, and subroutines; G.3 Statistical computing;
                 G.1.3 Numerical Linear Algebra; G.1.3 Linear systems
                 (direct and iterative methods); G.1.2 Approximation;
                 G.1.2 Elementary function approximation",
  descriptor =   "Software, PROGRAMMING LANGUAGES, Language Constructs,
                 Procedures, functions, and subroutines; Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Statistical
                 computing; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods); Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  fjournal =     "Journal of Multivariate Analysis",
  genterm =      "algorithms; theory; verification",
  guideno =      "1989-08483",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "Nov. 1989",
  subject =      "D. Software; D.3 PROGRAMMING LANGUAGES; G. Mathematics
                 of Computing; G.3 PROBABILITY AND STATISTICS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Chen:1989:FCR,
  author =       "S.-G. Chen and P. Y. Hsieh",
  title =        "Fast computation of the $ {N} $ th root",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "17",
  number =       "10",
  pages =        "1423--1427",
  month =        "????",
  year =         "1989",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(89)90024-2",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Thu Dec 29 08:01:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122189900242",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  remark =       "From the abstract: ``A new class of iterative methods
                 for computing a differentiable function is proposed,
                 which is based on Pad{\'e} approximation to Taylor's
                 series of the function. It leads to a faster algorithm
                 than Newton's method for $ x^{1 / N} $ and a different
                 interpretation of Newton's method.''",
}

@Article{Chen:1989:FCTa,
  author =       "S.-G. Chen and P. Y. Hsieh",
  title =        "Fast computation of the {$N$}-th root",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "17",
  number =       "10",
  pages =        "1423--1427",
  month =        "????",
  year =         "1989",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(89)90024-2",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:01:11 MST 2017",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122189900242",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  remark =       "From the abstract: ``A new class of iterative methods
                 for computing a differentiable function is proposed,
                 which is based on Pad{\'e} approximation to Taylor's
                 series of the function. It leads to a faster algorithm
                 than Newton's method for $ x^{1 / N} $ and a different
                 interpretation of Newton's method.''",
}

@Article{Corliss:1989:IIV,
  author =       "George Corliss and Gary Krenz",
  editor =       "L. Gatteschi",
  title =        "Indefinite Integration with Validation",
  journal =      j-TOMS,
  volume =       "15",
  number =       "4",
  pages =        "375--393",
  month =        dec,
  year =         "1989",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30 (65-04)",
  MRnumber =     "1 062 497",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p375-corliss/;
                 http://www.acm.org/pubs/toc/Abstracts/toms/76915.html",
  acknowledgement = ack-nhfb,
  bibno =        "393",
  content =      "ALGORITHMS; THEORY",
  CRclass =      "G.1.4 Quadrature and Numerical Differentiation; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.2 Approximation; G.1.2 Chebyshev approximation and
                 theory",
  CRnumber =     "1989-03199",
  descriptor =   "mathematics of computing, numerical analysis,
                 quadrature and numerical differentiation; mathematics
                 of computing, numerical analysis, approximation,
                 elementary function approximation; mathematics of
                 computing, numerical analysis, approximation, Chebyshev
                 approximation and theory",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  fortitle =     "ACM Trans. Math. Softw.",
  guideno =      "4",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  review =       "ACM CR 9007-0598",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.
                 {\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation. {\bf G.1.2}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Chebyshev
                 approximation and theory.",
  waffil =       "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Critchfield:1989:CEF,
  author =       "Charles L. Critchfield",
  title =        "Computation of elliptic functions",
  journal =      j-J-MATH-PHYS,
  volume =       "30",
  number =       "2",
  pages =        "295--297",
  month =        feb,
  year =         "1989",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.528444",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "33A25 (65D20)",
  MRnumber =     "89k:33004",
  MRreviewer =   "H. Hochstadt",
  bibdate =      "Mon Oct 31 11:58:32 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1985.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v30/i2/p295_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "3",
}

@Misc{Darley:1989:FPI,
  author =       "H. M. Darley and others",
  title =        "Floating Point\slash Integer Processor with Divide and
                 Square Root Functions",
  year =         "1989",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 4,878,190.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@Article{Dehling:1989:FLI,
  author =       "Herold Dehling",
  title =        "The functional law of the iterated logarithm for {von
                 Mises} functionals and multiple {Wiener} integrals",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "28",
  number =       "2",
  pages =        "177--189",
  month =        feb,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259x (print), 1095-7243 (electronic)",
  ISSN-L =       "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of G{\"o}ttingen, G{\"o}ttingen, FRG",
  bibno =        "64336",
  catcode =      "G.3; G.1.9; G.1.2",
  CRclass =      "G.3 Statistical computing; G.1.9 Integral Equations;
                 G.1.9 Integro-differential equations; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Integral Equations,
                 Integro-differential equations; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation",
  fjournal =     "Journal of Multivariate Analysis",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-08462",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "February 1989",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}

@Article{Demirbas:1989:MSE,
  author =       "K. Demirbas",
  title =        "Multidimensional state estimation using stacks for
                 dynamic systems with interference",
  journal =      j-AUTOMATICA,
  volume =       "25",
  number =       "4",
  pages =        "617--621",
  month =        jul,
  year =         "1989",
  CODEN =        "ATCAA9",
  ISSN =         "0005-1098 (print), 1873-2836 (electronic)",
  ISSN-L =       "0005-1098",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72661",
  catcode =      "G.1.2; G.1.2; G.1.3; G.1.5; H.1.1",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Linear
                 approximation; G.1.3 Numerical Linear Algebra; G.1.3
                 Linear systems (direct and iterative methods); G.1.5
                 Roots of Nonlinear Equations; H.1.1 Systems and
                 Information Theory; H.1.1 Information theory",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Linear approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative methods);
                 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations; Information Systems, MODELS AND
                 PRINCIPLES, Systems and Information Theory, Information
                 theory",
  fjournal =     "Automatica: the journal of IFAC, the International
                 Federation of Automatic Control",
  genterm =      "algorithms; theory",
  guideno =      "1989-03952",
  jrldate =      "July 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; H.
                 Information Systems; H.1 MODELS AND PRINCIPLES",
}

@TechReport{Dritz:1989:RPS,
  author =       "K. W. Dritz",
  title =        "Rationale for the Proposed Standard for a Generic
                 Package of Elementary Functions for {Ada}",
  type =         "Report",
  number =       "ANL-89/2 Rev. 1",
  institution =  "Argonne National Laboratory, Mathematics and Computer
                 Science Division",
  address =      "Argonne, IL, USA",
  pages =        "????",
  month =        oct,
  year =         "1989",
  bibdate =      "Thu Sep 01 12:08:24 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Duprat:1989:SRA,
  author =       "J. Duprat and Y. Herreros and J.-M. Muller",
  title =        "Some results about on-line computation of functions",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "112--118",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Dyn:1989:PEB,
  author =       "N. Dyn and A. Ron",
  title =        "Periodic exponential box splines on a three direction
                 mesh",
  journal =      j-J-APPROX-THEORY,
  volume =       "56",
  number =       "3",
  pages =        "287--296",
  month =        mar,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72251",
  catcode =      "G.1.2; F.2.2; G.1.2; G.1.2; G.1.2; G.2.1; G.3",
  CRclass =      "G.1.2 Approximation; G.1.2 Spline and piecewise
                 polynomial approximation; F.2.2 Nonnumerical Algorithms
                 and Problems; F.2.2 Geometrical problems and
                 computations; G.1.2 Approximation; G.1.2 Chebyshev
                 approximation and theory; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.1.2 Approximation;
                 G.1.2 Linear approximation; G.2.1 Combinatorics; G.2.1
                 Recurrences and difference equations; G.3 Statistical
                 computing",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Spline and piecewise polynomial
                 approximation; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Chebyshev approximation and
                 theory; Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Linear approximation; Mathematics of
                 Computing, DISCRETE MATHEMATICS, Combinatorics,
                 Recurrences and difference equations; Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Statistical
                 computing",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "algorithms; theory; design",
  guideno =      "1989-07809",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Mar. 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; G.2 DISCRETE MATHEMATICS; G.3
                 PROBABILITY AND STATISTICS",
}

@Article{Eberlein:1989:SAC,
  author =       "E. Eberlein",
  title =        "Strong approximation of continuous time stochastic
                 processes",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "31",
  number =       "2",
  pages =        "220--235",
  month =        nov,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259x (print), 1095-7243 (electronic)",
  ISSN-L =       "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. Freiburg, Freiburg, W. Germany",
  bibno =        "69316",
  catcode =      "D.4.8; F.1.2; G.1.2",
  CRclass =      "D.4.8 Performance; D.4.8 Stochastic analysis; F.1.2
                 Modes of Computation; F.1.2 Probabilistic computation;
                 G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Software, OPERATING SYSTEMS, Performance, Stochastic
                 analysis; Theory of Computation, COMPUTATION BY
                 ABSTRACT DEVICES, Modes of Computation, Probabilistic
                 computation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Journal of Multivariate Analysis",
  genterm =      "algorithms; performance; theory",
  guideno =      "1989-08486",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "Nov. 1989",
  subject =      "D. Software; D.4 OPERATING SYSTEMS; F. Theory of
                 Computation; F.1 COMPUTATION BY ABSTRACT DEVICES; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Egger:1989:PAC,
  author =       "A. Egger and R. Huotari",
  title =        "The {Polya} algorithm on convex sets",
  journal =      j-J-APPROX-THEORY,
  volume =       "56",
  number =       "2",
  pages =        "212--216",
  month =        feb,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72242",
  catcode =      "F.2.2; F.2.2; G.1.2; G.1.2; G.1.5",
  CRclass =      "F.2.2 Nonnumerical Algorithms and Problems; F.2.2
                 Geometrical problems and computations; F.2.2
                 Nonnumerical Algorithms and Problems; F.2.2
                 Computations on discrete structures; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.2 Approximation; G.1.2 Minimax approximation and
                 algorithms; G.1.5 Roots of Nonlinear Equations; G.1.5
                 Convergence",
  descriptor =   "Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Geometrical problems and computations; Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Computations on discrete structures; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Minimax
                 approximation and algorithms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Roots of Nonlinear Equations,
                 Convergence",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "algorithms; theory",
  guideno =      "1989-07801",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Feb. 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS",
}

@Article{Ehrenmark:1989:ONF,
  author =       "Ulf T. Ehrenmark",
  title =        "Overconvergence of the near-field expansion for
                 linearized waves normally incident on a sloping beach",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "49",
  number =       "3",
  pages =        "799--815",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "64945",
  catcode =      "G.1.7; G.1.2; F.2.1; G.1.2; F.2.2",
  CRclass =      "G.1.7 Ordinary Differential Equations; G.1.7
                 Convergence and stability; G.1.2 Approximation; G.1.2
                 Minimax approximation and algorithms; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computation of
                 transforms; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; F.2.2 Nonnumerical Algorithms
                 and Problems; F.2.2 Geometrical problems and
                 computations",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Convergence and stability;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Minimax approximation and algorithms;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computation of transforms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations",
  fjournal =     "SIAM Journal on Applied Mathematics",
  genterm =      "algorithms; theory; experimentation",
  guideno =      "1989-09714",
  journal-URL =  "http://epubs.siam.org/siap",
  journalabbrev = "SIAM J. Appl. Math.",
  jrldate =      "June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY",
}

@Article{Einmahl:1989:ERK,
  author =       "U. Einmahl",
  title =        "Extensions of results of {Komlos}, {Major}, and
                 {Tusnady} to the multivariate case",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "28",
  number =       "1",
  pages =        "20--68",
  month =        jan,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259x (print), 1095-7243 (electronic)",
  ISSN-L =       "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. zu Koln, West Germany",
  bibno =        "66700",
  catcode =      "G.3; G.1.2; F.2.1",
  CRclass =      "G.3 Statistical computing; G.1.2 Approximation; G.1.2
                 Elementary function approximation; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computation of
                 transforms",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computation of transforms",
  fjournal =     "Journal of Multivariate Analysis",
  genterm =      "algorithms; theory",
  guideno =      "1989-08456",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "Jan. 1989",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; F. Theory of Computation; F.2 ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY",
}

@Article{Epperson:1989:UIM,
  author =       "J. F. Epperson",
  title =        "On the use of iteration methods for approximating the
                 natural logarithm",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "96",
  number =       "9",
  pages =        "831--835",
  month =        nov,
  year =         "1989",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26A06 (26A09)",
  MRnumber =     "91a:26002",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "71703",
  catcode =      "G.1.2; G.1.2; K.3.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Spline and
                 piecewise polynomial approximation; K.3.2 Computer and
                 Information Science Education",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Spline and piecewise polynomial
                 approximation; Computing Milieux, COMPUTERS AND
                 EDUCATION, Computer and Information Science Education",
  fjournal =     "American Mathematical Monthly",
  genterm =      "algorithms; theory",
  guideno =      "1989-03518",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  journalabbrev = "Am. Math. Monthly",
  jrldate =      "Nov. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; K.
                 Computing Milieux; K.3 COMPUTERS AND EDUCATION",
}

@InProceedings{Ercegovac:1989:FRD,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "On-the-fly rounding for division and square root",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "169--173",
  year =         "1989",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_rounding.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
  summary =      "In division and square root implementation based on
                 digit-recurrence algorithms, the result is obtained in
                 digit-serial form, from most significant digit to least
                 significant. To reduce the complexity of the
                 result-digit selection and to allow the \ldots{}",
}

@InProceedings{Ercegovac:1989:IMC,
  author =       "M. D. Ercegovac and T. Lang",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 8--11 May 1989",
  title =        "Implementation of module combining multiplication,
                 division, and square root",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "150--153",
  year =         "1989",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The implementation of a module that performs radix-$2$
                 multiplication, division, and square root is presented.
                 The module is compact because most of the components
                 are shared by all three operations, the complexity
                 being similar to that of a radix-$2$ \ldots{}",
}

@InProceedings{Ercegovac:1989:RSR,
  author =       "Milo{\v{s}} D. Ercegovac and Tomas Lang",
  title =        "Radix-4 square root without initial {PLA}",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "162--168",
  year =         "1989",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_radix4.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
  summary =      "A systematic derivation of a radix-$4$ square root
                 algorithm using redundance in the partial residuals and
                 the result is presented. Unlike other similar schemes,
                 the algorithm does not use a table-lookup or
                 programmable logic array (PLA) for the \ldots{}",
}

@InProceedings{Fandrianto:1989:AHS,
  author =       "Jan Fandrianto",
  title =        "Algorithms for high-speed shared radix 8 division and
                 radix 8 square root",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "68--75",
  year =         "1989",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Fandrianto.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-9",
  summary =      "An algorithm for performing radix-$8$ division and
                 square root in a shared hardware is described. To
                 achieve short iteration cycle time, it utilizes an
                 optimized `next quotient/root prediction PLA' generally
                 used in a radix-$4$ SRT division with minimal
                 \ldots{}",
}

@Article{Ge:1989:OCL,
  author =       "Renpu Ge",
  title =        "Optimal choice of linear interval extension",
  journal =      j-APPL-MATH-COMP,
  volume =       "30",
  number =       "2",
  pages =        "165--189",
  month =        mar,
  year =         "1989",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "64710",
  catcode =      "G.1.6; G.1.2; G.1.2; G.2.1; F.2.2; G.1.2; G.1.1;
                 G.1.0",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
                 Approximation; G.1.2 Linear approximation; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.2.1 Combinatorics; G.2.1 Combinatorial algorithms;
                 F.2.2 Nonnumerical Algorithms and Problems; F.2.2
                 Computations on discrete structures; G.1.2
                 Approximation; G.1.2 Minimax approximation and
                 algorithms; G.1.1 Interpolation; G.1.1 Difference
                 formulas; G.1.0 General; G.1.0 Numerical algorithms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Linear
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, DISCRETE
                 MATHEMATICS, Combinatorics, Combinatorial algorithms;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Computations on discrete structures;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Minimax approximation and algorithms;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Difference formulas; Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms",
  fjournal =     "Applied Mathematics and Computation",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-03670",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  journalabbrev = "Appl. Math. Comput.",
  jrldate =      "March 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; G.2 DISCRETE MATHEMATICS",
}

@Article{Gersch:1989:SPT,
  author =       "W. Gersch and G. Kitagawa",
  title =        "Smoothness priors transfer function estimation",
  journal =      j-AUTOMATICA,
  volume =       "25",
  number =       "4",
  pages =        "603--608",
  month =        jul,
  year =         "1989",
  CODEN =        "ATCAA9",
  ISSN =         "0005-1098 (print), 1873-2836 (electronic)",
  ISSN-L =       "0005-1098",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72658",
  catcode =      "G.1.1; G.1.2; G.1.6",
  CRclass =      "G.1.1 Interpolation; G.1.1 Smoothing; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.6 Optimization; G.1.6 Gradient methods",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Smoothing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Gradient methods",
  fjournal =     "Automatica: the journal of IFAC, the International
                 Federation of Automatic Control",
  genterm =      "algorithms; theory",
  guideno =      "1989-03949",
  jrldate =      "July 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@InCollection{Glover:1989:THN,
  author =       "Keith Glover",
  editor =       "Jan C. Willems",
  booktitle =    "From data to model",
  title =        "A tutorial on {Hankel}-norm approximation",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "246",
  pages =        "26--48",
  year =         "1989",
  ISBN =         "0-387-51571-2",
  ISBN-13 =      "978-0-387-51571-7",
  LCCN =         "QA279 .F76 1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "70545",
  catcode =      "G.1.2; F.2.1; F.2.1",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; F.2.1 Numerical Algorithms and Problems;
                 F.2.1 Computations on matrices; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computation of
                 transforms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices; Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computation of
                 transforms",
  genterm =      "algorithms; theory",
  guideno =      "1989-01692",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY",
  waffil =       "Univ. of Groningen, Groningen, The Netherlands",
}

@InProceedings{Glynn:1989:OSS,
  author =       "P. W. Glynn",
  editor =       "Edward A. MacNair and Kenneth J. Musselman and Philip
                 Heidelberger",
  booktitle =    "1989 Winter Simulation Conference proceedings:
                 December 4--6, 1989, the Capital Hilton Hotel,
                 Washington, {DC}",
  title =        "Optimization of stochastic systems via simulation",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  bookpages =    "xx + 1139",
  pages =        "90--105",
  year =         "1989",
  ISBN =         "0-911801-58-8",
  ISBN-13 =      "978-0-911801-58-3",
  LCCN =         "QA76.9.C65 W56 1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "IEEE order no. 89CH2778-9.",
  URL =          "http://ieeexplore.ieee.org/servlet/opac?punumber=5823",
  acknowledgement = ack-nhfb,
  bibno =        "76750",
  catcode =      "I.6.3; G.1.6; G.3; G.1.2",
  CRclass =      "I.6.3 Applications; G.1.6 Optimization; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Computing Methodologies, SIMULATION AND MODELING,
                 Applications; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization; Mathematics of Computing,
                 PROBABILITY AND STATISTICS; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "algorithms; design; performance",
  guideno =      "1989-12012",
  procdate =     "December 4-6, 1989",
  procloc =      "Washington, D. C.",
  subject =      "I. Computing Methodologies; I.6 SIMULATION AND
                 MODELING; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY
                 AND STATISTICS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}

@Article{Gomes:1989:GGL,
  author =       "M. I. Gomes",
  title =        "Generalized {Gumbel} and likelihood ratio test
                 statistics in the multivariate {GEV} model",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "7",
  number =       "3",
  pages =        "259--267",
  month =        feb,
  year =         "1989",
  CODEN =        "CSDADW",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "70043",
  catcode =      "G.3; G.1.7; I.5.1; G.1.6; G.1.2",
  CRclass =      "G.3 Statistical computing; G.1.7 Ordinary Differential
                 Equations; G.1.7 Convergence and stability; I.5.1
                 Models; I.5.1 Statistical; G.1.6 Optimization; G.1.6
                 Nonlinear programming; G.1.2 Approximation; G.1.2
                 Elementary function approximation",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Convergence and stability; Computing Methodologies,
                 PATTERN RECOGNITION, Models, Statistical; Mathematics
                 of Computing, NUMERICAL ANALYSIS, Optimization,
                 Nonlinear programming; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Computational Statistics \& Data Analysis",
  genterm =      "algorithms; measurement; reliability; theory",
  guideno =      "1989-04403",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
  journalabbrev = "Comput. Stat. Data Anal.",
  jrldate =      "Feb. 1989",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; I. Computing Methodologies; I.5 PATTERN
                 RECOGNITION; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}

@InProceedings{Gonzaga:1989:ASL,
  author =       "Cl{\'o}vis C. Gonzaga",
  title =        "An algorithm for solving linear programming programs
                 in {$ O(n^3 L) $} operations",
  crossref =     "Megiddo:1989:PMP",
  pages =        "1--28",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "74172",
  catcode =      "G.1.6; G.1.2; F.2.1; I.1.2; I.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 F.2.1 Numerical Algorithms and Problems; F.2.1
                 Computations on matrices; I.1.2 Algorithms; I.1.2
                 Algebraic algorithms; I.1.2 Algorithms; I.1.2 Analysis
                 of algorithms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices; Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms; Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms, Analysis of algorithms",
  genterm =      "algorithms; theory",
  guideno =      "1989-12474",
  procdate =     "March 1-4, 1987",
  procloc =      "Pacific Grove, CA",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION",
}

@TechReport{Gragg:1989:FSE,
  author =       "W. Gragg and B. Neta",
  title =        "{Fortran} Subroutines for the Evaluation of the
                 Confluent Hypergeometric Functions",
  number =       "NPS-MA-89-014",
  institution =  inst-MATH-NPS,
  address =      inst-MATH-NPS:adr,
  year =         "1989",
  bibdate =      "Fri Nov 11 14:50:24 MST 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/n/neta-beny.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Software available URL http://math.nps.navy.mil",
}

@Article{Guo:1989:RCS,
  author =       "S.-S. Guo and M. K. Khan",
  title =        "On the rate of convergence of some operators on
                 functions of bounded variation",
  journal =      j-J-APPROX-THEORY,
  volume =       "58",
  number =       "1",
  pages =        "90--101",
  month =        jul,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "69424",
  catcode =      "F.2.1; G.1.2",
  CRclass =      "F.2.1 Numerical Algorithms and Problems; F.2.1
                 Computations on polynomials; G.1.2 Approximation; G.1.2
                 Elementary function approximation",
  descriptor =   "Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "algorithms; theory",
  guideno =      "1989-07854",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "July 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS",
}

@Article{Hornik:1989:MFN,
  author =       "K. Hornik and M. Stinchcombe and H. White",
  title =        "Multilayer feedforward networks are universal
                 approximators",
  journal =      j-NEURAL-NETWORKS,
  volume =       "2",
  number =       "5",
  pages =        "359--366",
  year =         "1989",
  CODEN =        "NNETEB",
  ISSN =         "0893-6080 (print), 1879-2782 (electronic)",
  ISSN-L =       "0893-6080",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Technisce Univ. Wien, Vienna, Austria; Univ. of
                 California, San Diego; Univ. of California, San Diego",
  bibno =        "70408",
  catcode =      "F.2.1; G.1.2; F.1.1; I.2.4",
  CRclass =      "F.2.1 Numerical Algorithms and Problems; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 F.1.1 Models of Computation; F.1.1 Unbounded-action
                 devices; I.2.4 Knowledge Representation Formalisms and
                 Methods",
  descriptor =   "Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Models of Computation, Unbounded-action devices;
                 Computing Methodologies, ARTIFICIAL INTELLIGENCE,
                 Knowledge Representation Formalisms and Methods",
  fjournal =     "Neural Networks",
  genterm =      "design; performance",
  guideno =      "1989-09273",
  journalabbrev = "Neural Networks",
  jrldate =      "1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.1
                 COMPUTATION BY ABSTRACT DEVICES; I. Computing
                 Methodologies; I.2 ARTIFICIAL INTELLIGENCE",
}

@Article{Jamieson:1989:RCI,
  author =       "M. J. Jamieson",
  title =        "Rapidly converging iterative formulae for finding
                 square roots and their computational efficiencies",
  journal =      j-COMP-J,
  volume =       "32",
  number =       "1",
  pages =        "93--94",
  month =        feb,
  year =         "1989",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/32.1.93",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  MRclass =      "65H05",
  MRnumber =     "89k:65063",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "This work generalizes the Pythagorean sums in
                 \cite{Dubrulle:1983:CNM,Moler:1983:RSR}.",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/tiff/93.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/tiff/94.tif",
  abstract =     "A derivation is given of rapidly converging iterative
                 formulae for finding square roots which include, as
                 special cases, some recently published examples. Their
                 computational efficiencies are investigated for
                 sequential and parallel implementation. It is concluded
                 that the most efficient method is equivalent to
                 sequential application of the Newton Raphson formula; a
                 simple modification is suggested which brings the
                 advantage of root bracketing at little extra
                 computational cost.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., Glasgow Univ., UK",
  affiliationaddress = "Glasgow, Scotl",
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  classification = "723; 921; B0290F (Interpolation and function
                 approximation); C4130 (Interpolation and function
                 approximation)",
  corpsource =   "Dept. of Comput. Sci., Glasgow Univ., UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "computational; Computational efficiencies;
                 Computational Efficiency; Computer Metatheory;
                 Convergence; convergence of numerical methods;
                 Converging iterative formulae; converging iterative
                 formulae; efficiencies; formula; function
                 approximation; Iterative Methods; iterative methods;
                 Newton Raphson; Newton Raphson formula, Mathematical
                 Techniques; Parallel implementation; parallel
                 implementation; Square Roots; Square roots; square
                 roots",
  thesaurus =    "Convergence of numerical methods; Function
                 approximation; Iterative methods",
  treatment =    "P Practical",
}

@Article{Jeffries:1989:GFA,
  author =       "John S. Jeffries and Donald R. Smith",
  title =        "A {Green} function approach for a singularly perturbed
                 vector boundary-value problem",
  journal =      j-ADV-APPL-MATH,
  volume =       "10",
  number =       "1",
  pages =        "1--50",
  month =        mar,
  year =         "1989",
  CODEN =        "????",
  ISSN =         "0196-8858 (print), 1090-2074 (electronic)",
  ISSN-L =       "0196-8858",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of California at San Diego, La Jolla; Univ. of
                 California at San Diego, La Jolla",
  bibno =        "64833",
  catcode =      "G.1.7; G.1.7; F.2.1; G.1.2; G.1.3; G.1.2; G.1.3",
  CRclass =      "G.1.7 Ordinary Differential Equations; G.1.7 Boundary
                 value problems; G.1.7 Ordinary Differential Equations;
                 G.1.7 Convergence and stability; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computation of
                 transforms; G.1.2 Approximation; G.1.2 Nonlinear
                 approximation; G.1.3 Numerical Linear Algebra; G.1.3
                 Eigenvalues; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; G.1.3 Numerical Linear Algebra;
                 G.1.3 Linear systems (direct and iterative methods)",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Boundary value problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Convergence and stability;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computation of transforms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Nonlinear
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Eigenvalues;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Linear systems (direct and iterative
                 methods)",
  fjournal =     "Advances in Applied Mathematics",
  genterm =      "algorithms; theory",
  guideno =      "1989-03271",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01968858",
  journalabbrev = "Adv. Appl. Math.",
  jrldate =      "March 1989",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS",
}

@Article{Johnson:1989:IMA,
  author =       "K. R. Johnson",
  title =        "An Iterative Method for Approximating Square Roots",
  journal =      j-MATH-MAG,
  volume =       "62",
  number =       "4",
  pages =        "253--259",
  month =        oct,
  year =         "1989",
  CODEN =        "MAMGA8",
  ISSN =         "0025-570X",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Mathematics Magazine",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
}

@Article{Kaishev:1989:SSC,
  author =       "A. I. Kaishev",
  title =        "A sharpened scheme for constructing an a posteriori
                 interval extension of an elementary function.
                 ({Russian})",
  journal =      "Voprosy Kibernet. (Moscow)",
  volume =       "149",
  pages =        "14--18",
  year =         "1989",
  ISBN =         "0134-6388",
  ISBN-13 =      "0134-6388",
  MRclass =      "65G10",
  MRnumber =     "91i:65090",
  MRreviewer =   "I. N. Molchanov",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@InProceedings{Kak:1989:BAS,
  author =       "S. C. Kak and A. O. Barbir",
  booktitle =    "Proceedings of the Twenty-First Southeastern Symposium
                 on System Theory, 26--28 March 1989",
  title =        "The {Brahmagupta} algorithm for square rooting",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "456--459",
  year =         "1989",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "An algorithm for square root evaluation is introduced.
                 Novel features of the algorithm include suitability for
                 parallel processing and multi-initial guesses of the
                 root. An extension of the algorithm to the nth rooting
                 is provided. A VLSI \ldots{}",
}

@Article{Kogan:1989:GBF,
  author =       "B. J. Kogan",
  title =        "General background of functional memory algorithms",
  journal =      j-TRANS-SOC-COMP-SIM,
  volume =       "5",
  number =       "4",
  pages =        "285--317",
  month =        oct,
  year =         "1989",
  CODEN =        "TSCSEV",
  ISSN =         "0740-6797",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of California, Los Angeles",
  bibno =        "69149",
  catcode =      "C.3; G.1.2; G.1.2; E.4",
  CRclass =      "C.3 Signal processing systems; G.1.2 Approximation;
                 G.1.2 Elementary function approximation; G.1.2
                 Approximation; G.1.2 Linear approximation; E.4 Data
                 compaction and compression",
  descriptor =   "Computer Systems Organization, SPECIAL-PURPOSE AND
                 APPLICATION-BASED SYSTEMS, Signal processing systems;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Linear approximation; Data, CODING AND
                 INFORMATION THEORY, Data compaction and compression",
  fjournal =     "Transactions of the Society for Computer Simulation",
  genterm =      "algorithms; design",
  guideno =      "1989-10680",
  journalabbrev = "Trans. Soc. Comput. Simul.",
  jrldate =      "Oct. 1989",
  subject =      "C. Computer Systems Organization; C.3 SPECIAL-PURPOSE
                 AND APPLICATION-BASED SYSTEMS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS; E. Data; E.4 CODING
                 AND INFORMATION THEORY",
}

@InProceedings{Kojima:1989:PDI,
  author =       "M. Kojima and S. Mizuno and A. Yoshise",
  title =        "A primal-dual interior point algorithm for linear
                 programming",
  crossref =     "Megiddo:1989:PMP",
  bookpages =    "x + 158",
  pages =        "29--47",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "74173",
  catcode =      "G.1.6; F.2.1; G.1.2; F.2.2; F.2.1; I.1.2; I.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; F.2.1
                 Numerical Algorithms and Problems; G.1.2 Approximation;
                 G.1.2 Elementary function approximation; F.2.2
                 Nonnumerical Algorithms and Problems; F.2.2 Geometrical
                 problems and computations; F.2.1 Numerical Algorithms
                 and Problems; F.2.1 Computations on matrices; I.1.2
                 Algorithms; I.1.2 Algebraic algorithms; I.1.2
                 Algorithms; I.1.2 Analysis of algorithms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Geometrical problems and computations; Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices; Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms; Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms, Analysis of algorithms",
  genterm =      "algorithms; theory",
  guideno =      "1989-12475",
  procdate =     "March 1-4, 1987",
  procloc =      "Pacific Grove, CA",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION",
}

@Article{Kraaikamp:1989:SEP,
  author =       "Cor Kraaikamp",
  title =        "Statistic and ergodic properties of {Minkowski}'s
                 diagonal continued fraction",
  journal =      j-THEOR-COMP-SCI,
  volume =       "65",
  number =       "2",
  pages =        "197--212",
  day =          "28",
  month =        jun,
  year =         "1989",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Amsterdam Univ., Amsterdam, The Netherlands and Univ.
                 de Provence, Marseille, France",
  bibno =        "70095",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Theoretical Computer Science",
  genterm =      "algorithms; theory",
  guideno =      "1989-10594",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
  journalabbrev = "Theor. Comput. Sci.",
  jrldate =      "28 June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Kreider:1989:WSA,
  author =       "K. L. Kreider",
  title =        "A wave splitting approach to time dependent inverse
                 scattering for the stratified cylinder",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "49",
  number =       "3",
  pages =        "932--943",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "64953",
  catcode =      "G.1.7; G.1.2; J.2; J.2; F.2.2; G.1.3; I.1.1",
  CRclass =      "G.1.7 Ordinary Differential Equations; G.1.7 Initial
                 value problems; G.1.2 Approximation; G.1.2 Elementary
                 function approximation; J.2 Physics; J.2 Electronics;
                 F.2.2 Nonnumerical Algorithms and Problems; F.2.2
                 Geometrical problems and computations; G.1.3 Numerical
                 Linear Algebra; G.1.3 Linear systems (direct and
                 iterative methods); I.1.1 Expressions and Their
                 Representation; I.1.1 Simplification of expressions",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Initial value problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Physics; Computer Applications, PHYSICAL
                 SCIENCES AND ENGINEERING, Electronics; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative methods);
                 Computing Methodologies, ALGEBRAIC MANIPULATION,
                 Expressions and Their Representation, Simplification of
                 expressions",
  fjournal =     "SIAM Journal on Applied Mathematics",
  genterm =      "algorithms; theory; experimentation; measurement",
  guideno =      "1989-09722",
  journal-URL =  "http://epubs.siam.org/siap",
  journalabbrev = "SIAM J. Appl. Math.",
  jrldate =      "June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; J.
                 Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; J. Computer Applications; J.2 PHYSICAL
                 SCIENCES AND ENGINEERING; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; I.
                 Computing Methodologies; I.1 ALGEBRAIC MANIPULATION",
}

@Article{Lin:1989:ANT,
  author =       "Jinn Tyan Lin",
  title =        "Approximating the normal tail probability and its
                 inverse for use on a pocket calculator",
  journal =      j-APPL-STAT,
  volume =       "38",
  number =       "1",
  pages =        "69--70",
  year =         "1989",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  MRclass =      "62E15",
  MRnumber =     "983 303",
  bibdate =      "Sat Apr 21 10:25:25 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/as1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}

@PhdThesis{Littlestone:1989:MBL,
  author =       "N. Littlestone",
  title =        "Mistake bounds and logarithmic linear-threshold
                 learning algorithms",
  type =         "{Ph.D} Thesis",
  school =       "University of California at Santa Cruz",
  address =      "Santa Cruz, CA, USA",
  pages =        "????",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "76493",
  catcode =      "I.2.6; J.4; H.1.2; G.1.2",
  CRclass =      "I.2.6 Learning; J.4 Psychology; H.1.2 User/Machine
                 Systems; H.1.2 Human information processing; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Computing Methodologies, ARTIFICIAL INTELLIGENCE,
                 Learning; Computer Applications, SOCIAL AND BEHAVIORAL
                 SCIENCES, Psychology; Information Systems, MODELS AND
                 PRINCIPLES, User/Machine Systems, Human information
                 processing; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "algorithms; human factors; performance",
  guideno =      "1989-12934",
  source =       "UMI Order No: GAX89-26506",
  subject =      "I. Computing Methodologies; I.2 ARTIFICIAL
                 INTELLIGENCE; J. Computer Applications; J.4 SOCIAL AND
                 BEHAVIORAL SCIENCES; H. Information Systems; H.1 MODELS
                 AND PRINCIPLES; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}

@Article{Lo:1989:RBP,
  author =       "Shaw-Hwa Lo and Jane-Ling Wang",
  title =        "Representations for the bivariate product limit
                 estimators and the bootstrap versions",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "28",
  number =       "2",
  pages =        "211--226",
  month =        feb,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259x (print), 1095-7243 (electronic)",
  ISSN-L =       "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of California, Davis; Univ. of California,
                 Davis",
  bibno =        "64339",
  catcode =      "G.3; G.1.2; G.1.4; G.1.7",
  CRclass =      "G.3 Statistical computing; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.1.4 Quadrature and
                 Numerical Differentiation; G.1.4 Gaussian quadrature;
                 G.1.7 Ordinary Differential Equations; G.1.7
                 Convergence and stability",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation,
                 Gaussian quadrature; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Convergence and stability",
  fjournal =     "Journal of Multivariate Analysis",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-08465",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "February 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G.3 PROBABILITY AND STATISTICS",
}

@Article{Lorentz:1989:NA,
  author =       "G. G. Lorentz",
  title =        "Notes on approximation",
  journal =      j-J-APPROX-THEORY,
  volume =       "56",
  number =       "3",
  pages =        "360--365",
  month =        mar,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72258",
  catcode =      "G.1.1; G.1.2; G.1.1",
  CRclass =      "G.1.1 Interpolation; G.1.1 Smoothing; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.1 Interpolation; G.1.1 Spline and piecewise
                 polynomial interpolation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Smoothing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Spline and piecewise
                 polynomial interpolation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "algorithms; theory",
  guideno =      "1989-07816",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Mar. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@InCollection{Lovelace:1989:SAE,
  author =       "Augusta Ada Lovelace",
  title =        "Sketch of the {Analytical Engine} (1843)",
  crossref =     "Campbell-Kelly:1989:WCB-3",
  pages =        "89--170",
  year =         "1989",
  bibdate =      "Tue Jan 22 17:54:41 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Bernoulli numbers",
}

@InProceedings{Lu:1989:VMI,
  author =       "P. Y. Lu and K. Dawallu",
  title =        "A {VLSI} Module for {IEEE} Floating-Point
                 Multiplication\slash Division\slash Square Root",
  crossref =     "IEEE:1989:PII",
  bookpages =    "xvii + 587",
  pages =        "366--368",
  year =         "1989",
  bibdate =      "Wed Nov 06 12:08:38 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The major objective of this VLSI module design is to
                 determine how to modify a fast floating-point
                 multiplier so that it can perform division and square
                 root in accordance with IEEE standards. This has been
                 achieved by applying the Newton-Ralphson iteration only
                 on the mantissa and adjusting the iterated result by a
                 rounding algorithm. Using 1.0- mu m CMOS standard cell
                 technology, the total area of this module is
                 approximately 7.0 mm*6.5 mm, which is just 25\% larger
                 than the floating-point multiplier. The module can
                 compute multiplication, division, and square root in 3,
                 31, and 43 cycles, respectively. The cycle time, under
                 nominal conditions, is expected to be 20 ns. (2
                 Refs.)",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "LSI Logic Corp., Menlo Park, CA, USA",
  classification = "B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C4130 (Interpolation and function
                 approximation); C5230 (Digital arithmetic methods)",
  keywords =     "1 Micron; 20 Ns; 7 To 6.5 mm; CMOS standard cell
                 technology; Cycle time; Fast floating-point multiplier;
                 Floating point division; Floating point square root;
                 IEEE standards; Iterated result; Mantissa; Multiplier
                 modification; Newton-Ralphson iteration; Rounding
                 algorithm; VLSI module design",
  numericalindex = "Time 2.0E-08 s; Size 1.0E-06 m; Size 6.5E-03 to
                 7.0E-03 m",
  thesaurus =    "Cellular arrays; CMOS integrated circuits; Digital
                 arithmetic; Dividing circuits; Iterative methods;
                 Modules; Multiplying circuits; VLSI",
}

@Article{Macleod:1989:SAA,
  author =       "Allan J. Macleod",
  title =        "Statistical Algorithms: {Algorithm AS 245}: a Robust
                 and Reliable Algorithm for the Logarithm of the Gamma
                 Function",
  journal =      j-APPL-STAT,
  volume =       "38",
  number =       "2",
  pages =        "397--402",
  month =        jun,
  year =         "1989",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  bibdate =      "Sat Apr 21 10:25:27 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://lib.stat.cmu.edu/apstat/245",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}

@InProceedings{Mansour:1989:CAS,
  author =       "Y. Mansour and B. Schieber and P. Tiwari",
  booktitle =    "30th Annual Symposium on Foundations of Computer
                 Science, 1989",
  title =        "The complexity of approximating the square root",
  crossref =     "IEEE:1989:ASF",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "325--330",
  year =         "1989",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The authors prove upper and lower bounds for
                 approximately computing the square root using a given
                 set of operations. The bounds are extended to hold for
                 approximating the kth root, for any fixed k. Several
                 tools from approximation \ldots{}",
}

@Article{Martin:1989:TPQ,
  author =       "Pablo Martin and Antonio Luis Guerrero",
  title =        "Two-point quasi-fractional approximations to the
                 {Bessel} function {$ J_\nu (x) $} of fractional order",
  journal =      j-J-COMPUT-PHYS,
  volume =       "85",
  number =       "2",
  pages =        "487--492",
  month =        dec,
  year =         "1989",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(89)90161-7",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Sun Jan 1 15:59:48 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999189901617",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
  remark =       "This work produces only 3D approximations.",
}

@InProceedings{Megiddo:1989:POS,
  author =       "N. Megiddo",
  title =        "Pathways to the optimal set in linear programming",
  crossref =     "Megiddo:1989:PMP",
  pages =        "131--158",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "74179",
  catcode =      "G.1.6; G.1.2; G.2.2; G.1.2; G.1.5; F.2.1; I.1.2; G.4;
                 G.4",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.2.2 Graph Theory; G.2.2 Path and circuit problems;
                 G.1.2 Approximation; G.1.2 Spline and piecewise
                 polynomial approximation; G.1.5 Roots of Nonlinear
                 Equations; G.1.5 Iterative methods; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computations on
                 matrices; I.1.2 Algorithms; I.1.2 Analysis of
                 algorithms; G.4 Algorithm analysis; G.4 Efficiency",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation,
                 Elementary function approximation; Mathematics of
                 Computing, DISCRETE MATHEMATICS, Graph Theory, Path and
                 circuit problems; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Spline and piecewise
                 polynomial approximation; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Roots of Nonlinear Equations,
                 Iterative methods; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices; Computing
                 Methodologies, ALGEBRAIC MANIPULATION, Algorithms,
                 Analysis of algorithms; Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis; Mathematics
                 of Computing, MATHEMATICAL SOFTWARE, Efficiency",
  genterm =      "algorithms; performance; theory",
  guideno =      "1989-12481",
  procdate =     "March 1-4, 1987",
  procloc =      "Pacific Grove, CA",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.2 DISCRETE MATHEMATICS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION; G. Mathematics of Computing;
                 G.4 MATHEMATICAL SOFTWARE; G. Mathematics of Computing;
                 G.4 MATHEMATICAL SOFTWARE",
}

@PhdThesis{Miler:1989:EEM,
  author =       "T. H. Miler",
  title =        "Error evaluation of microcomputer intrinsic
                 functions",
  type =         "{Ph.D} Thesis",
  school =       "University of Idaho",
  address =      "Moscow, ID",
  pages =        "????",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "76168",
  catcode =      "G.4; G.1.2; J.2",
  CRclass =      "G.4 Reliability and robustness; G.1.2 Approximation;
                 G.1.2 Elementary function approximation; J.2
                 Mathematics and statistics",
  descriptor =   "Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Computer Applications, PHYSICAL SCIENCES
                 AND ENGINEERING, Mathematics and statistics",
  genterm =      "algorithms; reliability",
  guideno =      "1989-12941",
  source =       "UMI order no: GAX89-22813",
  subject =      "G. Mathematics of Computing; G.4 MATHEMATICAL
                 SOFTWARE; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; J. Computer Applications; J.2 PHYSICAL
                 SCIENCES AND ENGINEERING",
}

@InProceedings{Montuschi:1989:EIH,
  author =       "Paolo Montuschi and Luigi Cinimera",
  title =        "On the efficient implementation of higher radix square
                 root algorithms",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "154--161",
  year =         "1989",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Montuschi.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
  summary =      "Square root nonrestoring algorithms operating with a
                 radix higher than two (but power of 2) are discussed.
                 Formulas are derived delimiting the feasibility space
                 of the class of algorithms considered as a function of
                 the different parameters. This \ldots{}",
}

@Book{Moshier:1989:MPM,
  author =       "Stephen L. B. Moshier",
  title =        "Methods and Programs for Mathematical Functions",
  publisher =    pub-ELLIS-HORWOOD,
  address =      pub-ELLIS-HORWOOD:adr,
  pages =        "vii + 415",
  year =         "1989",
  ISBN =         "0-7458-0289-3",
  ISBN-13 =      "978-0-7458-0289-3",
  LCCN =         "QA331 .M84 1989",
  MRclass =      "*65D20, 26-04, 33-04, 65-02, 65C99",
  bibdate =      "Thu Sep 01 10:33:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\pounds 48.00",
  URL =          "http://www.moshier.net/;
                 http://www.netlib.org/cephes",
  ZMnumber =     "0701.65011",
  acknowledgement = ack-nj,
  shorttableofcontents = "Preface / vii \\
                 1: Floating Point Arithmetic / 1 \\
                 2: Approximation Methods / 75 \\
                 3: Software Notes / 129 \\
                 4: Elementary Functions / 143 \\
                 5: Probability Distributions and Related Functions /
                 201 6: Bessel Functions / 263 \\
                 7: Other Special Functions / 333 \\
                 Bibliography / 411 \\
                 Index / 413",
  tableofcontents = "Preface / vii \\
                 1: Floating Point Arithmetic / 1 \\
                 1.1 Numeric Data Structures / 1 \\
                 1.2 Rounding / 5 \\
                 1.3 Addition and Subtraction / 6 \\
                 1.4 Multiplication / 7 \\
                 1.4.1 Long Multiplication in Binary Radix / 8 \\
                 1.4.2 Multiplication in Word Integer Radix / 8 \\
                 1.4.3 Fast Multiplication / 9 \\
                 1.5 Division / 10 \\
                 1.5.1 Long Division / 10 \\
                 1.5.2 Division by Taylor Series / 11 \\
                 1.5.3 Newton--Raphson Division / 11 \\
                 1.6 C Language / 12 \\
                 1.7 An Extended Double Arithmetic: ieee.c / 13 \\
                 1.8 Binary - Decimal Conversion / 46 \\
                 1.8.1 etoasc.c / 47 \\
                 1.8.2 asctoe.c / 54 \\
                 1.9 Analysis of Error / 58 \\
                 1.9.1 Roundoff and Cancellation / 58 \\
                 1.9.2 Error Propagation / 60 \\
                 1.9.3 Error as a Random Variable / 61 \\
                 1.9.4 Order of Summation / 62 \\
                 1.10 Complex Arithmetic / 62 \\
                 1.10.1 cmplx.c / 64 \\
                 1.10.2 Absolute Value: cabs.c / 67 \\
                 1.11 Rational Arithmetic / 69 \\
                 1.11.1 euclid.c / 70 \\
                 2: Approximation Methods / 75 \\
                 2.1 Power Series / 75 \\
                 2.2 Chebyshev Expansions / 76 \\
                 2.2.1 chbevl.c / 79 \\
                 2.3 Pad{\'e} Approximations / 80 \\
                 2.4 Least Maximum Approximations / 82 \\
                 2.4.1 Best Polynomial Approximations / 82 \\
                 2.4.2 Best Rational Approximations / 85 \\
                 2.4.3 Special Rational Forms / 87 \\
                 2.5 A Program to Find Best Approximations: remes.c / 88
                 \\
                 2.6 Forms of Approximation / 111 \\
                 2.7 Asymptotic Expansions / 113 \\
                 2.8 Continued Fractions / 114 \\
                 2.8.1 Continued Fractions from Recurrences / 115 \\
                 2.8.2 Recurrences from Differential Equations / 116 \\
                 2.8.3 Computing Continued Fractions / 117 \\
                 2.9 Polynomials / 117 \\
                 2.9.1 polevl.c / 118 \\
                 2.10 Newton--Raphson Iterations / 119 \\
                 2.10.1 Division / 120 \\
                 2.10.2 Exponent Separation / 121 \\
                 2.10.3 Square Root / 122 \\
                 2.10.4 sqrt.c / 123 \\
                 2.10.5 Longhand Square Root / 124 \\
                 2.10.6 esqrt.c / 124 \\
                 2.10.7 Cube Root / 126 \\
                 2.10.8 cbrt.c / 127 \\
                 3: Software Notes / 129 \\
                 3.1 Design Strategy / 129 \\
                 3.2 Testing / 131 \\
                 3.3 System Utilities / 132 \\
                 3.3.1 mconf.h / 132 \\
                 3.3.2 mtherr.c / 134 \\
                 3.3.3 const.c / 136 \\
                 3.4 Arithmetic Utilities / 137 \\
                 3.4.1 efloor.c / 138 \\
                 3.4.2 efrexp.c / 140 \\
                 3.4.3 eldexp.c / 140 \\
                 4: Elementary Functions / 143 \\
                 4.1 $e^x$ / 143 \\
                 4.1.1 exp.c / 145 \\
                 4.2 $\ln x$ / 147 \\
                 4.2.1 log.c / 149 \\
                 4.3 Argument Transformation for Circular Functions /
                 152 \\
                 4.4 Sine and cosine / 153 \\
                 4.4.1 sin.c / 154 \\
                 4.4.2 cos.c / 156 \\
                 4.5 Tangent and Cotangent / 157 \\
                 4.5.1 tan.c / 158 \\
                 4.6 Complex Circular Functions / 161 \\
                 4.7 $\sin^{-1} x $ / 162 \\
                 4.7.1 asin.c / 163 \\
                 4.8 $\cos^{-1} x $ / 165 \\
                 4.8.1 acos.c / 165 \\
                 4.9 $\tan^{-1} x$ / 166 \\
                 4.9.1 atan.c / 168 \\
                 4.9.2 atan2.c / 169 \\
                 4.10 Complex Inverse Circular Functions / 170 \\
                 4.11 $\sinh x$ / 170 \\
                 4.11.1 sinh.c / 171 \\
                 4.12 $\cosh x$ / 172 \\
                 4.12.1 cosh.c / 173 \\
                 4.13 $\tanh x$ / 173 \\
                 4.13.1 tanh.c / 174 \\
                 4.14 $\sinh^{-1} x $ / 175 \\
                 4.14.1 asinh.c / 176 \\
                 4.15 $\cosh^{-1} x $ / 177 \\
                 4.15.1 acosh.c / 178 \\
                 4.16 $\tanh^{-1} x$ / 179 \\
                 4.16.1 atanh.c / 180 \\
                 4.17 Power Function / 181 \\
                 4.17.1 Real Exponent / 182 \\
                 4.17.2 pow.c / 182 \\
                 4.17.3 Integer Exponent / 189 \\
                 4.17.4 powi.c / 190 \\
                 4.18 Testing / 192 \\
                 4.19 Single Precision Polynomial Approximations / 193
                 \\
                 4.19.1 $\cos x$ / 193 \\
                 4.19.2 $\cosh^{-1} x $ / 193 \\
                 4.19.3 $\exp x$ / 196 \\
                 4.19.4 $\ln x$ / 196 \\
                 4.19.5 $\sin x$ / 197 \\
                 4.19.6 $\sin^{-1} x $ / 197 \\
                 4.19.7 Square Root / 197 \\
                 4.19.8 $\tan x$ / 198 \\
                 4.19.9 $\tan^{-1} x$ / 198 \\
                 4.19.10 $\tanh x$ / 199 \\
                 4.19.11 $tanh^{-1} x$ / 199 \\
                 5: Probability Distributions and Related Functions /
                 201 \\
                 5.1 $n!$ / 202 \\
                 5.1.1 fac.c / 204 \\
                 5.2 $\Gamma(x)$ / 206 \\
                 5.2.1 gamma.c / 210 \\
                 5.2.2 lgam.c / 214 \\
                 5.3 Incomplete Gamma Integral / 217 \\
                 5.3.1 igamc.c / 218 \\
                 5.3.2 igam.c / 220 \\
                 5.3.3 Functional Inverse of Incomplete Gamma Integral /
                 221 \\
                 5.3.4 igami.c / 221 \\
                 5.4 Gamma Distribution / 222 \\
                 5.4.1 gdtr c / 222 \\
                 5.4.2 gdtrc.c / 223 \\
                 5.5 $\chi^2$ Distribution / 223 \\
                 5.5.1 chdtrc.c / 224 \\
                 5.5.2 chdtr.c / 224 \\
                 5.5.3 chdtrl.c / 224 \\
                 5.6 Poisson Distribution / 225 \\
                 5.6.1 pdtrc.c / 225 \\
                 5.6.2 pdtr.c / 226 \\
                 5.6.3 pdtri.c / 226 \\
                 5.7 Beta Function / 227 \\
                 5.7.1 beta.c / 227 \\
                 5.8 Incomplete Beta Integral / 229 \\
                 5.8.1 ibet.c / 231 \\
                 5.8.2 Functional Inverse of Incomplete Beta Integral /
                 238 \\
                 5.9 Beta Distribution / 241 \\
                 5.9.1 btdtr.c / 241 \\
                 5.10 Binomial Distribution / 241 \\
                 5.10.1 bdtrc.c / 242 \\
                 5.10.2 bdtr.c / 243 \\
                 5.10.3 bdtri.c / 244 \\
                 5.11 Negative Binomial Distribution / 244 \\
                 5.11.1 nbdtr.c / 245 \\
                 5.11.2 nbdtrc.c / 245 \\
                 5.12 F Distribution / 246 \\
                 5.12.1 fdtrc.c / 247 \\
                 5.12.2 fdtr.c / 247 \\
                 5.12.3 fdtrci.c / 248 \\
                 5.13 Student's $t$ distribution / 249 \\
                 5.13.1 stdtr.c / 250 \\
                 5.14 Gaussian Distribution / 252 \\
                 5.14.1 ndtr.c / 254 \\
                 5.14.2 erfc.c / 256 \\
                 5.14.3 erf.c / 257 \\
                 5.14.4 Functional Inverse of Gaussian Distribution /
                 258 \\
                 5.14.5 ndtri.c / 259 \\
                 6: Bessel Functions / 263 \\
                 6.1 $J_0(x)$ / 263 \\
                 6.1.1 jO.c / 265 \\
                 6.2 $Y_0(x)$ / 268 \\
                 6.2.1 yO.c / 269 \\
                 6.3 Modulus and Phase / 270 \\
                 6.4 $J_1(x)$ / 271 \\
                 6.4.1 jl.c / 272 \\
                 6.5 $Y_1(x)$ / 275 \\
                 6.5.1 yl.c / 275 \\
                 6.6 $J_n(x)$ / 276 \\
                 6.1 $I_0(x)$ / 277 \\
                 6.7.1 i0.c / 278 \\
                 6.8 $I_1(x)$ / 281 \\
                 6.8.1 i1.c / 283 \\
                 6.9 $I_\nu(x)$ / 285 \\
                 6.9.1 iv.c / 286 \\
                 6.10 $K_0(x)$ / 287 \\
                 6.10.1 kO.c / 287 \\
                 6.11 $K_1(x)$ / 291 \\
                 6.11.1 kl.c / 291 \\
                 6.12 $K_n(x)$ / 294 \\
                 6.12.1 kn.c / 295 \\
                 6.13 $J_\nu(x)$ / 299 \\
                 6.13.1 jv.c / 301 \\
                 6.14 Airy Functions / 315 \\
                 6.14.1 airy.c / 322 \\
                 6.15 $Y_n(x)$ / 328 \\
                 6.15.1 yn.c / 329 \\
                 6.16 Testing / 330 \\
                 7: Other Special Functions / 333 \\
                 7.1 Hypergeometric Functions / 333 \\
                 7.1.1 $_2F_1$ / 334 \\
                 7.1.2 hyp2fi.c / 335 \\
                 7.1.3 $_1F_1$ / 341 \\
                 7.1.4 hyplfi.c / 342 \\
                 7.1.5 $_2F_0$ / 346 \\
                 7.1.6 hyp2ffi.c / 346 \\
                 7.2 Struve Functions / 348 \\
                 7.2.1 hypl1f2.c / 348 \\
                 7.2.2 hyp3f0.c / 349 \\
                 7.2.3 yv.c / 351 \\
                 7.2.4 struve.c / 351 \\
                 7.3 $\psi(x)$ / 352 \\
                 7.3.1 psi.c / 354 \\
                 7.4 Exponential Integral / 355 \\
                 7.4.1 en.c / 356 \\
                 7.5 Sine and Cosine Integrals / 360 \\
                 7.5.1 sici.c / 362 \\
                 7.5.2 Hyperbolic Sine and Cosine Integrals / 367 \\
                 7.5.3 shichi.c / 370 \\
                 7.6 Dilogarithm / 374 \\
                 7.6.1 spence.c / 375 \\
                 7.7 Dawson's Integral / 377 \\
                 7.7.1 dawsn.c / 378 \\
                 7.8 Fresnel Integrals / 381 \\
                 7.8.1 fresnl.c / 383 \\
                 7.9 Elliptic Functions / 387 \\
                 7.9.1 $K(m)$ / 387 \\
                 7.9.2 ellpk.c / 388 \\
                 7.9.3 $F(\phi|m)$ / 389 \\
                 7.9.4 ellik.c / 390 \\
                 7.9.5 $E(m)$ / 392 \\
                 7.9.6 ellpe.c / 392 \\
                 7.9.7 $E(\phi|m)$ / 393 \\
                 7.9.8 ellie.c / 394 \\
                 7.9.9 Jacobian Elliptic Functions / 396 \\
                 7.9.10 ellpj.c / 398 \\
                 7.10 Zeta Functions / 400 \\
                 7.10.1 hurwiz.c / 400 \\
                 7.10.2 Riemann Zeta Function / 402 \\
                 7.10.3 zetac.c / 405 \\
                 Bibliography / 411 \\
                 Index / 413",
}

@Article{Norton:1989:PCA,
  author =       "Robert M. Norton",
  title =        "Pocket-Calculator Approximation for Areas under the
                 Standard Normal Curve",
  journal =      j-AMER-STAT,
  volume =       "43",
  number =       "1",
  pages =        "24--26",
  month =        feb,
  year =         "1989",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Jan 27 12:40:30 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326443;
                 https://www.math.utah.edu/pub/tex/bib/amstat1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2685163",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Rhee:1989:MII,
  author =       "W. T. Rhee and M. Talagrand",
  title =        "Martingale inequalities, interpolation and
                 {NP}-complete problems",
  journal =      j-MATH-OP-RES,
  volume =       "14",
  number =       "1",
  pages =        "91--96",
  month =        feb,
  year =         "1989",
  CODEN =        "MOREDQ",
  ISSN =         "0364-765x (print), 1526-5471 (electronic)",
  ISSN-L =       "0364-765X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ., Paris, Paris, France; Ohio State Univ.,
                 Columbus",
  bibno =        "67063",
  catcode =      "G.2.2; H.1.1; G.1.1; G.1.2; G.3; I.6.4; F.1.3",
  CRclass =      "G.2.2 Graph Theory; G.2.2 Path and circuit problems;
                 H.1.1 Systems and Information Theory; H.1.1 General
                 systems theory; G.1.1 Interpolation; G.1.1
                 Interpolation formulas; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.3 Probabilistic
                 algorithms (including Monte Carlo); I.6.4 Model
                 Validation and Analysis; F.1.3 Complexity Classes;
                 F.1.3 Reducibility and completeness",
  descriptor =   "Mathematics of Computing, DISCRETE MATHEMATICS, Graph
                 Theory, Path and circuit problems; Information Systems,
                 MODELS AND PRINCIPLES, Systems and Information Theory,
                 General systems theory; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Interpolation, Interpolation
                 formulas; Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Probabilistic algorithms (including Monte Carlo);
                 Computing Methodologies, SIMULATION AND MODELING, Model
                 Validation and Analysis; Theory of Computation,
                 COMPUTATION BY ABSTRACT DEVICES, Complexity Classes,
                 Reducibility and completeness",
  fjournal =     "Mathematics of Operations Research",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-09079",
  journal-URL =  "http://pubsonline.informs.org/loi/moor",
  journalabbrev = "Math. Oper. Res.",
  jrldate =      "Feb. 1989",
  subject =      "F. Theory of Computation; F.1 COMPUTATION BY ABSTRACT
                 DEVICES; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G.2 DISCRETE MATHEMATICS; G.3 PROBABILITY AND
                 STATISTICS; H. Information Systems; H.1 MODELS AND
                 PRINCIPLES; I. Computing Methodologies; I.6 SIMULATION
                 AND MODELING",
}

@Article{Ruymgaart:1989:SPB,
  author =       "F. H. Ruymgaart",
  title =        "Some properties of bivariate empirical hazard
                 processes under random censoring",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "28",
  number =       "2",
  pages =        "271--281",
  month =        feb,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259x (print), 1095-7243 (electronic)",
  ISSN-L =       "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "64343",
  catcode =      "G.3; G.1.2",
  CRclass =      "G.3 Statistical computing; G.1.2 Approximation; G.1.2
                 Elementary function approximation",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Journal of Multivariate Analysis",
  genterm =      "algorithms; theory; measurement",
  guideno =      "1989-08469",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "February 1989",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}

@Article{Rybicki:1989:DIS,
  author =       "George B. Rybicki",
  title =        "{Dawson}'s Integral and the Sampling Theorem",
  journal =      j-COMPUT-PHYS,
  volume =       "3",
  number =       "2",
  pages =        "85--87",
  month =        mar,
  year =         "1989",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.4822832",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:45:17 MDT 2019",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.4822832",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}

@InCollection{Saigo:1989:FID,
  author =       "Megumi Saigo",
  title =        "Fractional integrals and derivatives associated with
                 elementary functions and {Bessel} functions",
  crossref =     "Srivastava:1989:UFF",
  pages =        "283--306",
  year =         "1989",
  MRclass =      "26A33 (33C10)",
  MRnumber =     "93h:26011",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Ellis Horwood Ser. Math. Appl.",
  acknowledgement = ack-nhfb,
}

@Article{Sala:1989:TJA,
  author =       "Kenneth L. Sala",
  title =        "Transformations of the {Jacobian} amplitude function
                 and its calculation via the arithmetic-geometric mean",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "20",
  number =       "6",
  pages =        "1514--1528",
  month =        nov,
  year =         "1989",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33A25 (42A16 70D99)",
  MRnumber =     "90j:33003",
  MRreviewer =   "J. M. H. Peters",
  bibdate =      "Sun Nov 28 19:24:55 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/20/6;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@Article{Smith:1989:EMP,
  author =       "David M. Smith",
  title =        "Efficient multiple-precision evaluation of elementary
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "52",
  number =       "185",
  pages =        "131--134",
  month =        jan,
  year =         "1989",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D15 (26-04)",
  MRnumber =     "90c:65034",
  MRreviewer =   "Menachem Dishon",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C4120 (Functional analysis)",
  corpsource =   "Dept. of Math., Loyola Univ., Los Angeles, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "arithmetic; base b; elementary functions; function
                 evaluation; multiple-precision evaluation",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Stearns:1989:SFD,
  author =       "C. C. Stearns",
  title =        "Subtractive floating-point division and square root
                 for {VLSI DSP}",
  crossref =     "IEE:1989:EEC",
  pages =        "405--409",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper describes recent architectural developments
                 in VLSI design for real-time digital signal processing.
                 In particular, floating point division and floating
                 point square root architectures applicable to both
                 adaptive filtering, standard deviation computations,
                 and general purpose processing are discussed. Emphasis
                 here is on the internal architectures of the arithmetic
                 units not on their applications. The research presented
                 in this paper has been proven feasible and reliable
                 from extensive gate-level simulation and fabrication in
                 silicon.",
  acknowledgement = ack-nhfb,
  classification = "B1265F (Microprocessors and microcomputers); B1270F
                 (Digital filters); B2570D (CMOS integrated circuits);
                 C5230 (Digital arithmetic methods); C5240 (Digital
                 filters); C5260 (Digital signal processing)",
  keywords =     "Adaptive filtering; Arithmetic units; CMOS technology;
                 Floating point division; Floating point square root
                 architectures; Gate-level simulation; General purpose
                 processing; Real-time digital signal processing;
                 Semiconductor; Standard deviation computations; VLSI
                 DSP",
  thesaurus =    "Adaptive filters; CMOS integrated circuits; Digital
                 arithmetic; Digital signal processing chips; VLSI",
}

@TechReport{Tang:1989:TCA,
  author =       "Ping Tak Peter Tang",
  title =        "Testing Computer Arithmetic by Elementary Number
                 Theory",
  institution =  "Mathematics and Computer Science Division, Argonne
                 National Laboratory",
  address =      "Argonne, IL, USA",
  pages =        "????",
  month =        aug,
  year =         "1989",
  bibdate =      "Fri Jun 11 12:38:06 1999",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}

@Article{Tang:1989:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Exponential
                 Function in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "15",
  number =       "2",
  pages =        "144--157",
  month =        jun,
  year =         "1989",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:47:40 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://doi.acm.org/10.1145/63522.214389;
                 http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p144-tang/",
  abstract =     "Algorithms and implementation details for the
                 exponential function in both single- and
                 double-precision of IEEE 754 arithmetic are presented
                 here. With a table of moderate size, the
                 implementations need only working-precision arithmetic
                 and are provably accurate to within 0.54 ulp as long as
                 the final result does not underflow. When the final
                 result suffers gradual underflow, the error is still no
                 worse than 0.77 ulp.",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@TechReport{Thomas:1989:SNL,
  author =       "Marlin A. Thomas and Gary W. Gemmill and John R.
                 Crigler",
  title =        "{STATLIB}: {NSWC} Library of Statistical Programs and
                 Subroutines",
  type =         "Technical Report",
  number =       "NSWC TR 89-97",
  institution =  "Naval Surface Warfare Center",
  address =      "Dahlgren, VA 22448-5000, USA and Silver Spring, MD
                 20903-5000, USA",
  pages =        "viii + 280",
  month =        aug,
  year =         "1989",
  bibdate =      "Sat Nov 15 10:39:12 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.dtic.mil/dtic/tr/fulltext/u2/a221538.pdf",
  abstract =     "This document provides a description of each program
                 and subroutine in STATLIB, THE Naval Surface Warfare
                 Center library of statistical programs and subroutines
                 for its general purpose computers. The Library contains
                 thirty-four programs and twenty-four subroutines for
                 statistical analysis, probability evaluation, and
                 random number generation. It was written to enable
                 Center Scientists and Engineers to efficiently perform
                 a wide variety of analyses and to generate pseudo
                 random numbers from many different probability
                 distributions.",
  acknowledgement = ack-nhfb,
  onlinedate =   "255",
  tableofcontents = "Introduction / 1 \\
                 Overview of STATLIB / 1 \\
                 Origin of STATLIB / 1 \\
                 Establishment of STATLIB / 1 \\
                 Commercial Statistical Packages at NSWC / 2 \\
                 Using STATLIB / 5 \\
                 Library Organization / 5 \\
                 How to Call It / 5 \\
                 Information Needed to Run It / 5 \\
                 Examples / 9 \\
                 Program / 9 \\
                 Subroutine / 10 \\
                 Descriptions and Input Guides / 21 \\
                 Programs / 23 \\
                 Regression Analysis / 25 \\
                 GEMREG General Multiple Regression / 29 \\
                 DAMRCA Dahlgren Multiple Regression Comprehensive
                 Analysis / 35 \\
                 WEPORU Uncorrelated Weighted Polynomial Regression / 41
                 \\
                 WEPORC Correlated Weighted Polynomial Regression / 45
                 \\
                 MROP Multiple Regression Using Orthogonal Polynomials /
                 49 \\
                 CANON Canonical Analysis of Second Order Response
                 Functions / 57 \\
                 DURBWAT Durbin--Watson Test for Independence of
                 Residuals / 61 \\
                 NEARNEB Near Neighbor Estimation of Experimental Error
                 / 63 \\
                 Goodness of Fit Analysis / 67 \\
                 UNORGOF Univariate Normal Goodness of Fit / 69 \\
                 BNORGOF Bivariate Normal Goodness of Fit / 75 \\
                 EXPGOF Exponential Goodness of Fit / 81 \\
                 WBLGOF Weibull Goodness ot / 83 \\
                 PERGOF Pearson System Goodness of Fit / 87 \\
                 UNKSGOF Univariate Normal Kolmogorov--Smirnov Test of
                 Fit / 93 \\
                 RANDOM Test of Fit for Uniform Random Number Generators
                 / 99 \\
                 Power Evaluation / 103 \\
                 DISCRETE POWER EVALUATION / 107 \\
                 BINIPOW Power of the Test on a Binomial Proportion /
                 109 \\
                 BIN2POW Power of the Test on the Difference of Two
                 Binomial Proportions / 113 \\
                 POIIPOW Power of the Test on the Poisson Parameter /
                 121 \\
                 Continuous Power Evaluation / 125 \\
                 NORIPOW Power of the One-Sample Normal Test on the Mean
                 / 127 \\
                 NOR2PWE Power of the Two-Simple Normal Test on Means
                 with ample Sizes / 131 \\
                 NOR2PWU Power of the Two-Sample Normal Test on Means
                 with Unequal Sample Sizes / 135 \\
                 T1POW Power of the One-Sample $t$ Test on the Mean /
                 141 \\
                 T2POW Power of the Two-Sample (Pooled) $t$ Test on
                 Means / 147 \\
                 CHIVPOW Power of the Chi-square Test on the Variance /
                 153 \\
                 FVARPOW Power of the $F$ Test for the Equality of
                 Variances / 157 \\
                 FEMPOW Power of the Test for One-Way Fixed Effects
                 Analysis of Variance / 163 \\
                 REMPOW Power of the Test for One-Way Random Effects
                 Analysis of Variance / 167 \\
                 Probability Evaluation / 171 \\
                 BINVARP Binomial Probability Distribution with Unequal
                 Single Trial Probabilities / 173 \\
                 NEGBIN Negative Binomial Probability Distribution / 177
                 \\
                 Confidence Limit Evaluation / 179 \\
                 BINCL Confidence Limits for the Binomial Parameter p /
                 181 \\
                 CEPCL Confidence Limits for the CEP (Circular Probable
                 Error) / 185 \\
                 SEPCL Confidence Limits for the SEP (Spherical Probable
                 Error) / 191 \\
                 Miscellaneous Statistical Analysis / 197 \\
                 LD50EST Estimation of LD50 (Lethal Dose 50th
                 Percentile) / 199 \\
                 FFAC2K Analysis of the 2**k Fractional Factorial
                 Experiment / 203 \\
                 Subroutines / 211 \\
                 Random Number Generation / 213 \\
                 Discrete Random Number Generators, / 217 \\
                 RANARB Arbitrary (User Specified) Discrete Distribution
                 / 219 \\
                 RANBER Bernoulli Distribution / 221 \\
                 RANBIN Binomial Distribution / 223 \\
                 RANGEO Geometric Distribution / 225 \\
                 RANHYP Hypergeometric Distribution / 227 \\
                 RANNBI Negative Binomial Distribution / 229 \\
                 RANPOI Poisson Distribution / 231 \\
                 RANUWO Discrete Uniform Distribution (Without
                 Replacement) / 233 \\
                 RANUWR Discrete Uniform Distribution (With Replacement)
                 / 235 \\
                 Continuous Random Number Generators / 237 \\
                 RANBET Beta Distribution / 239 \\
                 RANCSQ Chi-square Distribution / 241 \\
                 RANEXP Exponential Distribution / 243 \\
                 RANFDI $F$ Distribution / 245 \\
                 RANGAM Gamma Distribution / 247 \\
                 RANLGS Logistic Distribution / 249 \\
                 RANLOG Lognormal Distribution / 251 \\
                 RANNOR Normal Distribution / 255 \\
                 RANNVE Multivariate Normal Distribution / 257 \\
                 RANPDI Pearson Distributions / 261 \\
                 RANTDI Student's $t$ Distribution / 265 \\
                 RANUNI Continuous Uniform Distribution (On a Line) /
                 267 \\
                 RANCIR Continuous Uniform Distribution (Within a
                 Circle) / 269 \\
                 RANWEI Three-parameter Weibull Distribution / 271 \\
                 RANMK1 1st Order Markov Process / 273 \\
                 Glossary / 275 \\
                 Distribution / 277",
}

@Article{Ubhaya:1989:LAN,
  author =       "V. A. Ubhaya",
  title =        "{$ L_p $} approximation from nonconvex subsets of
                 special classes of functions",
  journal =      j-J-APPROX-THEORY,
  volume =       "57",
  number =       "2",
  pages =        "223--238",
  month =        may,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72277",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "verification; theory",
  guideno =      "1989-07833",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "May 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@InProceedings{Vaidya:1989:LWB,
  author =       "P. M. Vaidya",
  title =        "A locally well-behaved potential function and a simple
                 {Newton}-type method for finding the center of a
                 polytype",
  crossref =     "Megiddo:1989:PMP",
  pages =        "79--90",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "74176",
  catcode =      "G.1.6; G.1.6; F.2.2; G.1.2; G.1.5; G.1.5; I.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.6
                 Optimization; G.1.6 Gradient methods; F.2.2
                 Nonnumerical Algorithms and Problems; F.2.2 Geometrical
                 problems and computations; G.1.2 Approximation; G.1.2
                 Elementary function approximation; G.1.5 Roots of
                 Nonlinear Equations; G.1.5 Convergence; G.1.5 Roots of
                 Nonlinear Equations; G.1.5 Iterative methods; I.1.2
                 Algorithms; I.1.2 Nonalgebraic algorithms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization, Gradient
                 methods; Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and
                 Problems, Geometrical problems and computations;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations, Convergence; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
                 Equations, Iterative methods; Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic
                 algorithms",
  genterm =      "algorithms; theory",
  guideno =      "1989-12478",
  procdate =     "March 1-4, 1987",
  procloc =      "Pacific Grove, CA",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION",
  xxpages =      "131--158",
}

@Article{VanHalen:1989:AAA,
  author =       "P. {Van Halen}",
  title =        "Accurate analytical approximations for error function
                 and its integral",
  journal =      j-ELECT-LETTERS,
  volume =       "25",
  number =       "9",
  pages =        "561--563",
  day =          "27",
  month =        apr,
  year =         "1989",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19890383",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Dec 16 18:15:17 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/19780/",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}

@PhdThesis{Vavasis:1989:CFP,
  author =       "S. A. Vavasis",
  title =        "Complexity of fixed point computations",
  type =         "{Ph.D} Thesis",
  school =       "Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "????",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "76220",
  catcode =      "J.4; G.1.2; F.1.3; G.1.2; G.2.2",
  CRclass =      "J.4 Economics; G.1.2 Approximation; G.1.2 Nonlinear
                 approximation; F.1.3 Complexity Classes; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.2.2 Graph Theory; G.2.2 Network problems",
  descriptor =   "Computer Applications, SOCIAL AND BEHAVIORAL SCIENCES,
                 Economics; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Nonlinear approximation;
                 Theory of Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Complexity Classes; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, DISCRETE
                 MATHEMATICS, Graph Theory, Network problems",
  genterm =      "algorithms; theory",
  guideno =      "1989-12859",
  source =       "UMI order no: GAX89-19486",
  subject =      "J. Computer Applications; J.4 SOCIAL AND BEHAVIORAL
                 SCIENCES; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; F. Theory of Computation; F.1 COMPUTATION BY
                 ABSTRACT DEVICES; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.2
                 DISCRETE MATHEMATICS",
}

@InProceedings{Vial:1989:APP,
  author =       "J.-P. Vial",
  title =        "Approximate projections in a projective method for the
                 linear feasibility problem",
  crossref =     "Megiddo:1989:PMP",
  bookpages =    "x + 158",
  pages =        "65--78",
  year =         "1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "74175",
  catcode =      "G.1.6; F.2.2; I.1.2; G.1.6; G.1.2; F.2.1; G.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; F.2.2
                 Nonnumerical Algorithms and Problems; F.2.2 Geometrical
                 problems and computations; I.1.2 Algorithms; I.1.2
                 Nonalgebraic algorithms; G.1.6 Optimization; G.1.6
                 Constrained optimization; G.1.2 Approximation; G.1.2
                 Elementary function approximation; F.2.1 Numerical
                 Algorithms and Problems; F.2.1 Computations on
                 matrices; G.1.2 Approximation; G.1.2 Minimax
                 approximation and algorithms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations; Computing
                 Methodologies, ALGEBRAIC MANIPULATION, Algorithms,
                 Nonalgebraic algorithms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Optimization, Constrained
                 optimization; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Minimax
                 approximation and algorithms",
  genterm =      "algorithms; experimentation; measurement; performance;
                 theory",
  guideno =      "1989-12477",
  procdate =     "March 1-4, 1987",
  procloc =      "Pacific Grove, CA",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; F. Theory of Computation; F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{vonRosen:1989:MLE,
  author =       "D. von Rosen",
  title =        "Maximum likelihood estimators in multivariate linear
                 normal models",
  journal =      j-J-MULTIVAR-ANAL,
  volume =       "31",
  number =       "2",
  pages =        "187--200",
  month =        nov,
  year =         "1989",
  CODEN =        "JMVAAI",
  ISSN =         "0047-259x (print), 1095-7243 (electronic)",
  ISSN-L =       "0047-259X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Stockholm, Stockholm, Sweden",
  bibno =        "69314",
  catcode =      "G.1.6; G.1.2; G.1.2",
  CRclass =      "G.1.6 Optimization; G.1.6 Linear programming; G.1.2
                 Approximation; G.1.2 Linear approximation; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming; Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Linear
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Journal of Multivariate Analysis",
  genterm =      "algorithms; theory",
  guideno =      "1989-08484",
  journalabbrev = "J. Multivariate Anal.",
  jrldate =      "Nov. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Book{Wang:1989:SF,
  author =       "Z. X. Wang and D. R. Guo",
  title =        "Special Functions",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "xiii + 422",
  year =         "1989",
  ISBN =         "9971-5-0659-9",
  ISBN-13 =      "978-9971-5-0659-9",
  LCCN =         "QA331 .W296 1989",
  bibdate =      "Mon Sep 3 16:10:24 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Functions",
}

@Article{Wasilkowski:1989:AIV,
  author =       "G. W. Wasilkowski",
  title =        "On adaptive information with varying cardinality for
                 linear problems with elliptically contoured measures",
  journal =      j-J-COMPLEXITY,
  volume =       "5",
  number =       "3",
  pages =        "363--368",
  month =        sep,
  year =         "1989",
  CODEN =        "JOCOEH",
  ISSN =         "0885-064X (print), 1090-2708 (electronic)",
  ISSN-L =       "0885-064X",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. of Kentucky, Lexington, KY",
  bibno =        "68756",
  catcode =      "G.1.2; G.1.2; F.1.3",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.2 Approximation; G.1.2 Nonlinear
                 approximation; F.1.3 Complexity Classes",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Nonlinear approximation; Theory of
                 Computation, COMPUTATION BY ABSTRACT DEVICES,
                 Complexity Classes",
  fjournal =     "Journal of complexity",
  genterm =      "algorithms; theory",
  guideno =      "1989-08045",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0885064X",
  journalabbrev = "J. Complexity",
  jrldate =      "Sept. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; F.
                 Theory of Computation; F.1 COMPUTATION BY ABSTRACT
                 DEVICES",
}

@Article{Weniger:1989:NST,
  author =       "Ernst Joachim Weniger",
  title =        "Nonlinear sequence transformations for the
                 acceleration of convergence and the summation of
                 divergent series",
  journal =      j-COMPUT-PHYS-REP,
  volume =       "10",
  number =       "5--6",
  pages =        "189--371",
  month =        dec,
  year =         "1989",
  CODEN =        "CPHREF",
  DOI =          "https://doi.org/10.1016/0167-7977(89)90011-7",
  ISSN =         "0167-7977 (print), 1878-1004 (electronic)",
  ISSN-L =       "0167-7977",
  bibdate =      "Thu Dec 01 10:13:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Available as math.NA/0306302.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Reports",
  keywords =     "convergence acceleration",
}

@Article{Yortsos:1989:LSI,
  author =       "Y. C. Yortsos and F. J. Hickernell",
  title =        "Linear stability of immiscible displacement in porous
                 media",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "49",
  number =       "3",
  pages =        "730--748",
  month =        jun,
  year =         "1989",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "64942",
  catcode =      "G.1.8; G.1.0; J.2; G.1.2; G.1.4; G.1.8",
  CRclass =      "G.1.8 Partial Differential Equations; G.1.8 Parabolic
                 equations; G.1.0 General; G.1.0 Stability (and
                 instability); J.2 Earth and atmospheric sciences; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.1.4 Quadrature and Numerical Differentiation; G.1.4
                 Finite difference methods; G.1.8 Partial Differential
                 Equations; G.1.8 Difference methods",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations, Parabolic equations;
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Stability (and instability); Computer Applications,
                 PHYSICAL SCIENCES AND ENGINEERING, Earth and
                 atmospheric sciences; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation,
                 Finite difference methods; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Partial Differential Equations,
                 Difference methods",
  fjournal =     "SIAM Journal on Applied Mathematics",
  genterm =      "algorithms; theory; experimentation",
  guideno =      "1989-09711",
  journal-URL =  "http://epubs.siam.org/siap",
  journalabbrev = "SIAM J. Appl. Math.",
  jrldate =      "June 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING",
}

@Article{Zalik:1989:NIE,
  author =       "R. A. Zalik",
  title =        "A new inequality for entire functions",
  journal =      j-J-APPROX-THEORY,
  volume =       "58",
  number =       "3",
  pages =        "281--283",
  month =        sep,
  year =         "1989",
  CODEN =        "JAXTAZ",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  bibno =        "72294",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  fjournal =     "Journal of Approximation Theory",
  genterm =      "verification; theory",
  guideno =      "1989-07871",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  journalabbrev = "J. Approx. Theory",
  jrldate =      "Sept. 1989",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Book{Ziemer:1989:WDF,
  author =       "William P. Ziemer",
  title =        "Weakly differentiable functions: {Sobolev} spaces and
                 functions of bounded variation",
  volume =       "120",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 308",
  year =         "1989",
  ISBN =         "0-387-97017-7",
  ISBN-13 =      "978-0-387-97017-2",
  LCCN =         "QA323 .Z53 1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Graduate texts in mathematics",
  acknowledgement = ack-nhfb,
  affiliation =  "Indiana Univ., Bloomington",
  bibno =        "69369",
  catcode =      "G.1.2; G.1.8; G.1.5",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.8 Partial Differential Equations;
                 G.1.5 Roots of Nonlinear Equations",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Roots of Nonlinear Equations",
  genterm =      "algorithms; theory",
  guideno =      "1989-01732",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Amos:1990:RPP,
  author =       "Donald E. Amos",
  title =        "Remark on ``{Algorithm 644}: a Portable Package for
                 {Bessel} Functions of a Complex Argument and
                 Nonnegative Order''",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "404--404",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/98267.98299",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:26:24 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See
                 \cite{Amos:1986:APP,Amos:1995:RAP,Kodama:2007:RA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p404-amos/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf F.2.2}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems.",
}

@Article{Anderson:1990:FIC,
  author =       "G. D. Anderson and M. K. Vamanamurthy and M.
                 Vuorinen",
  title =        "Functional Inequalities for Complete Elliptic
                 Integrals and Their Ratios",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "21",
  number =       "2",
  pages =        "536--549",
  month =        mar,
  year =         "1990",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33E05 (30C62 33C75)",
  MRnumber =     "91d:33039",
  MRreviewer =   "K. C. Gupta",
  bibdate =      "Sat Dec 5 18:14:13 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@Article{Bellalij:1990:SPC,
  author =       "M. Bellalij",
  title =        "A simultaneous process for convergence acceleration
                 and error control",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "33",
  number =       "2",
  pages =        "217--231",
  day =          "21",
  month =        dec,
  year =         "1990",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(90)90370-F",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65B99 (65G10)",
  MRnumber =     "1090897 (92a:65029)",
  MRreviewer =   "Thomas A. Atchison",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "convergence acceleration",
}

@Article{Bronstein:1990:IEF,
  author =       "Manuel Bronstein",
  title =        "Integration of elementary functions",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "9",
  number =       "2",
  pages =        "117--173",
  month =        feb,
  year =         "1990",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  MRclass =      "12H05 (68Q40)",
  MRnumber =     "91h:12017",
  MRreviewer =   "Alexandru Buium",
  bibdate =      "Sat May 10 15:54:09 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Theory/cathode.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C1120 (Analysis); C4160 (Numerical integration and
                 differentiation)",
  corpsource =   "Dept. of Math. Sci, IBM Res. Div., Thomas J. Watson
                 Res. Center, Yorktown Heights, NY, USA",
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
  keywords =     "algebraic extension; algebraic function; decision
                 procedure; elementary function field; elementary
                 functions; exponential; finite terms; indefinite;
                 integration; integration Risch ODEs oderef; logarithm;
                 proof; Trager",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Carre:1990:PEF,
  author =       "C. Carre",
  title =        "Plethysm of elementary functions",
  journal =      "Bayreuth. Math. Schr.",
  volume =       "31",
  pages =        "1--18",
  year =         "1990",
  ISSN =         "0172-1062",
  MRclass =      "20C30 (05E05 22E45)",
  MRnumber =     "91f:20013",
  MRreviewer =   "John R. Stembridge",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Ciminiera:1990:HRS,
  author =       "L. Ciminiera and P. Montuschi",
  title =        "Higher radix square rooting",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "10",
  pages =        "1220--1231",
  month =        oct,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.59853",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:04 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=59853",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A general discussion on nonrestoring square root
                 algorithms is presented, showing bounds and constraints
                 delimiting the space of feasible algorithms, for all
                 the choices of radix, digit set and representation of
                 the partial remainder. Two classes of \ldots{}",
}

@Article{Cody:1990:PEP,
  author =       "W. J. Cody",
  title =        "Performance Evaluation of Programs for the Error and
                 Complementary Error Functions",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "29--37",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.77628",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65G05)",
  MRnumber =     "1 073 407",
  bibdate =      "Tue Oct 09 09:29:47 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p29-cody/;
                 http://www.acm.org/pubs/toc/Abstracts/0098-3500/77628.html",
  abstract =     "This paper presents methods for performance evaluation
                 of computer programs for the functions $ \textrm
                 {erf}(x) $, $ \textrm {erfc}(x) $, and $ \e^{x^2}
                 \textrm {erfc}(x) $. Accuracy estimates are based on
                 comparisons using power series expansions and an
                 expansion in the repeated integrals of $ \textrm
                 {erfc}(x) $. Some suggestions for checking robustness
                 are also given. Details of a specific implementation of
                 a test program are included.",
  acknowledgement = ack-nhfb,
  affiliation =  "Argonne Nat. Lab., IL, USA",
  classification = "B0290B (Error analysis in numerical methods); B0290F
                 (Interpolation and function approximation); C4110
                 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Complementary error functions; Computer programs;
                 FORTRAN; Power series expansions; Repeated integrals;
                 Robustness; Test program",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms.",
  thesaurus =    "Error analysis; Function approximation; Performance
                 evaluation",
}

@TechReport{DiDonato:1990:SDC,
  author =       "Armido R. DiDonato",
  title =        "Significant Digit Computation of the Elliptical
                 Coverage Function",
  type =         "Technical Report",
  number =       "NAVSWC TR 90-513",
  institution =  "Naval Surface Warfare Center",
  address =      "Dahlgren, VA 22448-5000, USA and Silver Spring, MD
                 20903-5000, USA",
  pages =        "v + 13 + A-7 + B-9 + 5",
  month =        sep,
  year =         "1990",
  bibdate =      "Sat Nov 15 10:55:35 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.dtic.mil/dtic/tr/fulltext/u2/a230523.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Dunham:1990:FPF,
  author =       "C. B. Dunham",
  title =        "Feasibility of ``perfect'' function evaluation",
  journal =      j-SIGNUM,
  volume =       "25",
  number =       "4",
  pages =        "25--26",
  month =        oct,
  year =         "1990",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/122272.122276",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:19 MDT 2005",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@Article{Dvorak:1990:NCI,
  author =       "Steven L. Dvorak and Edward F. Kuester",
  title =        "Numerical computation of the incomplete
                 {Lipschitz--Hankel} integral {$ {\rm Je}_0 (a, z) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "87",
  number =       "2",
  pages =        "301--327",
  month =        apr,
  year =         "1990",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(90)90255-Y",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:55:40 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/002199919090255Y",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Ercegovac:1990:RSR,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "Radix-$4$ square root without initial {PLA}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1016--1024",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57040",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57040",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Germain-Bonne:1990:CAN,
  author =       "B. Germain-Bonne",
  title =        "Convergence acceleration of number-machine sequences",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "32",
  number =       "1--2",
  pages =        "83--88",
  day =          "26",
  month =        nov,
  year =         "1990",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(90)90419-Z",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65B05",
  MRnumber =     "1091778 (91m:65007)",
  MRreviewer =   "W. Govaerts",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Extrapolation and rational approximation (Luminy,
                 1989)",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "convergence acceleration",
}

@Article{Hashemian:1990:SRA,
  author =       "R. Hashemian",
  title =        "Square Rooting Algorithms for Integer and
                 Floating-Point Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-39",
  number =       "8",
  pages =        "1025--1029",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57041",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "An algorithm for evaluating the square root of
                 integers and real numbers is developed. The procedure
                 consists of two parts: one to obtain a close estimate
                 of the square root and the other to modify the initial
                 value, iteratively, until a precise root is evaluated.
                 The major effort in this development has been
                 concentrated on two objectives: high speed and no
                 division operation other than division by 2. The first
                 objective is achieved through a simple two-step
                 procedure for getting the first estimate, and then
                 modifying it by employing a fast converging iteration
                 technique. The second objective is also fulfilled
                 through applying bit-shift operation rather than
                 division operation. The algorithm is simulated for both
                 integer and real numbers, and the results are compared
                 to two methods being widely used. The results
                 (tabulated) show considerable improvement in speed
                 compared to these other two methods.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Dept. of Electr. Eng., Northern Illinois Univ.,
                 Dekalb, IL, USA",
  classification = "C1160 (Combinatorial mathematics); C4130
                 (Interpolation and function approximation); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Bit-shift operation; Close estimate; Division by 2;
                 Fast converging iteration; Floating-point numbers;
                 Initial value modification; Integer numbers; Precise
                 root; Real numbers; Square rooting algorithms",
  summary =      "An algorithm for evaluating the square root of
                 integers and real numbers is developed. The procedure
                 consists of two parts: one to obtain a close estimate
                 of the square root and the other to modify the initial
                 value, iteratively, until a precise \ldots{}",
  thesaurus =    "Digital arithmetic; Iterative methods; Number theory",
}

@Book{Holton:1990:IJE,
  author =       "P. G. W. Holton",
  title =        "An Introduction to the {Jacobian} Elliptic Functions
                 with some Applications",
  publisher =    "University of Newcastle upon Tyne",
  address =      "Newcastle upon Tyne, UK",
  pages =        "117",
  year =         "1990",
  LCCN =         "????",
  bibdate =      "Wed Mar 15 06:50:49 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Ifantis:1990:DIP,
  author =       "E. K. Ifantis and P. D. Siafarikas",
  title =        "Differential inequalities for the positive zeros of
                 {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "30",
  number =       "2",
  pages =        "139--143",
  day =          "28",
  month =        may,
  year =         "1990",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:45 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279090022R",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Kiernan:1990:FAE,
  author =       "J. M. Kiernan and T. B. Blachowiak",
  title =        "Fast, Accurate Elementary Functions For the {Cray
                 Y-MP} Computer",
  crossref =     "Cray:1990:PCU",
  pages =        "243--252",
  year =         "1990",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}

@Article{Kolbig:1990:BRC,
  author =       "K. S. K{\"o}lbig",
  title =        "Book Review: {{\booktitle{Computation of Functions on
                 Electronic Computers --- Handbook}} (in Russian).
                 Naukova Dumka, Kiev, 194, 599pp, by B. A. Popov, G. S.
                 Tesler}",
  journal =      j-MATH-COMPUT,
  volume =       "55",
  number =       "191",
  pages =        "395--397",
  month =        jul,
  year =         "1990",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2008818",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Jan 24 08:35:37 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  URL =          "http://www.jstor.org/stable/2008818",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Koren:1990:EEF,
  author =       "I. Koren and O. Zinaty",
  title =        "Evaluating Elementary Functions in a Numerical
                 Coprocessor Based on Rational Approximations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-39",
  number =       "8",
  pages =        "1030--1037",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57042",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Lentz:1990:CFC,
  author =       "William J. Lentz",
  title =        "Continued fraction calculation of spherical {Bessel}
                 functions",
  journal =      j-COMPUT-PHYS,
  volume =       "4",
  number =       "4",
  pages =        "403--407",
  month =        jul,
  year =         "1990",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168382",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  MRnumber =     "33C10 30B70 65-04",
  bibdate =      "Wed Mar 22 14:36:46 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168382",
  ZMnumber =     "0703.33001",
  abstract =     "An efficient new method of calculating spherical
                 Bessel functions of complex argument based on continued
                 fractions is developed. The method does not depend on
                 recurrence relations, and it allows accurate
                 calculations on computers with differing word lengths.
                 The method may be easily extended to other types of
                 Bessel functions and to complex orders.",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys.",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}

@Article{Levrie:1990:CAN,
  author =       "Paul Levrie and Adhemar Bultheel",
  title =        "Convergence Acceleration for the Numerical Solution of
                 Second-Order Linear Recurrence Relations",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "27",
  number =       "1",
  pages =        "166--177",
  month =        feb,
  year =         "1990",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65Q05 (40A15 65B99)",
  MRnumber =     "91a:65244",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  keywords =     "convergence acceleration",
}

@Article{Lin:1990:MSL,
  author =       "Jinn Tyan Lin",
  title =        "Miscellanea: a Simpler Logistic Approximation to the
                 Normal Tail Probability and its Inverse",
  journal =      j-APPL-STAT,
  volume =       "39",
  number =       "2",
  pages =        "255--257",
  year =         "1990",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  MRclass =      "62E15",
  MRnumber =     "1 060 209",
  bibdate =      "Sat Apr 21 10:25:45 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/as1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}

@Article{Magnus:1990:CFL,
  author =       "Arne Magnus and John McCabe",
  title =        "On a continued fraction for $ \log^2_e(1 + x) $",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "30",
  number =       "1",
  pages =        "81--86",
  day =          "10",
  month =        apr,
  year =         "1990",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:45 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279090007M",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Markstein:1990:CEF,
  author =       "P. W. Markstein",
  title =        "Computation of elementary functions on the {IBM RISC
                 System\slash 6000} processor",
  journal =      j-IBM-JRD,
  volume =       "34",
  number =       "1",
  pages =        "111--119",
  month =        jan,
  year =         "1990",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "65-04 (65D20)",
  MRnumber =     "1 057 659",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The additional speed and precision of the IBM RISC
                 System\slash 6000 floating-point unit have motivated
                 reexamination of algorithms to perform division, square
                 root, and the elementary functions. New results are
                 obtained which avoid the necessity of doing special
                 testing to get the last bit rounded correctly in
                 accordance with all of the IEEE rounding modes in the
                 case of division and square root. For the elementary
                 function library, a technique is described for always
                 getting the last bit rounded correctly in the selected
                 IEEE rounding mode.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Res. Div., Austin, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "Division; Elementary functions; Floating-point unit;
                 IBM RISC System\slash 6000 processor; IEEE rounding
                 modes; IEEE rounding modes, IBM RISC System/6000
                 processor; Square root",
  thesaurus =    "Digital arithmetic; IBM computers; Reduced instruction
                 set computing",
}

@Article{Matos:1990:CAM,
  author =       "Ana C. Matos",
  title =        "A convergence acceleration method based on a good
                 estimation of the absolute value of the error",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "10",
  number =       "2",
  pages =        "243--251",
  year =         "1990",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65B99",
  MRnumber =     "91m:65010",
  MRreviewer =   "K. B{\"o}hmer",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "convergence acceleration",
}

@InProceedings{Matula:1990:HPD,
  author =       "D. Matula",
  title =        "Highly parallel divide and square root algorithms for
                 a new generation floating point processor",
  crossref =     "Ullrich:1990:CCA",
  pages =        "??--??",
  year =         "1990",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@Article{McConnell:1990:LEP,
  author =       "C. R. McConnell",
  title =        "Letter to the {Editor}: Pocket computer approximation
                 for areas under the standard normal curve",
  journal =      j-AMER-STAT,
  volume =       "44",
  number =       "1",
  pages =        "63--63",
  month =        feb,
  year =         "1990",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Sat Dec 16 17:19:37 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2684963",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Montuschi:1990:SSR,
  author =       "P. Montuschi and P. M. Mezzalama",
  title =        "Survey of square rooting algorithms",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "137",
  number =       "1",
  pages =        "31--40",
  month =        jan,
  year =         "1990",
  CODEN =        "ICDTEA",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
  summary =      "The paper reviews the algorithms for the computation
                 of square roots for binary machines. After an initial
                 classification, the algorithms are analysed in detail
                 by considering their specific peculiarities and
                 properties. Finally, some comments are \ldots{}",
}

@InCollection{Mora:1990:EFI,
  author =       "Gerardo Mora and Edwin Castro and Ioan Muntean",
  booktitle =    "Mathematics in Costa Rica, Vol. 1 (Spanish) (San
                 Jos{\'e}, 1990)",
  title =        "Elementary functions. {I}. ({Spanish})",
  publisher =    "Univ. Costa Rica",
  address =      "San Jos{\'e}, Costa Rica",
  pages =        "76--86",
  year =         "1990",
  MRclass =      "26A09",
  MRnumber =     "1 111 714",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Spanish",
}

@TechReport{Morris:1990:NLM,
  author =       "Alfred H. {Morris, Jr.}",
  title =        "{NSWC} Library of Mathematics Subroutines",
  type =         "Report",
  number =       "NSWC TR 90-21",
  institution =  "Naval Surface Warfare Center",
  address =      "Dahlgren, VA 22448-5000, USA; Silver Spring, MD
                 20903-5000, USA",
  pages =        "xii + 492 + 9",
  month =        jan,
  year =         "1990",
  bibdate =      "Tue Jun 13 08:47:19 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran2.bib",
  note =         "See also later edition \cite{Morris:1993:NLM}.",
  URL =          "https://apps.dtic.mil/sti/citations/ADA476840;
                 https://apps.dtic.mil/sti/pdfs/ADA476840.pdf;
                 https://people.math.sc.edu/Burkardt/f_src/nswc/nswc.f90;
                 https://people.math.sc.edu/Burkardt/f_src/nswc/nswc.html",
  abstract =     "The NSWC library is a library of general-purpose
                 Fortran subroutines that provide a basic computational
                 capability in a variety of mathematical activities and
                 emphasis has been placed on the transportability of the
                 codes. Subroutines are available in the following areas
                 Elementary Operations, Geometry, Special Functions,
                 Polynomials, Vectors, Matrices, Large Dense Systems of
                 Linear Equations, Banded Matrices, Sparse Matrices,
                 Eigenvalues and Eigenvectors, Solution of Linear
                 Equations, Least-Squares Solution of Linear Equations,
                 Optimization, Transforms, Approximation of Functions,
                 Curve Fitting, Surface Fitting, Manifold Fitting,
                 Numerical Integration, Integral Equations,
                 Ordinary--Differential Equations, Partial Differential
                 Equations, and Random Number Generation.",
  acknowledgement = ack-nhfb,
  remark =       "The single Fortran 90 file of 99,021 nonblank lines
                 compiles into a library of 905 distinct functions and
                 subroutines: the source code appears to contain 139
                 functions and 762 subroutines (901 total entry
                 points).

                 The tableofcontents values in this entry is derived
                 from optical character recognition (OCR) of the 8-page
                 listing from the PDF files, with editorial correction
                 of spelling and OCR errors, and matching of uppercase
                 software names against the entry points of the compiled
                 library. There are about five names in the PDF table of
                 contents that disagree with subroutine names in the
                 source code: they have been edited here to reflect the
                 correct code names. There are numerous routine names in
                 the compiled library that are not mentioned in the
                 table of contents.",
  tableofcontents = "Introduction / 1 \\
                 \\
                 Elementary Operations \\
                 \\
                 Machine Constants --- SPMPAR, DPMPAR, IPMPAR / 3 \\
                 Sorting Lists --- ISHELL, SHELL, AORD, RISORT, SHELL2,
                 DSORT, DAORD, DISORT, DDSORT / 5 \\
                 Cube Root --- CBRT, DCBRT / 7 \\
                 Four Quadrant Arctangent --- ARTNQ, DARTNQ / 7 \\
                 Length of a Two-Dimensional Vector --- CPABS, DCPABS /
                 7 \\
                 Reciprocal of a Complex Number --- CREC, DCREC / 9 \\
                 Square Root of a Double Precision Complex Number ---
                 DCSQRT / 9 \\
                 Conversion of Polar to Cartesian Coordinates --- POCA /
                 11 \\
                 Conversion of Cartesian to Polar Coordinates --- CAPO /
                 11 \\
                 Rotation of Axes --- ROTA / 11 \\
                 Planar Givens Rotations --- SROTG, DROTG / 13 \\
                 Three Dimensional Rotations --- ROT3 / 15 \\
                 Rotation of a Point on the Unit Sphere to the North
                 Pole --- CONSTR / 17 \\
                 Hyperbolic Sine and Cosine Functions --- SNHCSH / 19
                 \\
                 Exponentials --- REXP, DREXP / 21 \\
                 Logarithms --- ALNREL, RLOG, RLOG1, DLNREL, DRLOG,
                 DRLOG1 / 23 \\
                 \\
                 Geometry \\
                 \\
                 Determining if a Point is Inside or Outside a Polygon
                 --- LOCPT / 25 \\
                 The Convex Hull for a Finite Planar Set --- HULL / 27
                 \\
                 Areas of Planar Polygons --- PAREA / 29 \\
                 Hamiltonian Circuits --- HC / 31 \\
                 \\
                 Special Functions \\
                 \\
                 Error Function --- CERF, CERFC, ERF, ERFC, ERFC1,
                 DCERF, DCERFC, DERF, DERFC, DERFC1 / 35 \\
                 Inverse Error Function --- ERFINV / 41 \\
                 Normal Probability Distribution Function --- PNDF / 43
                 \\
                 Inverse Normal Probability Distribution Function ---
                 PNINV / 45 \\
                 Dawson's Integral --- DAWSON / 47 \\
                 Complex Fresnel Integral --- CFRNLI / 49 \\
                 Real Fresnel Integrals --- FRESNEL / 51 \\
                 Exponential Integral Function --- CEXPLI, EXPLI, DEI,
                 DEI1 / 53 \\
                 Sine and Cosine Integral Functions --- SI, CIN / 57 \\
                 Dilogarithm Function --- CLI, ALI / 59 \\
                 Gamma Function --- CGAMMA, GAMMA, GAMLN, DCGAMA,
                 DGAMMA, DGAMLN / 61 \\
                 Diganma Function --- CPSI, PSI, DCPSI, DPSI / 65 \\
                 Logarithm of the Beta Function --- BETALN, DBETLN / 67
                 \\
                 Incomplete Gamma Ratio Functions --- GRATIO, RCOMP / 69
                 \\
                 Inverse Incomplete Gamma Ratio Function --- GAMINV / 71
                 \\
                 Incomplete Beta Function --- BRATIO, ISUBX, BRCOMP / 73
                 \\
                 Bessel Function $J_\nu(z)$ --- CBSSLJ, BSSLJ, BESJ / 75
                 \\
                 Bessel Function $Y_\nu(z)$ --- BSSLY / 77 \\
                 Modified Bessel Function $I_\nu(z)$ --- BSSLI, BESI /
                 79 \\
                 Modified Bessel Function $K_\nu(z)$ --- CBSSLK, BSSLK /
                 81 \\
                 Airy functions --- CAI, CBI, AI, AIE, BI, BIE / 83 \\
                 Complete Complex Elliptic Integrals of the First and
                 Second Kinds --- CK, CKE / 87 \\
                 Real Elliptic Integrals of the First and Second Kinds
                 --- ELLPI, RFVAL, RDVAL, DELLPI, DRFVAL, DRDVAL / 91
                 \\
                 Real Elliptic Integrals of the Third Kind --- EPI,
                 RJVAL, DEPI, DRJVAL / 95 \\
                 Jacobian Elliptic Functions --- ELLPF, ELPFC1 / 99 \\
                 Weierstrass Elliptic Function for the Equianharmonic
                 and Lemniscatic Cases --- PEQ, PEQ1, PLEM, PLEM1 / 103
                 \\
                 Integral of the Bivariate Density Function over
                 Arbitrary Polygons and Semi-infinite Angular Regions
                 --- VALR2 / 107 \\
                 Circular Coverage Function --- CIRCV / 109 \\
                 Elliptical Coverage Function --- PKILL, PKILL3 / 111
                 \\
                 \\
                 Polynomials \\
                 \\
                 Copying Polynomials --- PLCOPY, DPCOPY / 113 \\
                 Addition of Polynomials --- PADD, DPADD / 115 \\
                 Subtraction of Polynomials --- PSUBT, DPSUBT / 117 \\
                 Multiplication of Polynomials --- PMULT, DPMULT / 119
                 \\
                 Division of Polynomials --- PDIV, DPDIV / 121 \\
                 Real Powers of Polynomials --- PLPWR, DPLPWR / 123 \\
                 Inverses of Power Series --- PINV, DPINV / 125 \\
                 Derivatives and Integrals of Polynomials --- MPLNMV /
                 127 \\
                 Evaluation of Chebyshev Expansions --- CSEVL, DCSEVL /
                 129 \\
                 Lagrange Polynomials --- LGRNGN, LGRNGV, LGRNGX / 131
                 \\
                 Orthogonal Polynomials on Finite Sets --- ORTHOS,
                 ORTHOV, ORTHOX / 133 \\
                 \\
                 Solutions of Nonlinear Equations \\
                 \\
                 Zeros of Continuous Functions --- ZEROIN / 135 \\
                 Solution, of Systems of Nonlinear Equations --- HBRD /
                 137 \\
                 Solutions of Quadratic, Cubic, and Quartic Equations
                 --- QDCRT, CBCRT, QTCRT, DQDCRT, DCBCRT, DQTCRT / 139
                 \\
                 Double Precision Roots of Polynomials --- DRPOLY,
                 DCPOLY / 141 \\
                 Accuracy of the Roots of a Real Polynomial --- RBND /
                 143 \\
                 \\
                 Vectors \\
                 \\
                 Copying Vectors --- SCOPY, DCOPY, CCOPY / 145 \\
                 Interchanging Vectors --- SSWAP, DSWAP, CSWAP / 147 \\
                 Planar Rotation of Vectors --- SROT, DROT, CSROT / 149
                 \\
                 Dot Products of Vectors --- SDOT, DDOT, CDOTC, CDOTU /
                 151 \\
                 Scaling Vectors --- SSCAL, DSCAL, CSCAL, CSSCAL / 153
                 \\
                 Vector Addition --- SAXPY, DAXPY, CAXPY / 155 \\
                 $L_1$ Norm of a Vector-- SASUM, DASUM, SCASUM / 157 \\
                 $L_2$ Norm of a Vector --- SNRM2, DNRM2, SCNRM2 / 159
                 \\
                 $L_\infty$ Norm of a Vector --- ISAMAX, IDAMAX, ICAMAX
                 / 161 \\
                 \\
                 Matrices \\
                 \\
                 Packing and Unpacking Symmetric Matrices --- MCVFS,
                 DMCVFS, MCVSF, DMCVSF / 163 \\
                 Conversion of Real Matrices to and from Double
                 Precision Form --- MCVRD, MCVDR / 165 \\
                 Storage of Real Matrices in the Complex Matrix Format
                 --- MCVRC / 167 \\
                 The Real and Imaginary Parts of a Complex Matrix ---
                 CMREAL, CMIMAG / 169 \\
                 Copying Matrices --- MCOPY, SMCOPY, DMCOPY, CMCOPY /
                 171 \\
                 Computation of the Conjugate of a Complex Matrix ---
                 CMCONJ / 173 \\
                 Transposing Matrices --- TPOSE, DTPOSE, CTPOSE, TIP,
                 DTIP, CTIP / 175 \\
                 Computing Adjoints of Complex Matrices --- CMADJ,
                 CTRANS / 177 \\
                 Matrix Addition --- MADD, SMADD, DMADD, CMADD / 179 \\
                 Matrix Subtraction --- MSUBT, SMSUBT, DMSUBT, CMSUBT /
                 181 \\
                 Matrix Multiplication-- MTMS, DMTMS, CMTMS, MPROD,
                 DMPROD, CMPROD / 183 \\
                 Product of a Packed Symmetric Matrix and a Vector ---
                 SVPRD, DSVPRD / 185 \\
                 Transpose Matrix Products --- TMPROD / 187 \\
                 Symmetric Matrix Products --- SMPROD / 189 \\
                 Kronecker Product of Matrices --- KPROD, DKPROD, CKPROD
                 / 191 \\
                 Inverting General Real Matrices and Solving General
                 Systems of Real Linear Equations --- CROUT, KROUT,
                 NPIVOT, MSLV, DSMSLV / 193 \\
                 Solutions of Real Equations with Iterative Improvement
                 --- SLVMP / 197 \\
                 Solution of Almost Block Diagonal Systems of Linear
                 Equations --- ARCECO, ARCESL / 199 \\
                 Solution of Almost Block Tridiagonal Systems of Linear
                 Equations --- BTSLV / 201 \\
                 Inverting Symmetric Real Matrices and Solving Symmetric
                 Systems of Real Linear Equations --- SMSLV, DSMSLV /
                 203 \\
                 Inverting Positive Definite Symmetric Matrices and
                 Solving Positive Definite Symmetric Systems of Linear
                 Equations --- PCHOL, DPCHOL / 207 \\
                 Solution of Toeplitz Systems of Linear Equations ---
                 TOPLX, DTOPLX / 209 \\
                 Inverting General Complex Matrices and Solving General
                 Systems of Complex Linear Equations --- CMSLV, CMSLV1,
                 DCMSLV / 211 \\
                 Solution of Complex Equations with Iterative
                 Improvement --- CSLVMP / 215 \\
                 Singular Value Decomposition of a Matrix --- SSVDC,
                 DSVDC, CSVDC / 217 \\
                 Evaluation of the Characteristic Polynomial of a Matrix
                 --- DET, DPDET, CDET / 219 \\
                 Solution of the Matrix Equation $A X + X B = C$ ---
                 ABSLV, DABSLV / 221 \\
                 Solution of the Matrix Equation $A^t X + X B = C$ when
                 $C$ is Symmetric --- TASLV, DTASLV / 223 \\
                 Solution of the Matrix Equation $A X^2 + X B + C = 0$
                 --- SQUINT / 225 \\
                 Exponential of a Real Matrix --- MEXP, DMEXP / 227 \\
                 \\
                 Large Dense Systems of Linear Equations \\
                 \\
                 Solving systems of 200--400 Linear Equations --- LE,
                 DPLE, CLE / 229 \\
                 \\
                 Banded Matrices \\
                 \\
                 Band Matrix Storage / 231 \\
                 Conversion of Banded Matrices to and from the Standard
                 Format --- CVBR, CVBC, CVRB, CVCB, CVRB1, CVCB1 / 233
                 \\
                 Conversion of Banded Matrices to and from Sparse Form
                 --- MCVBS, CMCVBS, MCVSB, CMCVSB / 235 \\
                 Transposing Banded Matrices --- BPOSE, CBPOSE / 237 \\
                 Addition of Banded Matrices --- BADD, CBADD / 239 \\
                 Subtraction of Banded Matrices --- BSUBT, CBSUBT / 241
                 \\
                 Multiplication of Banded Matrices --- BPROD, CBPROD /
                 243 \\
                 Product of a Real Banded Matrix and Vector --- BVPRD,
                 BVPRD1, BTPRD, BTPRD1 / 245 \\
                 Product of a Complex Banded Matrix and Vector ---
                 CBVPD, CBVPD1, CBTPD, CBTPD1 / 247 \\
                 Solution of Banded Systems of Real Linear Equations ---
                 BSLV, BSLV1 / 249 \\
                 Solution of Banded Systems of Complex Linear Equations
                 --- CBSLV, CBSLV1 / 251 \\
                 \\
                 Sparse Matrices \\
                 \\
                 Storage of Sparse Matrices / 253 \\
                 Conversion of Sparse Matrices to and from the Standard
                 Format --- CVRS, CVDS, CVCS, CVSR, CVSD, CVSC / 255 \\
                 Conversion of Sparse Real Matrices to and from Double
                 Precision Form --- SCVRD, SCVDR / 257 \\
                 The Real and Imaginary Parts of a Sparse Complex Matrix
                 --- CSREAL, CSIMAG / 259 \\
                 \\
                 Computing $A + i D$ for Sparse Real Matrices $A$ and
                 $B$ --- SCVRC / 261 \\
                 Copying Sparse Matrices --- RSCOPY, DSCOPY, CSCOPY /
                 263 \\
                 Computing Conjugates of Sparse Complex Matrices ---
                 SCONJ / 265 \\
                 Transposing Sparse Real Matrices --- RPOSE, RPOSE1 /
                 267 \\
                 Transposing Sparse Double Precision Matrices --- DPOSE,
                 DPOSE1 / 269 \\
                 Transposing Sparse Complex Matrices --- CPOSE, CPOSE1 /
                 271 \\
                 Addition of Sparse Matrices --- SADD, DSADD, CSADD /
                 273 \\
                 Subtraction of Sparse Matrices --- SSUBT, DSSUBT,
                 CSSUBT / 275 \\
                 Multiplication of Sparse Matrices --- SPROD, DSPROD,
                 CSPROD / 277 \\
                 Product of a Real Sparse Matrix and Vector --- MVPRD,
                 MVPRD1, MTPRD, MTPRD1 / 279 \\
                 Product of a Double Precision Sparse Matrix and Vector
                 --- DVPRD, DVPRD1, DTPRD, DTPRD1 / 281 \\
                 Product of a Complex Sparse Matrix and Vector ---
                 CVPRD, CVPRD1, CTPRD, CTPRD1 / 283 \\
                 Ordering the Rows of a Sparse Matrix by Increasing
                 Length --- SPORD / 285 \\
                 Reordering Sparse Matrices into Block Triangular Form
                 --- BLKORD / 287 \\
                 Solution of Sparse Systems of Real Linear Equations ---
                 SPSLV, RSLV, TSLV / 289 \\
                 Double Precision Solution of Sparse Systems of Real
                 Linear Equations --- DSPSLV, DSLV, DTSLV / 293 \\
                 Solution of Sparse Systems of Complex Linear Equations
                 --- CSPSLV, CSLV, CTSLV / 297 \\
                 \\
                 Eigenvalues and Eigenvectors \\
                 \\
                 Computation of Eigenvalues of General Real Matrices ---
                 EIG, EIG1 / 301 \\
                 Computation of Eigenvalues and Eigenvectors of General
                 Real Matrices --- EIGV, EIGV1 / 303 \\
                 Double Precision Computation of Eigenvalues of Real
                 Matrices --- DEIG / 305 \\
                 Double Precision Computation of Eigenvalues and
                 Eigenvectors of Real Matrices --- DEIGV / 307 \\
                 Computation of Eigenvalues of Symmetric Real Matrices
                 --- SEIG, SEIG1 / 309 \\
                 Computation of Eigenvalues and Eigenvectors of
                 Symmetric Real Matrices --- SEIGV, SEIGV1 / 311 \\
                 Computation of Eigenvalues of Complex Matrices --- CEIG
                 / 313 \\
                 Computation of Eigenvalues and Eigenvectors of Complex
                 Matrices --- CEIGV / 315 \\
                 Double Precision Computation of Eigenvalues of Complex
                 Matrices --- DCEIG / 317 \\
                 Double Precision Computation of Eigenvalues and
                 Eigenvectors of Complex Matrices --- DCEIGV / 319 \\
                 \\
                 $\ell_1$ Solution of Linear Equations \\
                 \\
                 $\ell_1$ Solution of Systems of Linear Equations with
                 Equality and Inequality Constraints --- CL1 / 321 \\
                 \\
                 Least Squares Solution of Linear Equations \\
                 \\
                 Least Squares Solution of Systems of Linear Equations
                 --- LLSQ, HFTI, HFTI2 / 323 \\
                 Least Squares Solution of Overdetermined Systems of
                 Linear Equations with Iterative Improvement --- LLSQMP
                 / 327 \\
                 Double Precision Least Squares Solution of Systems of
                 Linear Equations --- DLLSQ, DHFTI, DHFTI2 / 329 \\
                 Least Squares Solution of Systems of Linear Equations
                 with Equality and Inequality Constraints --- LSEI / 333
                 \\
                 Least Squares Solution of Systems of Linear Equations
                 with Equality and Nonnegativity Constraints --- WNNLS /
                 337 \\
                 Least Squares Iterative Improvement Solution of Systems
                 of Linear Equations with Equality Constraints --- L2SLV
                 / 341 \\
                 Iterative Least Squares Solution of Banded Linear
                 Equations --- BLSQ / 345 \\
                 Iterative Least Squares Solution of Sparse Linear
                 Equations --- SPLSQ, STLSQ / 347 \\
                 \\
                 Optimization \\
                 \\
                 Minimization of Functions of a Single Variable --- FMIN
                 / 349 \\
                 Minimization of Functions of n Variables --- OPTF / 351
                 \\
                 Unconstrained Minimum of the Sum of Squares of
                 Nonlinear Functions --- LMDIFF / 353 \\
                 Linear Programming --- SMPLX, SSPLX / 355 \\
                 The Assignment Problem --- ASSGN / 359 \\
                 $0$--$1$ Knapsack Problem --- MKP / 361 \\
                 \\
                 Transforms \\
                 \\
                 Inversion of the Laplace Transform --- LAINV / 363 \\
                 Fast Fourier Transform --- FFT, FFT1 / 367 \\
                 Multivariate Fast Fourier Transform --- MFFT, MFFT1 /
                 369 \\
                 Discrete Cosine and Sine Transforms --- COSQI, COSQB,
                 COSQF, SINQB, SINQF / 371 \\
                 \\
                 Approximation of Functions \\
                 \\
                 Rational Minimax Approximation of Functions --- CHEBY /
                 375 \\
                 $L_p$ Approximation of Functions --- ADAPT / 377 \\
                 Calculation of the Taylor Series of a Complex Analytic
                 Function --- CPSC, DCPSC / 381 \\
                 \\
                 Curve Fitting \\
                 \\
                 Linear Interpolation --- TRP / 385 \\
                 Lagrange Interpolation --- LTRP / 387 \\
                 Hermite Interpolation --- HTRP / 389 \\
                 Conversion of Real Polynomials from Newton to Taylor
                 Series Form --- PCOEFF / 391 \\
                 Least Squares Polynomial Fit --- PFIT / 393 \\
                 Weighted Least Squares Polynomial Fit --- WPFIT / 395
                 \\
                 Cubic Spline Interpolation --- CBSPL, SPLIFT / 397 \\
                 Weighted Least Squares Cubic Spline Fitting --- SPFIT /
                 399 \\
                 Cubic Spline Evaluation --- SCOMP, SCOMP1, SCOMP2 / 401
                 \\
                 Cubic Spline Evaluation and Differentiation --- SEVAL,
                 SEVAL1, SEVAL2 / 403 \\
                 Integrals of Cubic Splines --- CSINT, CSINT1, CSINT2 /
                 405 \\
                 N-Dimensional Cubic Spline Closed Curve Fitting ---
                 CSLOOP, LOPCMP, LOPDF / 407 \\
                 Spline under Tension Interpolation --- CURV1 / 409 \\
                 Spline under Tension Evaluation --- CURV2 / 411 \\
                 Differentiation and Integration of Splines under
                 Tension --- CURVD, CURVI / 413 \\
                 Two Dimensional Spline under Tension Curve Fitting ---
                 KURV1, KURV2 / 415 \\
                 Two Dimensional Spline under Tension Closed Curve
                 Fitting --- KURVP1, KURVP2 / 417 \\
                 Three Dimensional Spline under Tension Curve Fitting
                 --- QURV1, QURV2 / 419 \\
                 B-Splines / 421 \\
                 Piecewise Polynomial Interpolation --- BSTRP / 423 \\
                 Conversion of Piecewise Polynomials from B-Spline to
                 Taylor Series Form --- BSPP / 425 \\
                 Piecewise Polynomial Evaluation --- PPVAL / 427 \\
                 Weighted Least Squares Piecewise Polynomial Fitting ---
                 BSL2 / 429 \\
                 \\
                 Surface Fitting over Rectangular Grids \\
                 \\
                 Bi-Splines under Tension / 431 \\
                 Bi-Spline under Tension Surface Interpolation --- SURF
                 / 433 \\
                 Bi-Spline under Tension Evaluation --- SURF2, NSURF2 /
                 435 \\
                 \\
                 Surface Fitting over Arbitrarily Positioned Data Points
                 \\
                 \\
                 Surface Interpolation for Arbitrarily Positioned Data
                 Points --- BVIP, BVIP2 / 437 \\
                 \\
                 Manifold Fitting \\
                 \\
                 Weighted Least Squares Fitting with Polynomials of $n$
                 Variables --- MFIT, DMFIT, MEVAL, DMEVAL / 441 \\
                 \\
                 Numerical Integration \\
                 \\
                 Evaluation of Integrals over Finite Intervals --- QAGS,
                 QSUBA, DQAGS / 445 \\
                 \\
                 Evaluation of Integrals over Infinite Intervals ---
                 QAGI, DQAGI / 449 \\
                 Evaluation of Double Integrals over Triangles ---
                 CUBTRI / 453 \\
                 \\
                 Integral Equations \\
                 \\
                 Solution of Fredholm Integral Equations of the Second
                 Kind --- IESLV / 455 \\
                 \\
                 Ordinary Differential Equations/Initial Value Problems
                 \\
                 \\
                 The Initial Value Solvers --- Introductory Comments /
                 459 \\
                 Adaptive Adams Solution of Nonstiff Differential
                 Equations --- ODE / 461 \\
                 Adaptive RKF Solution of Nonstiff Differential
                 Equations --- RKF45 / 465 \\
                 Adaptive RKF Solution of Nonstiff Differential
                 Equations with Global Error Estimation --- GERK / 469
                 \\
                 Adaptive Solution of Stiff Differential Equations ---
                 SFODE, SFODE1 / 473 \\
                 Fourth-Order Runge-Kutta --- RK / 477 \\
                 Eighth-Order Runge-Kutta --- RK8 / 479 \\
                 \\
                 Partial Differential Equations \\
                 \\
                 Separable Second-Order Elliptic Equations on
                 Rectangular Domains --- SEPDE / 481 \\
                 \\
                 Random Number Generation \\
                 \\
                 Uniform Random Number Generator --- URNG / 485 \\
                 Gaussian Random Number Generator using the
                 Box--M{\"u}ller Transformation --- NRNG / 487 \\
                 \\
                 Appendix. Installation of the NSWC Library / 489 \\
                 \\
                 Index / 491 \\
                 \\
                 Distribution",
}

@MastersThesis{Muller:1990:HCA,
  author =       "Volker M{\"u}ller",
  title =        "{Hochgenaue CORDIC-Algorithmen f{\"u}r reelle
                 Standardfunktionen mittels dynamischer
                 Defektberechnung} \toenglish {High-accuracy CORDIC
                 Algorithms for Real Elementary Functions by Means of
                 Dynamic Error Computation} \endtoenglish",
  type =         "Diplomarbeit",
  school =       "Institut f{\"u}r angewandte Mathematik,
                 Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  month =        dec,
  year =         "1990",
  bibdate =      "Fri Jun 11 12:38:17 1999",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}

@Article{Osada:1990:CAM,
  author =       "Naoki Osada",
  title =        "A Convergence Acceleration Method for Some
                 Logarithmically Convergent Sequences",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "27",
  number =       "1",
  pages =        "178--189",
  month =        feb,
  year =         "1990",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0727012",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65B05",
  MRnumber =     "1034928 (91b:65002)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  keywords =     "convergence acceleration",
}

@Article{Palmore:1990:CAC,
  author =       "J. Palmore and C. Herring",
  title =        "Computer arithmetic, chaos and fractals",
  journal =      j-PHYSICA-D,
  volume =       "42",
  number =       "1--3",
  pages =        "99--110",
  month =        jun,
  year =         "1990",
  CODEN =        "PDNPDT",
  DOI =          "https://doi.org/10.1016/0167-2789(90)90069-2",
  ISSN =         "0167-2789 (print), 1872-8022 (electronic)",
  ISSN-L =       "0167-2789",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Ninth Annual International Conference of the Center
                 for Nonlinear Studies on Self-Organizing, Collective
                 and Cooperative Phenomena in Natural and Artificial
                 Networks",
  abstract =     "The authors explore aspects of computer arithmetic
                 from the viewpoint of dynamical systems. They
                 demonstrate the effects of finite precision arithmetic
                 in three uniformly hyperbolic chaotic dynamical
                 systems: Bernoulli shifts, cat maps, and pseudorandom
                 number generators. They show that elementary
                 floating-point operations in binary computer arithmetic
                 possess an inherently fractal structure. Each of these
                 dynamical systems allows us to compare the exact
                 results in integer arithmetic with those obtained by
                 using floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Illinois Univ., Urbana, IL, USA",
  classification = "C1160 (Combinatorial mathematics); C5230 (Digital
                 arithmetic methods)",
  confdate =     "22-26 May 1989",
  conflocation = "Los Alamos, NM, USA",
  fjournal =     "Physica. D, Nonlinear phenomena",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01672789",
  keywords =     "Bernoulli shifts; Binary computer arithmetic; Cat
                 maps; Chaos; Computer arithmetic; Dynamical systems;
                 Elementary floating-point operations; Finite precision
                 arithmetic; Floating-point arithmetic; Fractal
                 structure; Integer arithmetic; Pseudorandom number
                 generators; Self-similar structure; Uniformly
                 hyperbolic chaotic dynamical systems",
  pubcountry =   "Netherlands",
  thesaurus =    "Chaos; Digital arithmetic; Fractals; Random number
                 generation; Roundoff errors",
}

@Article{Poppe:1990:AEC,
  author =       "G. P. M. Poppe and C. M. J. Wijers",
  title =        "{Algorithm 680}: Evaluation of the Complex Error
                 Function",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "47--47",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.77630",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "47. 65G05 (65-04)",
  MRnumber =     "91h:65068b",
  bibdate =      "Sun Sep 04 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Zaghloul:2019:RO}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p47-poppe/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Rational approximation.",
}

@Article{Poppe:1990:MEC,
  author =       "G. P. M. Poppe and C. M. J. Wijers",
  title =        "More Efficient Computation of the Complex Error
                 Function",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "38--46",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.77629",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G05 (65D20)",
  MRnumber =     "91h:65068a",
  bibdate =      "Sun Sep 04 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p38-poppe/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Algorithm analysis. {\bf G.1.2}: Mathematics
                 of Computing, NUMERICAL ANALYSIS, Approximation,
                 Rational approximation.",
}

@Article{Press:1990:EI,
  author =       "William H. Press and Saul A. Teukolsky",
  title =        "Elliptic Integrals",
  journal =      j-COMPUT-PHYS,
  volume =       "4",
  number =       "1",
  pages =        "92--??",
  month =        jan,
  year =         "1990",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.4822893",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:45:21 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.4822893",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}

@Article{Reemtsen:1990:MFR,
  author =       "Rembert Reemtsen",
  title =        "Modifications of the First {Remez} Algorithm",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "27",
  number =       "2",
  pages =        "507--518",
  month =        apr,
  year =         "1990",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0727031",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65D15",
  MRnumber =     "91a:65039",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}

@Article{Revfeim:1990:LEM,
  author =       "K. J. A. Revfeim",
  title =        "Letter to the {Editor}: More approximations for the
                 cumulative and inverse normal distribution",
  journal =      j-AMER-STAT,
  volume =       "44",
  number =       "1",
  pages =        "63--63",
  month =        feb,
  year =         "1990",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Jan 27 14:51:19 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326447;
                 https://www.math.utah.edu/pub/tex/bib/amstat1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2684963",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Sedogbo:1990:CAS,
  author =       "Guy Antoine Sedogbo",
  title =        "Convergence acceleration of some logarithmic
                 sequences",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "32",
  number =       "1--2",
  pages =        "253--260",
  day =          "26",
  month =        nov,
  year =         "1990",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(90)90435-3",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65B10 (40A25 65B99)",
  MRnumber =     "1091794 (91m:65009)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Extrapolation and rational approximation (Luminy,
                 1989)",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "convergence acceleration",
}

@Book{Swartzlander:1990:CA,
  author =       "Earl E. Swartzlander",
  title =        "Computer arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "various",
  year =         "1990",
  ISBN =         "0-8186-8931-5 (v. 1), 0-8186-5931-9 (v. 1
                 microfiche)",
  ISBN-13 =      "978-0-8186-8931-4 (v. 1), 978-0-8186-5931-7 (v. 1
                 microfiche)",
  LCCN =         "QA76.6.C633 1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Two volumes.",
  series =       "IEEE Computer Society Press tutorial",
  acknowledgement = ack-nhfb,
  annote =       "Vol. 1 is a reprint. Originally published:
                 Stroudsburg, Pa.: Dowden, Hutchinson and Ross, c1980.
                 Originally published in series: Benchmark papers in
                 electrical engineering and computer science; 21. Vol 2
                 is a sequel to the earlier collection. Vol. 1: 2nd
                 ed.",
  keywords =     "Computer arithmetic.; Electronic digital computers ---
                 Programming.; Floating-point arithmetic.",
  tableofcontents = "Arithmetic operations in a binary computer / R. F.
                 Shaw \\
                 High-speed arithmetic in binary computers / O. L.
                 MacSorley \\
                 Fast carry logic for digital computers / B. Gilchrist,
                 J. H. Pomerene, and S. Y. Wong \\
                 A logic for high-speed addition / A. Weinberger and J.
                 L. Smith \\
                 Conditional-sum addition logic / J. Sklansky \\
                 An evaluation of several two-summand binary adders / J.
                 Sklansky \\
                 Adder with distributed control / A. Svoboda \\
                 Multiple addition by residue threshold functions and
                 their representation by array logic / I. T. Ho and T.
                 C. Chen \\
                 Counting responders in an associative memory / C. C.
                 Foster and F. D. Stockton \\
                 Parallel counters / E. E. Swartzlander, Jr. \\
                 A signed binary multiplication technique / A. D. Booth
                 \\
                 Multiplying made easy for digital assemblies / C.
                 Ghest. A binary multiplication scheme based on squaring
                 / T. C. Chen \\
                 A suggestion for a fast multiplier / C. S. Wallace \\
                 Some schemes for parallel multipliers / L. Dadda \\
                 On parallel digital multipliers / L. Dadda \\
                 A compact high-speed parallel multiplication scheme /
                 W. J. Stenzel, W. J. Kubitz, and G. H. Garcia \\
                 A two's complement parallel array multiplication
                 algorithm / C. R. Baugh and B. A. Wooley \\
                 Comments on ``A two's complement parallel array
                 multiplication algorithm'' / P. E. Blankenship \\
                 The quasi-serial multiplier / E. E. Swartzlander, Jr.
                 \\
                 The two's complement quasi-serial multiplier / T. G.
                 McDaneld and R. K. Guha \\
                 A new class of digital division methods / J. E
                 Robertson \\
                 An algorithm for rapid binary division / J. B. Wilson
                 and R. S. Ledley. Digit-by-digit
                 transcendental-function computation / R. J. Linhardt
                 and H. S. Miller \\
                 A unified algorithm for elementary functions / J. S.
                 Walther \\
                 Some properties of iterative square-rooting methods
                 using high-speed multiplication /C. V. Ramamoorthy, J.
                 R. Goodman, and K. H. Kim \\
                 Radix-16 evaluation of certain elementary functions /
                 M. D. Ercegovac \\
                 On the distribution of numbers / R. W. Hamming \\
                 An analysis of floating-point addition / D. W. Sweeney
                 \\
                 The IBM\ldots{}Model 91: floating-point execution unit
                 / S. F. Anderson \ldots{} [et al.] \\
                 Design of large high-speed floating-point-arithmetic
                 units / J. B. Gosling \\
                 Analysis of rounding methods in floating-point
                 arithmetic / D. J. Kuck,D. S. Parker, Jr., and A. H.
                 Sameh. \\
                 cos x, tan-p1s x, and cot-p1s x / W. H. Specker.",
}

@Article{Tang:1990:AET,
  author =       "Ping Tak Peter Tang",
  title =        "Accurate and Efficient Testing of the Exponential and
                 Logarithm Functions",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "185--200",
  month =        sep,
  year =         "1990",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65G99)",
  MRnumber =     "1 070 797",
  bibdate =      "Sun Sep 04 23:14:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://doi.acm.org/10.1145/79505.79506;
                 http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p185-tang/",
  abstract =     "Table-driven techniques can be used to test highly
                 accurate implementation of EXP LOG. The largest error
                 observed in EXP and LOG accurately to within 1/500 unit
                 in the last place are reported in our tests. Methods to
                 verify the tests' reliability are discussed. Results of
                 applying the tests to our own as well as to a number of
                 other implementations of EXP and LOG are presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; languages; verification",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Portability.",
}

@InProceedings{Tang:1990:FAL,
  author =       "Ping Tak Peter Tang",
  title =        "A fast algorithm for linear complex {Chebyshev}
                 approximation",
  crossref =     "Mason:1990:AAI",
  pages =        "265--274",
  year =         "1990",
  bibdate =      "Wed Nov 29 14:12:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Tang:1990:PGE,
  author =       "Ping Tak Peter Tang",
  title =        "A Portable Generic Elementary Function Package in
                 {Ada} and an Accurate Test Suite",
  type =         "Technical report",
  number =       "ANL-90/35",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  pages =        "iii + 35",
  month =        nov,
  year =         "1990",
  bibdate =      "Fri Dec 28 11:36:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.osti.gov/bridge/servlets/purl/6310184-4n5sOR/6310184.PDF",
  abstract =     "A comprehensive set of elementary functions has been
                 implemented portably in Ada. The high accuracy of the
                 implementation has been confirmed by rigorous analysis.
                 Moreover, we present new test methods that are
                 efficient and offer a high resolution of 0.005 unit in
                 the last place, Tbese test methods have been
                 implemented portably here and confirm the accuracy of
                 our implemented functions. Reports on the accuracy of
                 other function libraries obtained by our test programs
                 are also presented.",
  acknowledgement = ack-nhfb,
}

@TechReport{Tang:1990:SSI,
  author =       "Ping Tak Peter Tang",
  title =        "Some Software Implementations of the Functions Sine
                 and Cosine",
  type =         "Technical report",
  number =       "ANL-90/3",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  month =        apr,
  year =         "1990",
  bibdate =      "Fri Dec 28 11:21:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www-fp.mcs.anl.gov/division/publications/abstracts/abstracts90.htm",
  abstract =     "This document presents several software
                 implementations of the elementary functions sin and cos
                 designed to fit a large class of machines.
                 Implementation details are provided. Also provided is a
                 detailed error analysis that bounds the errors of these
                 implementations, over the full range of input
                 arguments, from 0.721 to 0.912 units in the last place.
                 Tests performed on these codes give results that are
                 consistent with the error bounds.",
  acknowledgement = ack-nhfb,
  xxnote =       "Where is this? I can find no electronic version
                 online, other than the abstract at the given URL.",
}

@Article{Tang:1990:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Logarithm Function
                 in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "378--400",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:26:09 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://doi.acm.org/10.1145/98267.98294;
                 http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p378-tang/",
  abstract =     "Algorithms and implementation details for the
                 logarithm functions in both single and double precision
                 of IEEE 754 arithmetic are presented here. With a table
                 of moderate size, the implementation need only working-
                 precision arithmetic and are provably accurate to
                 within 0.57 ulp.",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; performance; reliability;
                 standardization; theory; verification",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@Article{Todd:1990:WMP,
  author =       "John Todd",
  title =        "The {Weierstrass} mean. {I}. The periods of $ \wp (z
                 \vert e_1, e_2, e_3) $",
  journal =      j-NUM-MATH,
  volume =       "57",
  number =       "8",
  pages =        "737--746",
  month =        aug,
  year =         "1990",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65D20 (33E05)",
  MRnumber =     "91m:65057",
  MRreviewer =   "Syvert P. N{\o}rsett",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290 (Numerical analysis); C4100 (Numerical
                 analysis)",
  corpsource =   "California Inst. of Technol., Pasadena, CA, USA",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "convergence; elliptic objects; limits; numerical
                 methods; Weierstrass mean",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Watson:1990:NMC,
  author =       "G. Alistair Watson",
  title =        "Numerical methods for {Chebyshev} approximation of
                 complex-valued functions",
  crossref =     "Mason:1990:AAI",
  pages =        "246--264",
  year =         "1990",
  bibdate =      "Wed Nov 29 14:09:32 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Wells:1990:LE,
  author =       "Martin T. Wells and Ram C. Tiwari and I. Arizono and
                 H. Ohta and James W. Mergerson and Gabriella M. Belli
                 and Christopher Cox and Murray A. Jorgensen and Jacques
                 Benichou and Mitchell H. Gail and Warren F. Kuhfeld and
                 Brian Dawkins and Walter B. Studdiford and Colin
                 Goodall and W. D. Kaigh and Stephen W. Looney and
                 Robert Kinnison and James A. Gibbons and Joel R. Levin
                 and Ronald C. Serlin and K. J. A. Revfeim and Charles
                 R. McConnell and Robert M. Norton and R. W. Farebrother
                 and I. J. Good and Stanley Lebergott and Vedula N.
                 Murty",
  title =        "Letters to the Editor",
  journal =      j-AMER-STAT,
  volume =       "44",
  number =       "1",
  pages =        "56--65",
  month =        feb,
  year =         "1990",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Jan 27 14:51:19 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326447;
                 https://www.math.utah.edu/pub/tex/bib/amstat1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2684963",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Weniger:1990:RAM,
  author =       "Ernst Joachim Weniger and Ji{\v{r}}i
                 C{\'\i}{\v{z}}ek",
  title =        "Rational approximations for the modified {Bessel}
                 function of the second kind",
  journal =      j-COMP-PHYS-COMM,
  volume =       "59",
  number =       "3",
  pages =        "471--493",
  month =        jul,
  year =         "1990",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(90)90089-J",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:29:12 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/001046559090089J",
  abstract =     "Various different rational approximations for the
                 modified Bessel function $ K_\nu (z) $ are compared
                 with respect to their ability of computing $ K_\nu (z)
                 $ efficiently and reliably in the troublesome region of
                 moderately large arguments $z$. The starting point for
                 the construction of the rational approximations is the
                 asymptotic series $_2 F_0$ for $ K_\nu (z) $, which
                 diverges for all finite arguments $z$ but is Borel
                 summable and Stieltjes summable. The numerical tests
                 showed that Pad{\'e} approximants for $ K_\nu (z) $ are
                 significantly less efficient than the other rational
                 approximations which were considered. The best results
                 were produced by some recently derived sequence
                 transformations (E. J. Weniger, Comput. Phys. Rep. {\bf
                 10} (1989) 189), which are closely related to Levin's
                 sequence transformations (D. Levin, Int. J. Comput.
                 Math. B {\bf 3} (1973) 371).",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Bartoloni:1991:MFU,
  author =       "A. Bartoloni and C. Battista and S. Cabasino and N.
                 Cabibbo and F. Del Prete and F. Marzano and P. S.
                 Paolucci and R. Sarno and G. Salina and G. M. Todesco
                 and M. Torelli and R. Tripiccione and W. Tross and E.
                 Zanetti",
  title =        "{MAD}, a floating-point unit for massively-parallel
                 processors",
  journal =      "Particle World",
  volume =       "2",
  number =       "3",
  pages =        "65--73",
  month =        "????",
  year =         "1991",
  CODEN =        "PARWEG",
  ISSN =         "1043-6790",
  bibdate =      "Tue Dec 12 09:26:54 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The authors describe in detail the architecture and
                 implementation of the MAD chip. It is a floating point
                 unit, used as the elementary processing element of the
                 APE100 array processor. The design has been accurately
                 tailored to the requirements of a SIMD floating point
                 intensive machine.",
  acknowledgement = ack-nhfb,
  affiliation =  "Roma Univ., Italy",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5220P (Parallel architecture);
                 C5230 (Digital arithmetic methods); C7320 (Physics and
                 Chemistry)",
  keywords =     "APE100 array processor; Architecture; Elementary
                 processing element; Floating-point unit;
                 Massively-parallel processors; SIMD floating point
                 intensive machine",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic; Microprocessor chips; Parallel
                 architectures; Physics computing",
}

@TechReport{Beebe:1991:ASR,
  author =       "Nelson H. F. Beebe",
  title =        "Accurate Square Root Computation",
  institution =  inst-CSC,
  address =      inst-CSC:adr,
  pages =        "23",
  day =          "4",
  month =        feb,
  year =         "1991",
  bibdate =      "Sat Feb 8 10:28:55 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supplemental class notes prepared for Mathematics
                 118.",
}

@Article{Boersma:1991:UAB,
  author =       "J. Boersma",
  title =        "Uniform asymptotics of a {Bessel}-function series
                 occurring in a transmission-line problem",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "37",
  number =       "1--3",
  pages =        "143--159",
  day =          "18",
  month =        nov,
  year =         "1991",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:02:22 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279190113X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Bohlender:1991:SEF,
  author =       "G. Bohlender and W. Walter and P. Kornerup and D. W.
                 Matula",
  title =        "Semantics for exact floating point operations",
  crossref =     "Kornerup:1991:PIS",
  bookpages =    "xiii + 282",
  pages =        "22--26",
  year =         "1991",
  bibdate =      "Wed Dec 13 13:13:34 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "IEEE Catalog number 91CH3015-5.",
  abstract =     "Semantics are given for the four elementary arithmetic
                 operations and the square root, to characterize what
                 are termed exact floating point operations. The
                 operands of the arithmetic operations and the argument
                 of the square root are all floating point numbers in
                 one format. In every case, the result is a pair of
                 floating point numbers in the same format with no
                 accuracy lost in the computation. These semantics make
                 it possible to realize the following principle: it
                 shall be a user option to discard any information in
                 the result of a floating point arithmetic operation.
                 The reliability and portability previously associated
                 with only mathematical software implementations in
                 integer arithmetic can thus be attained exploiting the
                 generally higher efficiency of floating point
                 hardware.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe Univ., Germany",
  classification = "C1160 (Combinatorial mathematics); C5230 (Digital
                 arithmetic methods)",
  confdate =     "26-28 June 1991",
  conflocation = "Grenoble, France",
  confsponsor =  "IEEE; CNRS; IMAG",
  keywords =     "Argument; Elementary arithmetic operations; Exact
                 floating point operations; Floating point arithmetic;
                 Floating point hardware; Floating point numbers;
                 Integer arithmetic; Mathematical software; Operands;
                 Portability; Reliability; Semantics; Square root",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Number theory",
}

@Book{Brezinski:1991:EMT,
  author =       "Claude Brezinski and Michela {Redivo Zaglia}",
  title =        "Extrapolation methods: theory and practice",
  volume =       "2",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "ix + 464",
  year =         "1991",
  ISBN =         "0-444-88814-4",
  ISBN-13 =      "978-0-444-88814-3",
  LCCN =         "QA281 .B74 1991",
  bibdate =      "Mon May 24 09:18:52 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "Studies in computational mathematics",
  acknowledgement = ack-nhfb,
  subject =      "extrapolation; data processing",
}

@Article{Bunch:1991:DFA,
  author =       "K. J. Bunch and W. N. Cain and R. W. Grow",
  title =        "A data fitting approach to series convergence
                 acceleration",
  journal =      j-APPL-MATH-COMP,
  volume =       "42",
  number =       "2 (part II)",
  pages =        "189--195",
  month =        "????",
  year =         "1991",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/0096-3003(91)90050-W",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  MRclass =      "65B10 (65D10)",
  MRnumber =     "1094414 (91k:65015)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "convergence acceleration",
}

@Article{Carlson:1991:TEI,
  author =       "B. C. Carlson",
  title =        "A table of elliptic integrals: {One} quadratic
                 factor",
  journal =      j-MATH-COMPUT,
  volume =       "56",
  number =       "193",
  pages =        "267--280",
  month =        jan,
  year =         "1991",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33E05 (65A05)",
  MRnumber =     "92b:33056",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290R (Integral equations); B0290M (Numerical
                 integration and differentiation); C4180 (Integral
                 equations); C4160 (Numerical integration and
                 differentiation)",
  corpsource =   "Dept. of Math., Iowa State Univ., Ames, IA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "conjugate complex zeros; elliptic integrals; Fortran
                 programs; integral equations; integration; polynomial;
                 R-functions; square root",
  treatment =    "P Practical",
}

@TechReport{Cody:1991:CPT,
  author =       "W. J. Cody",
  title =        "{CELEFUNT}: a Portable Test Package for Complex
                 Elementary Functions",
  type =         "Technical Report",
  number =       "ANL-91/1",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  pages =        "iii + 21",
  month =        jan,
  year =         "1991",
  bibdate =      "Fri Sep 23 23:39:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Corless:1991:NEA,
  author =       "R. M. Corless and D. J. Jeffrey and H. Rasmussen",
  title =        "Numerical evaluation of {Airy} functions with complex
                 arguments",
  journal =      j-J-COMPUT-PHYS,
  volume =       "93",
  number =       "1",
  pages =        "252--253",
  month =        mar,
  year =         "1991",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(91)90089-4",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:55:47 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999191900894",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Crenshaw:1991:SRS,
  author =       "J. W. Crenshaw",
  title =        "Square roots are simple?",
  journal =      j-EMBED-SYS-PROG,
  volume =       "4",
  number =       "11",
  pages =        "30--52",
  month =        nov,
  year =         "1991",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Wed Sep 14 19:14:52 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Embedded Systems Programming",
}

@Article{DeDoelder:1991:SSC,
  author =       "P. J. {De Doelder}",
  title =        "On some series containing $ \psi (x) - \psi (y >) $
                 and $ (\psi (x) - \psi (y >))^2 $ for certain values of
                 $x$ and $y$",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "37",
  number =       "1--3",
  pages =        "125--141",
  day =          "18",
  month =        nov,
  year =         "1991",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(91)90112-W",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:02:22 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279190112W",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Dritz:1991:IPS,
  author =       "Kenneth W. Dritz",
  title =        "Introduction to the proposed standard for the
                 elementary functions in {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "3--8",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics)",
  corpsource =   "Dept. of Math. and Comput. Sci., Argonne Nat. Lab.,
                 IL, USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; committees; elementary functions; generic
                 package; ISO standard; mathematics computing;
                 secondary; standards",
  treatment =    "P Practical",
}

@Article{Dritz:1991:PSGa,
  author =       "K. W. Dritz",
  title =        "Proposed standard for a generic package of elementary
                 functions for {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "9--46",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C6110B (Software
                 engineering techniques); C7310 (Mathematics)",
  corpsource =   "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "ACM SIGAda Numerics Working; Ada; Ada-Europe Numerics
                 Working Group; basic; elementary functions;
                 ELEMENTARY-FUNCTIONS-; EXCEPTIONS; generic package;
                 GENERIC-ELEMENTARY-FUNCTIONS; Group; international
                 standard; joint proposal; mathematical routines;
                 mathematics computing; NRG; Rapporteur Group; reusable
                 applications; SC22; software reusability;
                 specification; standards; WG9 Numerics",
  treatment =    "P Practical",
}

@Article{Dritz:1991:PSGb,
  author =       "K. W. Dritz",
  title =        "Proposed standard for a generic package of primitive
                 functions for {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "66--82",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics)",
  corpsource =   "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; compliable Ada; elementary functions; generic
                 package; GENERIC-; mathematical; mathematics computing;
                 primitive functions; primitive operations;
                 PRIMITIVE-FUNCTIONS; software; specification;
                 standards",
  treatment =    "P Practical",
}

@Article{Dritz:1991:RPS,
  author =       "K. W. Dritz",
  title =        "Rationale for the proposed standard for a generic
                 package of elementary functions for {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "47--65",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics);
                 C6110 (Systems analysis and programming)",
  corpsource =   "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "ACM SIGAda Numerics Working Group; Ada; Ada-Europe
                 Numerics; collateral; elementary functions standard;
                 mathematics computing; numerical software; portability;
                 programming; robustness; standards; Working Group",
  treatment =    "P Practical",
}

@Article{Duprat:1991:WND,
  author =       "J. Duprat and J.-M. Muller",
  title =        "Writing numbers differently for faster calculation",
  journal =      j-TECHNIQUE-SCI-INFORMATIQUES,
  volume =       "10",
  number =       "3",
  pages =        "211--224",
  month =        "????",
  year =         "1991",
  CODEN =        "TTSIDJ",
  ISSN =         "0752-4072, 0264-7419",
  ISSN-L =       "0752-4072",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Instead of Avizienis' or the carry save methods a
                 borrow save (BS) notation is proposed. Examples are
                 given of BS addition, subtraction, shifting and
                 multiplication with the necessary elementary cells
                 being proposed and circuits for testing zero and sign
                 being described. Floating point arithmetic is
                 explained, involving pseudo normalisation and
                 applications are covered including the Cordic
                 algorithm.",
  acknowledgement = ack-nhfb,
  affiliation =  "Ecole Normale Superieure de Lyon, France",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Technique et science informatiques : TSI",
  keywords =     "Addition; Borrow save; Carry save methods; Cordic
                 algorithm; Floating point arithmetic; Multiplication;
                 Pseudo normalisation; Shifting; Subtraction; Zero",
  language =     "French",
  pubcountry =   "France",
  thesaurus =    "Digital arithmetic",
}

@InProceedings{Ferguson:1991:AMA,
  author =       "W. E. {Ferguson, Jr.} and T. Brightman",
  title =        "Accurate and Monotone Approximations of Some
                 Transcendental Functions",
  crossref =     "Kornerup:1991:PIS",
  pages =        "237--244",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
}

@Article{Gal:1991:AEM,
  author =       "Shmuel Gal and Boris Bachelis",
  title =        "An Accurate Elementary Mathematical Library for the
                 {IEEE} Floating Point Standard",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "26--45",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65-04 65D15)",
  MRnumber =     "92a:65069",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/toms/103151.html",
  abstract =     "The algorithms used by the IBM Israel Scientific
                 Center for the elementary mathematical library using
                 the IEEE standard for binary floating point arithmetic
                 are described. The algorithms are based on the
                 ``accurate tables method.'' This methodology achieves
                 high performance and produces very accurate results. It
                 overcomes one of the main problems encountered in
                 elementary mathematical functions computations:
                 achieving last bit accuracy. The results obtained are
                 correctly rounded for almost all argument values.
                 \par

                 Our main idea in the accurate tables method is to use
                 ``nonstandard tables,'' which are different from the
                 natural tables of equally spaced points in which the
                 rounding error prevents obtaining last bit accuracy. In
                 order to achieve a small error we use the following
                 idea: Perturb the original, equally spaced, points in
                 such a way that the table value (or tables values in
                 case we need several tables) will be very close to
                 numbers which can be exactly represented by the
                 computer (much closer than the usual double precision
                 representation). Thus we were able to control the error
                 introduced by the computer representation of real
                 numbers and extended the accuracy without actually
                 using extended precision arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation.",
}

@Article{Gray:1991:GMA,
  author =       "H. L. Gray and Suojin Wang",
  title =        "A General Method for Approximating Tail
                 Probabilities",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "86",
  number =       "413",
  pages =        "159--166",
  month =        mar,
  year =         "1991",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:06:12 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314297;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1990.bib",
  URL =          "http://www.jstor.org/stable/2289726",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@InProceedings{Gustafson:1991:CAA,
  author =       "Sven-{\AA}ke Gustafson and Frank Stenger",
  title =        "Convergence acceleration applied to {Sinc}
                 approximation with application to approximation of $
                 |x|^\alpha $",
  crossref =     "Bowers:1991:CCI",
  pages =        "161--171",
  year =         "1991",
  MRclass =      "41A30 (93B40)",
  MRnumber =     "MR1140021",
  bibdate =      "Thu May 10 16:31:10 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "0746.41034",
  abstract =     "The author studies mainly the role of Chebyshev
                 acceleration of Sinc approximation. Then he considers
                 various methods of approximating $ \vert x \vert^\alpha
                 $ and applies Chebyshev acceleration to the various
                 type of approximants for the case of $ \alpha = 1 $.",
  acknowledgement = ack-nhfb,
  classmath =    "*41A65 (Abstract approximation theory)",
  keywords =     "Chebyshev acceleration; convergence acceleration",
  reviewer =     "Zhang Ganglu (Dongying)",
}

@Article{Hamza:1991:MBD,
  author =       "K. M. Hamza and M. A. H. Abdul-Karim",
  title =        "Microprocessor Based Direct Square Root Extractor",
  journal =      "Modelling",
  volume =       "34",
  number =       "1",
  pages =        "45--48",
  month =        "????",
  year =         "1991",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Ifantis:1991:PZS,
  author =       "E. K. Ifantis and C. G. Kokologiannaki and C. B.
                 Kouris",
  title =        "On the positive zeros of the second derivative of
                 {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "34",
  number =       "1",
  pages =        "21--31",
  day =          "10",
  month =        feb,
  year =         "1991",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042791901449",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Ikebe:1991:CZO,
  author =       "Yasuhiko Ikebe and Yasushi Kikuchi and Issei
                 Fujishiro",
  title =        "Computing zeros and orders of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "38",
  number =       "1--3",
  pages =        "169--184",
  day =          "23",
  month =        dec,
  year =         "1991",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:02:23 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279190169K",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Iserles:1991:CDC,
  author =       "A. Iserles",
  title =        "Complex dynamics of convergence acceleration",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "11",
  number =       "2",
  pages =        "205--240",
  year =         "1991",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65B05 (65E05)",
  MRnumber =     "92h:65006",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "convergence acceleration",
}

@Article{Laforgia:1991:BMB,
  author =       "Andrea Laforgia",
  title =        "Bounds for modified {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "34",
  number =       "3",
  pages =        "263--267",
  day =          "26",
  month =        apr,
  year =         "1991",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:49 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279190087Z",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Levrie:1991:CAF,
  author =       "Paul Levrie",
  title =        "Convergence acceleration for $n$-fractions",
  journal =      j-APPL-NUM-MATH,
  volume =       "7",
  number =       "6",
  pages =        "481--492",
  month =        jun,
  year =         "1991",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "40A15 (65B05)",
  MRnumber =     "92k:40001",
  MRreviewer =   "Claude Brezinski",
  bibdate =      "Sat Feb 8 10:09:54 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}

@Article{Levrie:1991:CFC,
  author =       "Paul Levrie",
  title =        "$ {G} $-continued fractions and convergence
                 acceleration in the solution of third-order linear
                 recurrence relations of {Poincar{\'e}} type",
  journal =      j-APPL-NUM-MATH,
  volume =       "8",
  number =       "3",
  pages =        "225--242",
  month =        oct,
  year =         "1991",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1090/surv/037",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65B99 (65Q05)",
  MRnumber =     "92m:65012",
  MRreviewer =   "J. Albrycht",
  bibdate =      "Sat Feb 8 10:09:54 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}

@InProceedings{Lyons:1991:FMF,
  author =       "Ken Lyons",
  title =        "A fast method for finding an integer square root",
  crossref =     "Koopman:1991:PST",
  pages =        "27--30",
  year =         "1991",
  bibdate =      "Tue May 4 05:57:50 MDT 1999",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/plan/259965/p27-lyons/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Markstein:1991:WFF,
  author =       "V. Markstein and P. Markstein and T. Nguyen and S.
                 Poole",
  title =        "Wide Format Floating-Point Math Libraries",
  crossref =     "IEEE:1991:PSA",
  pages =        "130--138",
  year =         "1991",
  bibdate =      "Wed Dec 13 18:34:51 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The authors present the performance and accuracy
                 evaluations of eleven transcendental functions found in
                 64- and 128-bit floating-point formats in math
                 libraries on the Cray Y-MP, the IBM 3090E/VF, the
                 Convex C-240, the Hewlett--Packard 9000/720, and the
                 IBM System/6000. Both architecture and algorithms are
                 shown to impact the results.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "ISQUARE, Inc., Austin, TX, USA",
  classification = "C5230 (Digital arithmetic methods); C5470
                 (Performance evaluation and testing); C7310
                 (Mathematics)",
  confdate =     "18-22 Nov. 1991",
  conflocation = "Albuquerque, NM, USA",
  confsponsor =  "IEEE; ACM",
  keywords =     "128 Bit; 64 Bit; Accuracy evaluations; Convex C-240;
                 Cray Y-MP; Floating-point formats; Hewlett--Packard
                 9000/720; IBM 3090E/VF; IBM System/6000; Math
                 libraries; Performance; Transcendental functions; Wide
                 format floating point math libraries",
  numericalindex = "Word length 6.4E+01 bit; Word length 1.28E+02 bit",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Mathematics computing; Parallel
                 processing; Performance evaluation",
}

@Article{Maximon:1991:EIP,
  author =       "Leonard C. Maximon",
  title =        "On the evaluation of the integral over the product of
                 two spherical {Bessel} functions",
  journal =      j-J-MATH-PHYS,
  volume =       "32",
  number =       "3",
  pages =        "642--648",
  month =        mar,
  year =         "1991",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.529405",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "33C55",
  MRnumber =     "92f:33018",
  MRreviewer =   "S. K. Chatterjea",
  bibdate =      "Tue Nov 1 08:57:23 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v32/i3/p642_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "7",
}

@Article{McQuillan:1991:HPV,
  author =       "S. E. McQuillan and J. V. McCanny and R. F. Woods",
  title =        "High performance {VLSI} architecture for division and
                 square root",
  journal =      j-ELECT-LETTERS,
  volume =       "27",
  number =       "1",
  pages =        "19--21",
  day =          "3",
  month =        jan,
  year =         "1991",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "A novel high performance bit parallel architecture to
                 perform square root and division is proposed. Relevant
                 VLSI design issues have been addressed. By employing
                 redundant arithmetic and a semisystolic schedule, the
                 throughput has been made \ldots{}",
}

@InProceedings{McQuillan:1991:VAM,
  author =       "S. E. McQuillan and J. V. McCanny",
  booktitle =    "1991 International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP-91, 14--17} April 1991",
  title =        "A {VLSI} architecture for multiplication, division and
                 square root",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1205--1208",
  year =         "1991",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "A high-performance VLSI architecture to perform
                 combined multiply-accumulate, divide, and square root
                 operations is proposed. The circuit is highly regular,
                 requires only minimal control, and can be reconfigured
                 for every cycle. The execution time \ldots{}",
}

@Article{Midy:1991:CSE,
  author =       "P. Midy and Y. Yakovlev",
  title =        "Computing some elementary functions of a complex
                 variable",
  journal =      j-MATH-COMP-SIM,
  volume =       "33",
  number =       "1",
  pages =        "33--49",
  year =         "1991",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  MRclass =      "65Y10 (65D20)",
  MRnumber =     "MR1122989",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784754",
}

@Article{Montuschi:1991:OAE,
  author =       "P. Montuschi and M. Mezzalama",
  title =        "Optimal Absolute Error Starting Values for
                 {Newton--Raphson} Calculation of Square Root",
  journal =      j-COMPUTING,
  volume =       "46",
  number =       "1",
  pages =        "67--86",
  month =        mar,
  year =         "1991",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65H05 (65G99)",
  MRnumber =     "92a:65161",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database; OCLC Contents1st database",
  acknowledgement = ack-nhfb,
  affiliation =  "Politecnico di Torino",
  affiliationaddress = "Torino, Italy",
  classification = "723; 921",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput Vienna New York",
  keywords =     "Absolute Error; Computer Programming --- Algorithms;
                 Mathematical Techniques; Newton--Raphson Method;
                 Optimization; Square Roots",
}

@InProceedings{Montuschi:1991:SRD,
  author =       "Paolo Montuschi and Luigi Ciminiera",
  title =        "Simple radix 2 division and square root with skipping
                 of some addition steps",
  crossref =     "Kornerup:1991:PIS",
  pages =        "202--209",
  year =         "1991",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Montuschi.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
  summary =      "The authors present a novel algorithm for shared radix
                 2 division and square root whose main characteristic is
                 the ability to avoid any addition when the digit 0 has
                 been selected. The solution presented uses a redundant
                 representation of the \ldots{}",
}

@Article{OGrady:1991:HOA,
  author =       "E. Pearse O'Grady and Baek-Kyu Young",
  title =        "A hardware-oriented algorithm for floating-point
                 function generation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "2",
  pages =        "237--241",
  month =        feb,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.73596",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "An algorithm is presented for performing accurate,
                 high-speed, floating-point function generation for
                 univariate functions defined at arbitrary breakpoints.
                 Rapid identification of the breakdown interval, which
                 includes the input argument, is the key operation in
                 the algorithm. A hardware implementation which makes
                 extensive use of read/write memories illustrates the
                 algorithm.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Okabe:1991:LDC,
  author =       "Y. Okabe and N. Takagi and S. Yaima",
  key =          "OTY91",
  title =        "Log-Depth Circuits for Elementary Functions Using
                 Residue Number System",
  journal =      j-ELECTRON-COMMUN-JPN,
  volume =       "74",
  number =       "8",
  pages =        "31--37",
  year =         "1991",
  CODEN =        "ECOJAL",
  ISSN =         "0424-8368",
  bibdate =      "Mon May 19 15:16:09 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Translated from Denshi Joho Tsushin Gakkai Ronbunshi,
                 vol.\ 21-DI, no.\ 9, September 1990, pp.\ 723-728",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics and communications in Japan",
}

@Article{Olver:1991:UEIb,
  author =       "F. W. J. Olver",
  title =        "Uniform, Exponentially Improved, Asymptotic Expansions
                 for the Confluent Hypergeometric Function and Other
                 Integral Transforms",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "22",
  number =       "5",
  pages =        "1475--1489",
  month =        sep,
  year =         "1991",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "41A60 (33C15)",
  MRnumber =     "92g:41035",
  MRreviewer =   "Hans-J{\"u}rgen Glaeske",
  bibdate =      "Sun Nov 28 19:25:21 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/22/5;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@Article{Press:1991:BFF,
  author =       "William H. Press and Saul A. Teukolsky",
  title =        "{Bessel} Functions of Fractional Order",
  journal =      j-COMPUT-PHYS,
  volume =       "5",
  number =       "2",
  pages =        "244--??",
  month =        mar,
  year =         "1991",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.4822982",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:45:28 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.4822982",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}

@Article{Press:1991:MBF,
  author =       "William H. Press and Saul A. Teukolsky",
  title =        "Modified {Bessel} Functions of Fractional Order",
  journal =      j-COMPUT-PHYS,
  volume =       "5",
  number =       "3",
  pages =        "330--??",
  month =        may,
  year =         "1991",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.4822991",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:45:29 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.4822991",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}

@Book{Saan:1991:VFP,
  author =       "T. Saan",
  title =        "{{\cyr Vychislenie {\`e}lementarnykh funktsi{\u\i}s
                 pomoshch'yu drobno-ratsional'nykh priblizheni{\u\i}}}.
                 ({Russian}) [Calculation of elementary functions by
                 means of rational approximations]",
  publisher =    "{\`E}ston. Nauchno-Proizvod. Ob\cdprime ed. Vychisl.
                 Tekhn. Inform., Tartu",
  pages =        "139",
  year =         "1991",
  MRclass =      "65-04 (65D15)",
  MRnumber =     "94f:65008",
  MRreviewer =   "W. Govaerts",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Smith:1991:AFP,
  author =       "David M. Smith",
  title =        "Algorithm 693: {A FORTRAN} Package for Floating-Point
                 Multiple-Precision Arithmetic",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "273--283",
  month =        jun,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:44:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/toms/108585.html",
  abstract =     "FM is a collection of FORTRAN-77 routines which
                 performs floating-point multiple-precision arithmetic
                 and elementary functions. Results are almost always
                 correctly rounded, and due to improved algorithms used
                 for elementary functions, reasonable efficiency is
                 obtained.",
  acknowledgement = ack-nhfb,
  affiliation =  "Loyola Marymount Univ., Los Angeles, CA, USA",
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods); C7310
                 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Accuracy; Algorithms; Elementary functions;
                 Floating-point multiple-precision arithmetic; FM;
                 FORTRAN-77 routines; Mathematical library; Portable
                 software; Rounding off",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf D.3.2}:
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77.",
  thesaurus =    "Digital arithmetic; Function approximation;
                 Mathematics computing; Software packages; Subroutines",
}

@Article{Squire:1991:ANS,
  author =       "Jon S. Squire",
  title =        "{Ada} numerics standardization and testing",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  address =      "New York, NY, USA",
  pages =        "1--286",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  annote =       "``A special edition from SIGAda \ldots{} presented by
                 SIGAda Numerics Working Group and Ada-Europe Numerics
                 Working Group and ISO- IEC/JTC1/SC22/WG9 Numerics
                 Rapporteur Group.''--Cover. Includes bibliographies.
                 Introduction to the proposed standard for the
                 elementary functions in Ada / Kenneth W. Dritz ---
                 Proposed standard for a generic package of elementary
                 functions for Ada / edited by Kenneth W. Dritz ---
                 Rationale for the proposed standard for a generic
                 package of elementary functions for Ada; Proposed
                 standard for a generic package of primitive functions
                 for Ada; Rationale for the proposed standard for a
                 generic package of primitive functions for Ada /
                 Kenneth W. Dritz --- Proposed standard for packages of
                 real and complex type declarations and basic operations
                 for Ada (including vector and matrix types) / edited by
                 Graham S. Hodgson --- Rationale for the proposed
                 standard for packages of real and complex type
                 declarations and basic operations for Ada (including
                 vector and matrix types) / Graham S. Hodgson. Proposed
                 standard for a generic package of complex elementary
                 functions / edited by Jon S. Squire --- Rationale for
                 the proposed standard for a generic package of complex
                 elementary functions / Jon S. Squire --- A portable
                 generic elementary function package in Ada and an
                 accurate test suite / Ping Tak Peter Tang --- Towards
                 validation of generic elementary functions and other
                 standard Ada numerics packages / Jon S. Squire ---
                 Floating point attributes in Ada / Dik T. Winter --- An
                 Ada math library for real-time avionics / Donald A.
                 Celarier and Donald W. Sando --- Predifined floating
                 point type names, uniformity rapporteur group UI-48 /
                 edited by Jon S. Squire.",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada (Computer program language)",
}

@Article{Squire:1991:PSG,
  author =       "J. S. Squire",
  title =        "Proposed standard for a generic package of complex
                 elementary functions ({Ada})",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "140--165",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics);
                 C6110B (Software engineering techniques)",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "ACM SIGAda; Ada; Ada-Europe Numerics Working Group;
                 applications; complex elementary functions; complex
                 mathematical routines; COMPLEX-ELEMENTARY-FUNCTIONS;
                 generic package; GENERIC-; international standard;
                 joint proposal; mathematics computing; Numerics Working
                 Group; portable; reusable; software reusability;
                 standards; WG9 Numerics Rapporteur Group",
  treatment =    "P Practical",
}

@Article{Squire:1991:RPS,
  author =       "Jon S. Squire",
  title =        "Rationale for the proposed standard for a generic
                 package of complex elementary functions ({Ada})",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "166--179",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C7310 (Mathematics);
                 C6110B (Software engineering techniques)",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "ACM SIGAda Numerics Working Group; Ada; Ada-; basic
                 complex mathematical; complex;
                 COMPLEX-ELEMENTARY-FUNCTIONS; elementary functions;
                 error bounds; Europe Numerics Working Group; generic
                 package; GENERIC-; mathematics computing; proposed
                 standard; reusable applications; routines; software
                 reusability; specification; standards",
  treatment =    "P Practical",
}

@Article{Squire:1991:TVG,
  author =       "J. S. Squire",
  title =        "Towards validation of generic elementary functions and
                 other standard {Ada} numerics packages",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "217--243",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6150G (Diagnostic, testing, debugging and evaluating
                 systems); C7310 (Mathematics); C6140D (High level
                 languages)",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; Ada listings; computing; conformance testing;
                 conformance tests; generic elementary functions;
                 implementors guide; mathematics; program testing;
                 proposed ISO; prototype tests; standard Ada numerics
                 packages; standards; test suite",
  treatment =    "P Practical",
}

@Article{Tang:1991:PGE,
  author =       "Ping Tak Peter Tang",
  title =        "A portable generic elementary function package in
                 {Ada} and an accurate test suite",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "181--216",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C7310 (Mathematics); C6140D (High level languages);
                 C6110B (Software engineering techniques); C6150G
                 (Diagnostic, testing, debugging and evaluating
                 systems)",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "accurate test; Ada; function libraries; mathematics
                 computing; portability; portable generic elementary
                 function package; program testing; resolution; rigorous
                 analysis; software; suite; test programs",
  treatment =    "P Practical",
}

@InProceedings{Tang:1991:TLA,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Lookup Algorithms for Elementary Functions and
                 Their Error Analysis",
  crossref =     "Kornerup:1991:PIS",
  pages =        "232--236",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
}

@InProceedings{Wong:1991:FHA,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast Hardware-based Algorithms for Elementary Function
                 Computations",
  crossref =     "Anonymous:1991:PIS",
  pages =        "56--65",
  year =         "1991",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  searchkey =    "ti:elementary function",
}

@Article{Zeilberger:1991:MPP,
  author =       "Doron Zeilberger",
  title =        "A {Maple} program for proving hypergeometric
                 identities",
  journal =      j-SIGSAM,
  volume =       "25",
  number =       "3",
  pages =        "4--13",
  month =        jul,
  year =         "1991",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Fri Feb 8 18:27:01 MST 2002",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Gives the listing of a MAPLE program for implementing
                 an algorithm for proving any terminating definite
                 hypergeometric identity, and more generally, for
                 finding the linear recurrence satisfied by any definite
                 hypergeometric sum R(n):= Sigma /sub k/F(n,k), where
                 F(n,k) has the form x/sup k/( Pi /sub i=1//sup m/(
                 alpha /sub i/n+ beta /sub i/k+c/sub i/)!/ Pi /sub
                 i'=1//sup m'/( alpha '/sub i'/n+ beta '/sub i'/k+c'/sub
                 i'/)!). The algorithm for definite hypergeometric
                 summation relies on Gosper's (1978) ingenious decision
                 procedure for indefinite summation, but not in the
                 obvious way!.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math. and Comput. Sci., Drexel Univ.,
                 Philadelphia, PA, USA",
  classcodes =   "C7310 (Mathematics)",
  classification = "C7310 (Mathematics)",
  corpsource =   "Dept. of Math. and Comput. Sci., Drexel Univ.,
                 Philadelphia, PA, USA",
  fjournal =     "SIGSAM Bulletin",
  issue =        "97",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
  keywords =     "definite; Definite hypergeometric summation;
                 hypergeometric identity; hypergeometric summation;
                 linear recurrence; Linear recurrence; manipulation;
                 MAPLE program; mathematics computing; proofs; Proofs;
                 public domain software; shareware; Shareware; symbol;
                 terminating definite; Terminating definite
                 hypergeometric identity; theorem proving",
  thesaurus =    "Mathematics computing; Public domain software; Symbol
                 manipulation; Theorem proving",
  treatment =    "P Practical",
}

@Article{Ziv:1991:FEE,
  author =       "Abraham Ziv",
  title =        "Fast Evaluation of Elementary Mathematical Functions
                 with Correctly Rounded Last Bit",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "410--423",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/toms/116813.html",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; standardization; theory",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency.",
}

@Book{Achieser:1992:TA,
  author =       "N. I. Achieser",
  title =        "Theory of Approximation",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "x + 307",
  year =         "1992",
  ISBN =         "0-486-67129-1 (paperback)",
  ISBN-13 =      "978-0-486-67129-1 (paperback)",
  LCCN =         "QA221 .A533 1992",
  bibdate =      "Fri Oct 20 08:06:59 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Dover books on advanced mathematics",
  acknowledgement = ack-nhfb,
  remark =       "Translation of Russian original, Lek{\"e}t{\`\i}sii po
                 teorii approksima{\"e}t{\`\i}sii. Reprint of English
                 translation \cite{Achieser:1956:TA}.",
  subject =      "Mathematical analysis",
  tableofcontents = "Approximation Problems in Linear Normalized Spaces
                 \\
                 Formulation of the Principal Problem in the Theory of
                 Approximation / 1 \\
                 The Concept of Metric Space / 1 \\
                 The Concept of Linear Normalized Space / 2 \\
                 Examples of Linear Normalized Spaces / 3 \\
                 The Inequalities of Holder and Minkowski / 4 \\
                 Additional Examples of Linear Normalized Spaces / 7 \\
                 Hilbert Space / 8 \\
                 The Fundamental Theorem of Approximation Theory in
                 Linear Normalized Spaces / 10 \\
                 Strictly Normalized Spaces / 11 \\
                 An Example of Approximation in the Space $L^p$ / 12 \\
                 Geometric Interpretation / 13 \\
                 Separable and Complete Spaces / 14 \\
                 Approximation Theorems in Hilbert Space / 15 \\
                 An Example of Approximation in Hilbert Space / 19 \\
                 More About the Approximation Problem in Hilbert Space /
                 21 \\
                 Orthonormalized Vector Systems in Hilbert Space / 22
                 \\
                 Orthogonalization of Vector Systems / 23 \\
                 Infinite Orthonormalized Systems / 25 \\
                 An Example of a Non-Separable System / 29 \\
                 Weierstrass' First Theorem / 29 \\
                 Weierstrass' Second Theorem / 32 \\
                 The Separability of the Space C / 33 \\
                 The Separability of the Space $L^p$ / 34 \\
                 Generalization of Weierstrass' Theorem to the Space
                 $L^p$ / 37 \\
                 The Completeness of the Space $L^p$ / 38 \\
                 Examples of Complete Orthonormalized Systems in
                 L[superscript 2] / 40 \\
                 Muntz's Theorem / 43 \\
                 The Concept of the Linear Functional / 46 \\
                 F. Riesz's Theorem / 47 \\
                 A Criterion for the Closure of a Set of Vectors in
                 Linear Normalized Spaces / 49 \\
                 P. L. Tchebysheff's Domain of Ideas \\
                 Statement of the Problem / 51 \\
                 A Generalization of the Theorem of de la Vallee-Poussin
                 / 52 \\
                 The Existence Theorem / 53 \\
                 Tchebysheff's Theorem / 55 \\
                 A Special Case of Tchebysheff's Theorem / 57 \\
                 The Tchebysheff Polynomials of Least Deviation from
                 Zero / 57 \\
                 A Further Example of P. Tchebysheff's Theorem / 58 \\
                 An Example for the Application of the General Theorem
                 of de la Vallee-Poussin / 60 \\
                 An Example for the Application of P. L. Tchebysheff's
                 General Theorem / 62 \\
                 The Passage to Periodic Functions / 64 \\
                 An Example of Approximating with the Aid of Periodic
                 Functions / 66 \\
                 The Weierstrass Function / 66 \\
                 Haar's Problem / 67 \\
                 Proof of the Necessity of Haar's Condition / 68 \\
                 Proof of the Sufficiency of Haar's Condition / 69 \\
                 An Example Related to Haar's Problem / 72 \\
                 P. L. Tchebysheff's Systems of Functions / 73 \\
                 Generalization of P. L. Tchebysheff's Theorem / 74 \\
                 On a Question Pertaining to the Approximation of a
                 Continuous Function in the Space $L$ / 76 \\
                 A. A. Markoff's Theorem / 82 \\
                 Special Cases of the Theorem of A. A. Markoff / 85 \\
                 Elements of Harmonic Analysis \\
                 The Simplest Properties of Fourier Series / 89 \\
                 Fourier Series for Functions of Bounded Variation / 93
                 \\
                 The Parseval Equation for Fourier Series / 97 \\
                 Examples of Fourier Series / 98 \\
                 Trigonometric Integrals / 101 \\
                 The Riemann--Lebesgue Theorem / 103 \\
                 Plancherel's Theory / 104 \\
                 Watson's Theorem / 106 \\
                 Plancherel's Theorem / 108 \\
                 Fejer's Theorem / 110 \\
                 Integral-Operators of the Fejer Type / 113 \\
                 The Theorem of Young and Hardy / 116 \\
                 Examples of Kernels of the Fejer Type / 118 \\
                 The Fourier Transformation of Integrable Functions /
                 120 \\
                 The Faltung of two Functions / 122 \\
                 V. A. Stekloff's Functions / 123 \\
                 Multimonotonic Functions / 125 \\
                 Conjugate Functions / 126 \\
                 Certain Extremal Properties of Integral Transcendental
                 Functions of the Exponential Type \\
                 Integral Functions of the Exponential Type / 130 \\
                 The Borel Transformation / 132 \\
                 The Theorem of Wiener and Paley / 134 \\
                 Integral Functions of the Exponential Type which are
                 Bounded along the Real Axis / 137 \\
                 S. N. Bernstein's Inequality / 140 \\
                 B. M. Levitan's Polynomials / 146 \\
                 The Theorem of Fejer and Riesz. A Generalization of
                 This Theorem / 152 \\
                 A Criterion for the Representation of Continuous
                 Functions as Fourier--Stieltjes Integrals / 154 \\
                 Questions Regarding the Best Harmonic Approximation of
                 Functions Preliminary Remarks / 160 \\
                 The Modulus of Continuity / 161 \\
                 The Generalization to the Space $L^p$ ($p \geq 1$) /
                 162 \\
                 An Example of Harmonic Approximation / 165 \\
                 Some Estimates for Fourier Coefficients / 169 \\
                 More about V. A. Stekloff's Functions / 173 \\
                 Two Lemmas / 175 \\
                 The Direct Problem of Harmonic Approximation / 176 \\
                 A Criterion due to B. Sz.-Nagy / 183 \\
                 The Best Approximation of Differentiable Functions /
                 187 \\
                 Direct Observations Concerning Periodic Functions / 195
                 \\
                 Jackson's Second Theorem / 199 \\
                 The Generalized Fejer Method / 201 \\
                 Berstein's Theorem / 206 \\
                 Priwaloff's Theorem / 210 \\
                 Generalizations of Bernstein's Theorems to the Space
                 $L^p$ ($p \geq 1$) / 211 \\
                 The Best Harmonic Approximation of Analytic Functions /
                 214 \\
                 A Different Formulation of the Result of the Preceding
                 Section / 218 \\
                 The Converse of Bernstein's Theorem / 221 \\
                 Wiener's Theorem on Approximation \\
                 Wiener's Problem / 224 \\
                 The Necessity of Wiener's Condition / 224 \\
                 Some Definitions and Notation / 225 \\
                 Several Lemmas / 227 \\
                 The Wiener--Levy Theorem / 230 \\
                 Proof of the Sufficiency of Wiener's Condition / 233
                 \\
                 Wiener's General Tauber Theorem / 234 \\
                 Weakly Decreasing Functions / 235 \\
                 Remarks on the Terminology / 237 \\
                 Ikehara's Theorem / 238 \\
                 Carleman's Tauber Theorem / 241 \\
                 Various Addenda and Problems \\
                 Elementary Extremal Problems and Certain Closure
                 Criteria / 243 \\
                 Szego's Theorem and Some of Its Applications / 256 \\
                 Further Examples of Closed Sequences of Functions / 267
                 \\
                 The Caratheodory--Fejer Problem and Similar Problems /
                 270 \\
                 Solotareff's Problems and Related Problems / 280 \\
                 The Best Harmonic Approximation of the Simplest
                 Analytic Functions / 289 \\
                 Notes / 296 \\
                 Index / 306",
}

@Article{Anderson:1992:FIH,
  author =       "G. D. Anderson and M. K. Vamanamurthy and M.
                 Vuorinen",
  title =        "Functional Inequalities for Hypergeometric Functions
                 and Complete Elliptic Integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "23",
  number =       "2",
  pages =        "512--524",
  month =        mar,
  year =         "1992",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33C05 (33C75)",
  MRnumber =     "93b:33001",
  MRreviewer =   "J. M. H. Peters",
  bibdate =      "Sat Dec 5 18:14:13 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@Book{Baker:1992:CMF,
  author =       "Louis Baker",
  title =        "{C} mathematical function handbook",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xviii + 757",
  year =         "1992",
  ISBN =         "0-07-911158-0",
  ISBN-13 =      "978-0-07-911158-6",
  LCCN =         "QA351.B17 1991; QA351 .B17 1992",
  bibdate =      "Fri Aug 31 18:54:02 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "McGraw-Hill programming tools for scientists and
                 engineers",
  acknowledgement = ack-nhfb,
  remark =       "System requirements for computer disk: PC; C or C++
                 compiler.",
  subject =      "Functions, Special; Computer programs; C (Computer
                 program language)",
}

@Article{Baker:1992:LCE,
  author =       "H. G. Baker",
  title =        "Less Complex Elementary Functions",
  journal =      j-SIGPLAN,
  volume =       "27",
  number =       "11",
  pages =        "15--16",
  month =        nov,
  year =         "1992",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Thu Sep 08 08:11:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@Article{Bohman:1992:FRP,
  author =       "Jan Bohman and Carl-Erik Fr{\"o}berg",
  title =        "The {$ {\Gamma } $}-function revisited: power series
                 expansions and real-imaginary zero lines",
  journal =      j-MATH-COMPUT,
  volume =       "58",
  number =       "197",
  pages =        "315--322",
  month =        jan,
  year =         "1992",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33B15 (11Y70 65D20)",
  MRnumber =     "92e:33001",
  MRreviewer =   "A. de Castro Brzezicki",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Borwein:1992:FEG,
  author =       "J. M. Borwein and I. J. Zucker",
  title =        "Fast evaluation of the gamma function for small
                 rational fractions using complete elliptic integrals of
                 the first kind",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "12",
  number =       "4",
  pages =        "519--526",
  year =         "1992",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65D20",
  MRnumber =     "93g:65028",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@Article{Buhring:1992:GHF,
  author =       "Wolfgang B{\"u}hring",
  title =        "Generalized hypergeometric functions at unit
                 argument",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "114",
  number =       "1",
  pages =        "145--153",
  month =        "????",
  year =         "1992",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "33C20",
  MRnumber =     "MR1068116 (92c:33004)",
  bibdate =      "Thu Dec 01 09:52:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "Zbl 0754.33003",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  remark =       "The paper treats $_{p + 1F}_p$ (or equivalently, $_p
                 F_{p - 1}$ ).",
}

@Article{Carlson:1992:TEI,
  author =       "B. C. Carlson",
  title =        "A Table of Elliptic Integrals: Two Quadratic Factors",
  journal =      j-MATH-COMPUT,
  volume =       "59",
  number =       "199",
  pages =        "165--180",
  month =        jul,
  year =         "1992",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20 (33C75 33E05)",
  MRnumber =     "92k:65027",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Corless:1992:NEAa,
  author =       "R. M. Corless and D. J. Jeffrey and H. Rasmussen",
  title =        "Numerical evaluation of {Airy} functions with complex
                 arguments",
  journal =      j-J-COMPUT-PHYS,
  volume =       "98",
  number =       "2",
  pages =        "347--347",
  month =        feb,
  year =         "1992",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(92)90150-W",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:55:53 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/002199919290150W",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Corless:1992:NEAb,
  author =       "R. M. Corless and D. J. Jeffrey and H. Rasmussen",
  title =        "Numerical evaluation of {Airy} functions with complex
                 arguments",
  journal =      j-J-COMPUT-PHYS,
  volume =       "99",
  number =       "1",
  pages =        "106--114",
  month =        mar,
  year =         "1992",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(92)90279-8",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  MRclass =      "65D20 (33E30)",
  MRnumber =     "92k:65028",
  bibdate =      "Mon Jan 2 07:55:54 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021999192902798",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
  keywords =     "Maple",
}

@Article{Croft:1992:ACA,
  author =       "A. Croft",
  title =        "An application of convergence acceleration techniques
                 to a class of two-point boundary value problems on a
                 semi-infinite domain",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "2",
  number =       "3--4",
  pages =        "307--320",
  month =        sep,
  year =         "1992",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65L10 (65B99)",
  MRnumber =     "93g:65097",
  bibdate =      "Fri Nov 6 18:06:29 MST 1998",
  bibsource =    "http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "C4130 (Interpolation and function approximation);
                 C4170 (Differential equations)",
  corpsource =   "Dept. of Math. Sci., Leicester Polytech., UK",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "boundary condition; boundary-value problems;
                 convergence acceleration; convergence acceleration
                 algorithms; convergence of numerical methods;
                 extrapolate; extrapolation; semi-infinite domain;
                 two-point boundary value problems; unbounded domains",
  pubcountry =   "Switzerland",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Dattoli:1992:GFM,
  author =       "G. Dattoli and C. Chiccoli and S. Lorenzutta and G.
                 Maino and M. Richetta and A. Torre",
  title =        "Generating functions of multivariable generalized
                 {Bessel} functions and {Jacobi}-elliptic functions",
  journal =      j-J-MATH-PHYS,
  volume =       "33",
  number =       "1",
  pages =        "25--36",
  month =        jan,
  year =         "1992",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.529959",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "33E05 (33C10 34B30 42A16 42A85)",
  MRnumber =     "92m:33037",
  MRreviewer =   "J. M. H. Peters",
  bibdate =      "Tue Nov 1 08:57:37 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v33/i1/p25_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "12",
}

@Article{DiDonato:1992:ASD,
  author =       "Armido R. {DiDonato} and Alfred H. {Morris, Jr.}",
  title =        "{Algorithm 708}: Significant Digit Computation of the
                 Incomplete Beta Function Ratios",
  journal =      j-TOMS,
  volume =       "18",
  number =       "3",
  pages =        "360--373",
  month =        sep,
  year =         "1992",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:14:47 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Brown:1994:CAS}.",
  URL =          "http://doi.acm.org/10.1145/131766.131776;
                 http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p360-didonato/",
  abstract =     "An algorithm is given for evaluating the incomplete
                 beta function ratio $ I_x(a, b) $ and its complement $
                 1 - I^x(a, b) $. A new continued fraction and a new
                 asymptotic series are used with classical results. A
                 transportable Fortran subroutine based on this
                 algorithm is currently in use. It is accurate to 14
                 significant digits when precision is not restricted by
                 inherent error.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation.",
}

@InProceedings{Dubois:1992:CFQ,
  author =       "D. Dubois and H. Prade",
  title =        "Calculation with fuzzy quantities",
  crossref =     "EC2:1992:DJN",
  bookpages =    "384",
  pages =        "24--27",
  year =         "1992",
  bibdate =      "Thu Dec 14 17:22:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "In some instances where numerical data are either
                 provisional, incomplete, or variable within a limited
                 range, the classical calculation of confidence
                 intervals can be extended in a fuzzy-set approach,
                 distinguishing between more or less plausible values.
                 The simultaneous use of relatively wide intervals
                 containing all possible values, and generally much
                 narrower intervals covering only the most likely ones,
                 can give sufficiently informative results. Some
                 precautions advisable in arithmetic operations on
                 imprecisely known quantities are outlined. Examples of
                 application include provisional budgeting, resource
                 estimation, evaluation of candidates, and extension of
                 PERT to projects involving precedence among elementary
                 tasks with uncertain durations and/or starting times.
                 Computer-aided engineering design can also benefit from
                 fuzzy specifications for values eventually to be
                 optimised.",
  acknowledgement = ack-nhfb,
  affiliation =  "IRIT, Paul Sabatier Univ., Toulouse, France",
  classification = "C1160 (Combinatorial mathematics); C4210 (Formal
                 logic); C7310 (Mathematics)",
  confdate =     "2-3 Nov. 1992",
  conflocation = "Nimes, France",
  keywords =     "Arithmetic operations; Candidates; Confidence
                 intervals; Engineering design; Fuzzy quantities; Fuzzy
                 specifications; Fuzzy-set approach; Imprecisely known
                 quantities; Numerical data; PERT; Provisional
                 budgeting; Resource estimation",
  language =     "French",
  pubcountry =   "France",
  thesaurus =    "Fuzzy logic; Fuzzy set theory; Statistical analysis",
}

@Article{Feinsilver:1992:BFR,
  author =       "P. Feinsilver and R. Schott",
  title =        "On {Bessel} functions and rate of convergence of zeros
                 of {Lommel} polynomials",
  journal =      j-MATH-COMPUT,
  volume =       "59",
  number =       "199",
  pages =        "153--156",
  month =        jul,
  year =         "1992",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33C10 (33C45)",
  MRnumber =     "93a:33007",
  MRreviewer =   "Boro D{\"o}ring",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  affiliation =  "Southern Illinois Univ., Carbondale, IL, USA",
  classcodes =   "B0220 (Analysis); B0290P (Differential equations);
                 B0290F (Interpolation and function approximation);
                 B0210 (Algebra); C1120 (Analysis); C4170 (Differential
                 equations); C4130 (Interpolation and function
                 approximation); C1110 (Algebra)",
  classification = "B0210 (Algebra); B0220 (Analysis); B0290F
                 (Interpolation and function approximation); B0290P
                 (Differential equations); C1110 (Algebra); C1120
                 (Analysis); C4130 (Interpolation and function
                 approximation); C4170 (Differential equations)",
  corpsource =   "Southern Illinois Univ., Carbondale, IL, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "average case analysis; Average case analysis; Bessel
                 function; Bessel functions; convergence of numerical
                 methods; convergence rate; Convergence rate; data
                 structures; differential equations; dynamic; Dynamic
                 data structures; Lommel; Lommel polynomials; Maple
                 program; polynomials; rate of convergence; Rate of
                 convergence; zeros; Zeros",
  thesaurus =    "Bessel functions; Convergence of numerical methods;
                 Differential equations; Polynomials",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Fillebrown:1992:FCB,
  author =       "Sandra Fillebrown",
  title =        "Faster computation of {Bernoulli} numbers",
  journal =      j-J-ALG,
  volume =       "13",
  number =       "3",
  pages =        "431--445",
  month =        sep,
  year =         "1992",
  CODEN =        "JOALDV",
  DOI =          "https://doi.org/10.1016/0196-6774(92)90048-H",
  ISSN =         "0196-6774 (print), 1090-2678 (electronic)",
  ISSN-L =       "0196-6774",
  bibdate =      "Tue Dec 11 09:15:18 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jalg.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/019667749290048H",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Algorithms",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01966774",
  remark =       "The author gives algorithms for computing Bernoulli
                 numbers of high order that require at most $ \lfloor 2
                 n \lg n \rfloor $ bits. One algorithm requires $ O(n^2
                 \log n) $ multiplications of numbers of $ O(n \log n) $
                 bits, and the other need $ O(n) $ multiplications of
                 numbers of $ O(n \log n) $ bits.",
}

@Article{Giordano:1992:FMC,
  author =       "Carla Giordano and Lucia G. Rodon{\`o}",
  title =        "Further monotonicity and convexity properties of the
                 zeros of cylinder functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "42",
  number =       "2",
  pages =        "245--251",
  day =          "12",
  month =        oct,
  year =         "1992",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:54 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279290078C",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Ifantis:1992:DIP,
  author =       "E. K. Ifantis and P. D. Siafarikas",
  title =        "A differential inequality for the positive zeros of
                 {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "44",
  number =       "1",
  pages =        "115--120",
  day =          "9",
  month =        dec,
  year =         "1992",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:56 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042792900553",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Jiang:1992:CCM,
  author =       "Thomas J. Jiang and Joseph B. Kadane and James M.
                 Dickey",
  title =        "Computation of {Carlson}'s Multiple Hypergeometric
                 Function {$R$} for {Bayesian} Applications",
  journal =      j-J-COMPUT-GRAPH-STAT,
  volume =       "1",
  number =       "3",
  pages =        "231--251",
  month =        sep,
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10618600.1992.10474583",
  ISSN =         "1061-8600 (print), 1537-2715 (electronic)",
  ISSN-L =       "1061-8600",
  MRclass =      "33C90 (62F15 65D20)",
  MRnumber =     "95e:33021",
  MRreviewer =   "P. N. Rathie",
  bibdate =      "Thu Aug 13 10:27:39 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputgraphstat.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/10618600.1992.10474583",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Graphical Statistics",
  journal-URL =  "http://www.amstat.org/publications/jcgs/;
                 http://www.tandfonline.com/loi/ucgs20",
  onlinedate =   "21 Feb 2012",
  xxtitle =      "Computation of {Carlson}'s multiple hypergeometric
                 function {$ {\cal R} $} for {Bayesian} applications",
}

@Book{Johnson:1992:UDD,
  author =       "Norman Lloyd Johnson and Samuel Kotz and Adrienne W.
                 Kemp and Norman Lloyd. Discrete distributions Johnson",
  title =        "Univariate discrete distributions",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Second",
  pages =        "xx + 565",
  year =         "1992",
  ISBN =         "0-471-54897-9 (hardcover)",
  ISBN-13 =      "978-0-471-54897-3 (hardcover)",
  LCCN =         "QA273.6 .J64 1992",
  bibdate =      "Sat Feb 7 17:19:01 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computstatdataanal1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley series in probability and mathematical
                 statistics. Applied probability and statistics",
  URL =          "http://www.loc.gov/catdir/description/wiley031/92011685.html;
                 http://www.loc.gov/catdir/enhancements/fy0607/92011685-b.html;
                 http://www.loc.gov/catdir/toc/onix01/92011685.html",
  acknowledgement = ack-nhfb,
  remark =       "Revised edition of \booktitle{Discrete distributions},
                 Norman L. Johnson, Samuel Kotz. 1969.",
  subject =      "Distribution (Probability theory)",
}

@Article{Kearfott:1992:IPF,
  author =       "Baker Kearfott and Milind Dawande and Kaisheng Du and
                 Chen-Yi Hu",
  title =        "{INTLIB}: a Portable {FORTRAN} 77 Elementary Function
                 Library",
  journal =      j-INTERVAL-COMP,
  volume =       "3",
  number =       "5",
  pages =        "96--105",
  year =         "1992",
  ISSN =         "0135-4868",
  MRclass =      "65G10",
  MRnumber =     "1 253 132",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Interval '92 (Moscow, 1992).",
  acknowledgement = ack-nhfb,
  fjournal =     "Interval Computations = Interval'nye vychisleniia",
}

@Article{Kzaz:1992:CAS,
  author =       "M. Kzaz",
  title =        "Convergence acceleration of some {Gaussian} quadrature
                 formulas for analytic functions",
  journal =      j-APPL-NUM-MATH,
  volume =       "10",
  number =       "6",
  pages =        "481--496",
  month =        nov,
  year =         "1992",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65B10 (65D32)",
  MRnumber =     "93j:65004",
  MRreviewer =   "J. Kofro{\v{n}}",
  bibdate =      "Sat Feb 8 10:09:54 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}

@Article{Lang:1992:HRS,
  author =       "T. Lang and P. Montuschi",
  title =        "Higher radix square root with prescaling",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "996--1009",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156542",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A scheme for performing higher radix square root based
                 on prescaling of the radicand is presented to reduce
                 the complexity of the result-digit selection. The
                 scheme requires several steps, namely multiplication
                 for prescaling the radicand, square \ldots{}",
}

@Article{Lee:1992:LCF,
  author =       "Chu-In Charles Lee",
  title =        "On {Laplace} continued fraction for the normal
                 integral",
  journal =      j-ANN-INST-STAT-MATH-TOKYO,
  volume =       "44",
  number =       "1",
  pages =        "107--120",
  month =        mar,
  year =         "1992",
  CODEN =        "AISXAD",
  DOI =          "https://doi.org/10.1007/BF00048673",
  ISSN =         "0020-3157 (print), 1572-9052 (electronic)",
  ISSN-L =       "0020-3157",
  bibdate =      "Sat Jan 31 16:59:48 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/anninststatmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/BF00048673",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the Institute of Statistical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10463",
}

@InProceedings{Liu:1992:QBS,
  author =       "K. J. R. Liu and E. Frantzeskakis",
  booktitle =    "Workshop on {VLSI} Signal Processing, V, 1992",
  title =        "Qrd-based Square Root Free and Division Free
                 Algorithms and Architectures",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "459--468",
  year =         "1992",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Not \ldots{}",
}

@Misc{Lynch:1992:HSD,
  author =       "T. Lynch and S. McIntyre and K. Tseng and S. Shaw and
                 T. Hurson",
  title =        "High speed divider with square root capability",
  year =         "1992",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,128,891.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@Article{Martin:1992:TPQa,
  author =       "Pablo Martin and Ricardo P{\'e}rez and Antonio L.
                 Guerrero",
  title =        "Two-point quasi-fractional approximations to the
                 {Airy} function {$ {\rm Ai}(x) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "98",
  number =       "2",
  pages =        "349--349",
  month =        feb,
  year =         "1992",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(92)90165-U",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:55:53 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/002199919290165U",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Martin:1992:TPQb,
  author =       "Pablo Mart{\'\i}n and Ricardo P{\'e}rez and Antonio L.
                 Guerrero",
  title =        "Two-point quasi-fractional approximations to the
                 {Airy} function {$ {\rm Ai}(x) $}",
  journal =      j-J-COMPUT-PHYS,
  volume =       "99",
  number =       "2",
  pages =        "337--340",
  month =        apr,
  year =         "1992",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/0021-9991(92)90212-H",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:55:55 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/002199919290212H",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Matos:1992:CAP,
  author =       "Ana C. Matos",
  title =        "Convergence and acceleration properties for the vector
                 $ \epsilon $-algorithm",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "3",
  number =       "1--4",
  pages =        "313--319",
  month =        dec,
  year =         "1992",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65B99",
  MRnumber =     "93h:65006",
  bibdate =      "Fri Nov 6 18:06:29 MST 1998",
  bibsource =    "http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Extrapolation and rational approximation (Puerto de la
                 Cruz, 1992).",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  conflocation = "Puerto de la Cruz, Spain; 13-17 Jan. 1992",
  conftitle =    "International Mathematical Congress on Extrapolation
                 and Rational Approximation",
  corpsource =   "Fac. de Ciencias, Porto Univ., Portugal",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "acceleration; convergence acceleration; convergence of
                 numerical methods; convergence speed; exactness;
                 extrapolation; extrapolation algorithm; speed of
                 convergence; vector $\epsilon$-algorithm; vector
                 sequences",
  pubcountry =   "Switzerland",
  treatment =    "T Theoretical or Mathematical",
}

@Article{McQuillan:1992:VMH,
  author =       "S. E. McQuillan and J. V. McCanny",
  title =        "{VLSI} module for high-performance multiply, square
                 root and divide",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "139",
  number =       "6",
  pages =        "505--510",
  month =        nov,
  year =         "1992",
  CODEN =        "ICDTEA",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
  summary =      "A high-performance VLSI architecture to perform
                 multiply-accumulate, division and square root
                 operations is proposed. The circuit is highly regular,
                 requires only minimal control and ean be pipelined
                 right down to the bit level. The system can also
                 \ldots{}",
}

@Article{Mikami:1992:NDO,
  author =       "N. Mikami and M. Kobayashi and Y. Yokoyama",
  title =        "A New {DSP}-Oriented Algorithm for Calculation of the
                 Square Root Using a Nonlinear Digital Filter",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "40",
  number =       "7",
  pages =        "1663--1669",
  month =        jul,
  year =         "1992",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.143438",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "A high-speed algorithm for calculating the square root
                 is proposed. This algorithm, which can be regarded as
                 calculation of the step response of a kind of nonlinear
                 IIR filter, requires no divisions. Therefore, it is
                 suitable for a VLSI digital \ldots{}",
}

@Article{Mitchell:1992:VFA,
  author =       "H. B. Mitchell",
  title =        "Very fast accurate square-root algorithm for use with
                 gradient edge operators",
  journal =      j-ELECT-LETTERS,
  volume =       "28",
  number =       "10",
  pages =        "922--923",
  day =          "7",
  month =        may,
  year =         "1992",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "Commonly used gradient edge operators such as the
                 Sobel, Prewitt and Roberts operators all required a
                 square root operation; this is, however,
                 computationally intensive and, consequently, simple but
                 very inaccurate approximations are often used
                 \ldots{}",
}

@Article{Paris:1992:EIA,
  author =       "R. B. Paris and A. D. Wood",
  title =        "Exponentially-improved asymptotics for the gamma
                 function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "41",
  number =       "1--2",
  pages =        "135--143",
  day =          "20",
  month =        aug,
  year =         "1992",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:53 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279290243Q",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Paszkowski:1992:CAC,
  author =       "Stefan Paszkowski",
  title =        "Convergence acceleration of continued fractions of
                 {Poincar{\'e}}'s type $1$",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "2",
  number =       "2",
  pages =        "155--170",
  month =        "????",
  year =         "1992",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65B05 (40A15)",
  MRnumber =     "93c:65006",
  MRreviewer =   "A. Bultheel",
  bibdate =      "Fri Nov 6 18:06:29 MST 1998",
  bibsource =    "http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Instytut Niskich Temp. i Badan Strukturalnych PAN,
                 Wroclaw, Poland",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "asymptotic behaviour; continued fractions; convergence
                 acceleration; convergence of numerical methods;
                 function approximation",
  pubcountry =   "Switzerland",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Prudnikov:1992:IS,
  author =       "Anatolij P. Prudnikov and Jurij A. Bry{\v{c}}kov and
                 Oleg I. Mari{\v{c}}ev",
  title =        "Integrals and series. {More} special functions",
  volume =       "3",
  publisher =    "Gordon and Breach Science Publishers",
  address =      "New York, NY, USA",
  pages =        "xx + 618",
  year =         "1992",
  ISBN =         "2-88124-097-6",
  ISBN-13 =      "978-2-88124-097-3",
  LCCN =         "QA308 P68 1986",
  bibdate =      "Thu Nov 2 15:54:36 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "Translated from the Russian by N. M. Queen.",
  seriestableofcontents = "v. 1. Elementary functions \\
                 v. 2. Special functions \\
                 v. 3. More special functions \\
                 v. 4. Direct Laplace transforms \\
                 v. 5. Inverse Laplace transforms",
  subject =      "Mathematics",
}

@Article{Salwin:1992:UPE,
  author =       "Arthur E. Salwin",
  title =        "Using the Proposed Elementary Functions Standard to
                 Build a Strongly Typed Trig Package",
  journal =      j-SIGADA-LETTERS,
  volume =       "12",
  number =       "5",
  pages =        "59--63",
  month =        sep # "\slash " # oct,
  year =         "1992",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:46 MDT 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages)",
  corpsource =   "Mitre Corp., McLean, VA, USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; compiler; elementary functions standard;
                 standards; strong typing; strongly typed trig package;
                 trigonometric functions",
  treatment =    "P Practical",
}

@Article{Saunders:1992:EFS,
  author =       "L. R. Saunders",
  title =        "An Exact Formula for the Symmetrical Incomplete Beta
                 Function Where the Parameter Is an Integer or
                 Half-Integer",
  journal =      j-AUST-J-STAT,
  volume =       "34",
  number =       "2",
  pages =        "261--264",
  month =        jun,
  year =         "1992",
  CODEN =        "AUJSA3",
  DOI =          "https://doi.org/10.1111/j.1467-842X.1992.tb01358.x",
  ISSN =         "0004-9581",
  ISSN-L =       "0004-9581",
  bibdate =      "Fri Jul 15 14:28:59 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/anzjs.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Australian Journal of Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-842X/issues",
}

@MastersThesis{Schulte:1992:AHD,
  author =       "Michael Joseph Schulte and Function generation",
  title =        "Algorithms and hardware designs for parallel
                 elementary function generation",
  type =         "Thesis ({M.S.} in Engin.)",
  school =       "University of Texas at Austin",
  address =      "Austin, TX, USA",
  pages =        "ix + 73",
  year =         "1992",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer input-output equipment -- Design and
                 construction.; Computer science -- Mathematics.;
                 Numerical analysis.; Parallel processing (Electronic
                 computers)",
  searchkey =    "ti:elementary n1 function",
}

@Article{Tang:1992:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the {{\tt Expm1}}
                 Function in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "211--222",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146928",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15",
  MRnumber =     "1 167 891",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See independent analysis and accuracy confirmation of
                 this algorithm in \cite{Kramer:1998:PWC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p211-tang/",
  abstract =     "Algorithms and implementation details for the function
                 $ e^x - 1 $ in both single and double precision of IEEE
                 754 arithmetic are presented here. With a table of
                 moderate size, the implementations need only
                 working-precision arithmetic and are provably accurate
                 to within 0.58 ulp.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@Article{Temme:1992:AII,
  author =       "N. M. Temme",
  title =        "Asymptotic Inversion of Incomplete Gamma Functions",
  journal =      j-MATH-COMPUT,
  volume =       "58",
  number =       "198",
  pages =        "755--764",
  month =        apr,
  year =         "1992",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33B20",
  MRnumber =     "93a:33003",
  MRreviewer =   "F. W. J. Olver",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Wong:1992:DSR,
  author =       "W. F. Wong and E. Goto",
  title =        "Division and square-rooting using a split multiplier",
  journal =      j-ELECT-LETTERS,
  volume =       "28",
  number =       "18",
  pages =        "1758--1759",
  day =          "27",
  month =        aug,
  year =         "1992",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "A modification is proposed to the traditional design
                 of a fast floating point multiplication circuit such
                 that instead of just performing A$\times$B where A and
                 B are m bits long, it is also capable of \ldots{}",
}

@TechReport{Wood:1992:CP,
  author =       "David C. Wood",
  title =        "The Computation of Polylogarithms",
  type =         "Report",
  institution =  "University of Kent",
  address =      "Canterbury, Kent CT2 7NZ, UK",
  year =         "1992",
  bibdate =      "Fri Jun 30 10:12:54 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.cs.kent.ac.uk/pubs/1992/110/content.pdf",
  abstract =     "The polylogarithm function, $ \Li_p(z) $, is defined,
                 and a number of algorithms are derived for its
                 computation, valid in different ranges of its real
                 parameter $p$ and complex argument $z$.",
  acknowledgement = ack-nhfb,
  keywords =     "polylogarithm",
  remark =       "Undated, but its URL suggests the year. The PDF file
                 was created 20-Mar-2014. The latest reference is to a
                 1992 journal article.",
}

@InProceedings{Woods:1992:HPD,
  author =       "R. F. Woods and S. E. McQuillan and J. Dowling and J.
                 V. McCanny",
  booktitle =    "Proceedings of Fifth Annual {IEEE} International
                 {ASIC} Conference and Exhibit, 1992",
  title =        "High performance {DSP} {ASIC} for multiply, divide and
                 square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "209--213",
  year =         "1992",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The design of a high-speed ASIC that combines the
                 operations of multiplication, division and square root
                 is described. The chip is based on a systolic array
                 architecture that uses a redundant number system and
                 allows multiplication, division, and \ldots{}",
}

@Article{Yeyios:1992:TSA,
  author =       "A. K. Yeyios",
  title =        "On two sequences of algorithms for approximating
                 square roots",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "40",
  number =       "1",
  pages =        "63--72",
  month =        jun,
  year =         "1992",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Alzer:1993:SGF,
  author =       "Horst Alzer",
  title =        "Some gamma function inequalities",
  journal =      j-MATH-COMPUT,
  volume =       "60",
  number =       "201",
  pages =        "337--346",
  month =        jan,
  year =         "1993",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33B15 (26D20)",
  MRnumber =     "93f:33001",
  MRreviewer =   "Aurelio Cannizzo",
  bibdate =      "Sat Jan 11 13:29:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Periodical{Anonymous:1993:ITS,
  author =       "Anonymous",
  title =        "Integral transforms and special functions",
  publisher =    "Gordon and Breach Science Publishers",
  address =      "Yverdon, Switzerland",
  year =         "1993",
  ISSN =         "1065-2469, 1476-8291",
  ISSN-L =       "1065-2469",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Appears with variable frequency from 1993--2001, and
                 six times yearly from 2002--date.",
  acknowledgement = ack-nhfb,
}

@Article{Arenstorf:1993:SMZ,
  author =       "R. F. Arenstorf and L. L. Brewer",
  title =        "A study of the motion of zeros of the {Epstein} zeta
                 function associated to $ m^2 + y^2 n^2 $ as $y$ varies
                 from $1$ to $ \sqrt {6}$",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "26",
  number =       "5",
  pages =        "57--69",
  month =        sep,
  year =         "1993",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(93)90074-6",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:11:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122193900746",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Bailey:1993:AMT,
  author =       "D. H. Bailey",
  title =        "Algorithm 719: Multiprecision Translation and
                 Execution of {FORTRAN} Programs",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "288--319",
  month =        sep,
  year =         "1993",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Dec 13 18:37:31 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The author describes two Fortran utilities for
                 multiprecision computation. The first is a package of
                 Fortran subroutines that perform a variety of
                 arithmetic operations and transcendental functions on
                 floating point numbers of arbitrarily high precision.
                 This package is in some cases over 200 times faster
                 than that of certain other packages that have been
                 developed for this purpose. The second utility is a
                 translator program, which facilitates the conversion of
                 ordinary Fortran programs to use this package. By means
                 of source directives (special comments) in the original
                 Fortran program, the user declares the precision level
                 and specifies which variables in each subprogram are to
                 be treated as multiprecision. The translator program
                 reads this source program and outputs a program with
                 the appropriate multiprecision subroutine calls. This
                 translator supports multiprecision integer, real, and
                 complex datatypes. The required array space for
                 multiprecision data types is automatically allocated.
                 In the evaluation of computational expressions, all of
                 the usual conventions for operator precedence and mixed
                 mode operations are upheld. Furthermore, most of the
                 Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP
                 are supported and produce true multiprecision values.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "NASA Ames Res. Center, Moffett Field, CA, USA",
  classification = "C5230 (Digital arithmetic methods); C6120 (File
                 organisation); C6140D (High level languages); C6150C
                 (Compilers, interpreters and other processors); C7310
                 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithm 719; Arithmetic operations; Array space;
                 Complex data types; Computational expressions; Floating
                 point numbers; Fortran programs; Fortran subroutines;
                 Fortran utilities; Fortran-77 intrinsics; Mixed mode
                 operations; Multiprecision computation; Multiprecision
                 data types; Multiprecision subroutine calls;
                 Multiprecision translation; Operator precedence; Source
                 directives; Transcendental functions; Translator
                 program",
  pubcountry =   "USA",
  thesaurus =    "Data structures; Digital arithmetic; FORTRAN;
                 Mathematics computing; Program interpreters;
                 Subroutines",
}

@Article{Barrera:1993:IBS,
  author =       "Tony Barrera and Pelle Olsson",
  title =        "An Integer Based Square Root Algorithm",
  journal =      j-BIT,
  volume =       "33",
  number =       "2",
  pages =        "253--261",
  month =        jun,
  year =         "1993",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01989748",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "68M07",
  MRnumber =     "1 326 017",
  bibdate =      "Wed Jan 4 18:52:23 MST 2006",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=33&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit33.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=33&issue=2&spage=253",
  abstract =     "The authors propose a fast integer based method for
                 computing square roots of floating point numbers. This
                 implies high accuracy and robustness, since no
                 precision will be lost during the computation. Only
                 integer addition and shifts are necessary to obtain the
                 square root. Comparisons made with the modified Newton
                 method indicate that the suggested method is twice as
                 fast for computing floating point square roots. (5
                 Refs.)",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "AB Consonant, Uppsala, Sweden",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "Floating point numbers; floating-point arithmetic;
                 Integer based square root algorithm; Modified Newton
                 method; Robustness",
  pubcountry =   "Denmark",
  thesaurus =    "Digital arithmetic",
  xxpages =      "254--261??",
}

@InCollection{Bohlender:1993:PAF,
  author =       "G. Bohlender and D. Cordes and A. Knofel and U.
                 Kulisch and R. Lohner and W. V. Walter",
  title =        "Proposal for accurate floating-point vector
                 arithmetic",
  crossref =     "Adams:1993:ACA",
  bookpages =    "x + 612",
  pages =        "87--102",
  year =         "1993",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Many computers provide accurate and reliable scalar
                 arithmetic for floating point numbers. An accurate
                 definition of the four elementary floating-point
                 operations +, -, *, / is given in the IEEE standards
                 for floating-point arithmetic and was well established
                 long before. An increasing number of computers
                 (especially PC's and workstations) feature IEEE
                 arithmetic. In many numerical algorithms, however,
                 compound operations such as the summation of a sequence
                 of numbers or the dot product of two vectors are highly
                 common. A simulation of these compound operations by
                 means of elementary floating-point operations leads to
                 accumulation of rounding errors and may suffer from
                 catastrophic cancellation of leading digits. Existing
                 standards for floating-point arithmetic do not improve
                 this situation. The goal of the proposal is to define
                 vector operations in a manner consistent with the
                 elementary scalar arithmetic operations. The rounding
                 modes and accuracy requirements as well as the data
                 formats of the operands and results of the vector
                 operations described in the proposal are chosen to be
                 fully consistent with the existing scalar
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe Univ., Germany",
  classification = "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques); C7310 (Mathematics)",
  keywords =     "Accuracy requirements; Catastrophic cancellation;
                 Compound operations; Data formats; Dot product;
                 Elementary floating-point operations; Elementary scalar
                 arithmetic operations; Floating point numbers; IEEE
                 arithmetic; IEEE standards; Leading digits; Numerical
                 algorithms; Operands; Rounding errors; Rounding modes;
                 Scalar floating-point arithmetic; Sequence; Standards;
                 Summation; Vector operations",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Mathematics computing; Roundoff
                 errors; Standards",
}

@Article{Cody:1993:ACP,
  author =       "W. J. Cody",
  title =        "{Algorithm 714}: {CELEFUNT}: a Portable Test Package
                 for Complex Elementary Functions",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "1--21",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151272",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 20 18:24:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p1-cody/;
                 http://www.acm.org/pubs/toc/Abstracts/toms/151272.html",
  abstract =     "This paper discusses CELEFUNT, a package of Fortran
                 programs for testing complex elementary functions.",
  abstract-2 =   "The author discusses CELEFUNT, a package of Fortran
                 programs for testing complex elementary functions.
                 CELEFUNT is a collection of test programs for the
                 complex floating-point elementary functions required by
                 the 1978 ANSI Fortran Standard (CABS), CSQRT, CLOG,
                 CEXP, CSIN/CCOS, and the complex power function.",
  acknowledgement = ack-nhfb,
  affiliation =  "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  classification = "C4100 (Numerical analysis); C5230 (Digital
                 arithmetic methods); C7310 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; CABS; CELEFUNT; CEXP; CLOG; Complex
                 elementary functions; Complex power function;
                 CSIN/CCOS; CSQRT; Floating-point elementary functions;
                 Fortran programs; measurement; performance; Portable
                 test package",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
  thesaurus =    "Conformance testing; Digital arithmetic; FORTRAN;
                 Mathematics computing; Numerical analysis; Program
                 testing; Software packages",
}

@Article{Cody:1993:ASP,
  author =       "W. J. {Cody, Jr.}",
  title =        "Algorithm 715: {SPECFUN}: {A} Portable {FORTRAN}
                 Package of Special Function Routines and Test Drivers",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "22--32",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151273",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 20 18:24:38 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/0098-3500/151273.html",
  abstract =     "SPECFUN is a package containing transportable FORTRAN
                 special function programs for real arguments and
                 accompanying test drivers. Components include Bessel
                 functions, exponential integrals, error functions and
                 related functions, and gamma functions and related
                 functions.",
  acknowledgement = ack-nhfb,
  affiliation =  "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  classification = "C7310 (Mathematics); C4100 (Numerical analysis)",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://portal.acm.org/toc.cfm?idx=J782",
  keywords =     "SPECFUN; Portable FORTRAN package; Special function
                 routines; Test drivers; Real arguments; Bessel
                 functions; Exponential integrals; Error functions;
                 Gamma functions; algorithms",
  pubcountry =   "USA",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
  thesaurus =    "FORTRAN; Mathematics computing; Numerical analysis;
                 Software packages; Software portability",
}

@Article{duToit:1993:BFI,
  author =       "C. F. du Toit",
  title =        "{Bessel} functions {$ J_n(z) $} and {$ Y_n(z) $} of
                 integer order and complex argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "78",
  number =       "1--2",
  pages =        "181--189",
  month =        dec,
  year =         "1993",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(93)90153-4",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:29:41 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465593901534",
  abstract =     "This paper describes computer subroutines which were
                 developed to compute Bessel functions of the first and
                 second kind ($ J_n(z) $ and $ Y_n(z) $, respectively)
                 for a complex argument $z$ and a range of integer
                 orders. A novel way of determining the starting point
                 of backward recurrence is used, and the algorithm for $
                 Y_n(z) $ improves on previous algorithms in terms of
                 accuracy and restrictions on the range of orders.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Book{Feinsilver:1993:ASO,
  author =       "Philip J. (Philip Joel) Feinsilver and Ren{\'e}
                 Schott",
  title =        "Algebraic structures and operator calculus",
  volume =       "241, 292, 347",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "?????",
  year =         "1993, 1994, 1996",
  ISBN =         "0-7923-2116-2 (v. 1), 0-7923-2921-X (v. 2),
                 0-7923-3834-0 (v. 3)",
  ISBN-13 =      "978-0-7923-2116-3 (v. 1), 978-0-7923-2921-3 (v. 2),
                 978-0-7923-3834-5 (v. 3)",
  LCCN =         "QA432 .F45 1993",
  bibdate =      "Sat Oct 30 17:31:34 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  note =         "Volume 1: Representations and probability theory.
                 Volume 2: Special functions and computer science.
                 Volume 3: Representations of Lie groups",
  series =       "Mathematics and its applications",
  acknowledgement = ack-nhfb,
  subject =      "Calculus, Operational; Probabilities; Representations
                 of groups",
}

@Article{Fowkes:1993:HEA,
  author =       "R. E. Fowkes",
  title =        "Hardware Efficient Algorithms for Trigonometric
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "2",
  pages =        "235--239",
  month =        feb,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.204796",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:47 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=204796",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Frappier:1993:QFI,
  author =       "Cl{\'e}ment Frappier and Patrick Olivier",
  title =        "A quadrature formula involving zeros of {Bessel}
                 functions",
  journal =      j-MATH-COMPUT,
  volume =       "60",
  number =       "201",
  pages =        "303--316",
  month =        jan,
  year =         "1993",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "41A55 (65D32)",
  MRnumber =     "93d:41025",
  MRreviewer =   "Hans Strauss",
  bibdate =      "Tue Mar 25 15:38:13 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 B0290M (Numerical integration and differentiation);
                 C4130 (Interpolation and function approximation); C4160
                 (Numerical integration and differentiation)",
  corpsource =   "Dept. de Math. Appliqu{\'e}es, Montreal, Que.,
                 Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Bessel functions; integration; interpolation; poles
                 and; polynomials; quadrature formula; sampling theorem;
                 zeros",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Han:1993:CAS,
  author =       "Weimin Han and Florian A. Potra",
  title =        "Convergence acceleration for some rootfinding
                 methods",
  crossref =     "Albrecht:1993:VNT",
  volume =       "9",
  pages =        "67--78",
  year =         "1993",
  CODEN =        "COSPDM",
  ISSN =         "0344-8029",
  bibdate =      "Sun Oct 17 11:55:48 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       j-COMPUTING-SUPPLEMENTUM,
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
}

@Article{Higginbotham:1993:ISR,
  author =       "T. F. Higginbotham",
  title =        "The integer square root of {$N$} via a binary search",
  journal =      j-SIGCSE,
  volume =       "25",
  number =       "4",
  pages =        "41--45",
  month =        dec,
  year =         "1993",
  CODEN =        "SIGSD3",
  DOI =          "https://doi.org/10.1145/164205.164229",
  ISSN =         "0097-8418 (print), 2331-3927 (electronic)",
  ISSN-L =       "0097-8418",
  bibdate =      "Sat Nov 17 18:57:24 MST 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib",
  abstract =     "An algorithm is presented which may be used to find
                 the integer square root of N. The method is intended
                 for use on a binary computer, where only addition,
                 subtraction, multiplication, or division by 2 is
                 required. The problem arose when the author was working
                 on factoring large numbers, where the machine, the
                 Honeywell DPS 8, had double precision integer addition
                 and subtraction, and the simulation of multiplication
                 was easy. The actual factoring of the large number was
                 to be Fermat's Method, requiring only addition and
                 subtraction, but the integer square root is required in
                 order to test for termination. The algorithm is
                 implemented in FORTRAN for ease of reading. Students
                 enjoy the unconventional approach to solving this
                 problem. It isn't long before some of them think of
                 other unusual solutions.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGCSE Bulletin (ACM Special Interest Group on
                 Computer Science Education)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J688",
}

@Article{Hu:1993:BRS,
  author =       "Chen-Yi Hu and R. Baker Kearfott and Abdulhamid Awad",
  title =        "On Bounding the Range of Some Elementary Functions in
                 {FORTRAN} 77",
  journal =      j-INTERVAL-COMP,
  volume =       "1993",
  number =       "3",
  pages =        "29--39",
  year =         "1993",
  ISSN =         "0135-4868",
  MRclass =      "65G10",
  MRnumber =     "1 305 844",
  bibdate =      "Wed Dec 4 11:13:33 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kearfott-r-baker.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the International Conference on
                 Numerical Analysis with Automatic Result Verification
                 (Lafayette, LA, 1993)",
  acknowledgement = ack-nhfb,
  fjournal =     "Interval Computations = Interval'nye vychisleniia",
}

@TechReport{Karp:1993:HPD,
  author =       "A. H. Karp and P. Markstein",
  title =        "High precision division and square root",
  number =       "HPL-93-42",
  institution =  "Hewlett--Packard Lab.",
  address =      "Palo Alto, CA, USA",
  pages =        "20",
  month =        jun,
  year =         "1993",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors present division and square root
                 algorithms for calculations with more bits than are
                 handled by the floating point hardware. These
                 algorithms avoid the need to multiply two high
                 precision numbers, speeding up the last iteration by as
                 much as a factor of ten.",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "Division; Floating point hardware; Square root
                 algorithms",
  thesaurus =    "Digital arithmetic",
}

@InCollection{Kramer:1993:MPC,
  author =       "Walter Kr{\"a}mer",
  booktitle =    "Mathematics in Science and Engineering: Scientific
                 Computing with Automatic Result Verification",
  title =        "Multiple-Precision Computations with Result
                 Verification",
  volume =       "189",
  publisher =    "Elsevier BV",
  address =      "Amsterdam, The Netherlands",
  pages =        "325--356",
  year =         "1993",
  DOI =          "https://doi.org/10.1016/s0076-5392(08)62851-9",
  bibdate =      "Tue Mar 14 19:20:47 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "arithmetic-geometric mean iteration; computation of $
                 e^\pi $; computation of a large number of digits of
                 $\pi$; computation of elliptic integrals; computation
                 of guaranteed bounds for the natural logarithm;
                 interval arithmetic; PASCAL-XSC",
}

@Article{Laforgia:1993:AMR,
  author =       "Andrea Laforgia and Maria Luisa Mathis",
  title =        "Additional monotonicity results for the zeros of
                 {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "47",
  number =       "1",
  pages =        "135--139",
  day =          "28",
  month =        jun,
  year =         "1993",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279390095S",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Lee:1993:DAE,
  author =       "Joong-Eon Lee and Oh-Young Kwon and Tack-Don Han",
  title =        "Design of an area efficient unit for floating-point
                 division and square root",
  journal =      j-J-KOREA-INFO-SCI-SOCIETY,
  volume =       "20",
  number =       "7",
  pages =        "1060--1071",
  month =        jul,
  year =         "1993",
  CODEN =        "HJKHDC",
  ISSN =         "0258-9125",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors propose an algorithm for a high
                 performance floating point division and square root
                 unit that uses a parallel multiplier. The basic
                 algorithm used in the design is the continued-product
                 normalization method. In this method, an arbitrary
                 number is constantly multiplied to the divisor and
                 dividend and dividend/divisor ends up with quotient/1
                 and the desired result attained. However this method
                 requires computation of x*(2-x) and x*(3-x)/2 and this
                 is quite an overhead. Therefore they propose a new
                 algorithm to compute (2-x) and (3-x)/2 by using the
                 modified Booth algorithm. When applied to the
                 continued-product normalization method, this algorithm
                 can maximize the inherent parallelism of the
                 continued-product normalization method, and reduce
                 computation time by effectively applying pipelining,
                 and also achieve area efficient design by eliminating
                 one register and one carry propagate adder needed for
                 computing (2-x) and (3-x)/2. When the designed unit is
                 used with the seed generator which has the accuracy of
                 2/sup -7/, division can be executed in eight cycles and
                 the square root operation in 13 cycles.",
  acknowledgement = ack-nhfb,
  classification = "B1265B (Logic circuits); C4240P (Parallel
                 programming and algorithm theory); C5120 (Logic and
                 switching circuits); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "Journal of the Korea Information Science Society =
                 Chongbo Kwahakhoe nonmunji",
  keywords =     "Area efficient unit; Continued-product normalization
                 method; Floating-point division; Modified Booth
                 algorithm; Parallel multiplier; Pipelining; Seed
                 generator; Square root",
  language =     "Korean",
  pubcountry =   "South Korea",
  thesaurus =    "Adders; Digital arithmetic; Parallel algorithms",
}

@Article{Li:1993:CAF,
  author =       "Y. Li and X. Dong and S. Pan",
  title =        "Computation of Auxiliary Functions in {STO} Molecular
                 Integrals up to Arbitrary Accuracy. {I}. {Evaluation}
                 of Incomplete Gamma Function {E$_n$ (X)} by Forward
                 Recursion",
  journal =      j-IJQC,
  volume =       "45",
  number =       "1",
  pages =        "3--??",
  year =         "1993",
  CODEN =        "IJQCB2",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Wed Jan 3 14:24:13 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
}

@TechReport{Litvinov:1993:ACR,
  author =       "Grigori L. Litvinov",
  title =        "Approximate construction of rational approximations
                 and the effect of error autocorrection",
  type =         "Technical report",
  number =       "8",
  institution =  "Institute of Mathematics, University of Oslo",
  address =      "Oslo, Norway",
  month =        may,
  year =         "1993",
  bibdate =      "Tue Mar 24 20:51:52 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Litvinov:1994:ACR}.",
  acknowledgement = ack-nhfb,
}

@Article{Liu:1993:DSC,
  author =       "Hui Min Liu",
  title =        "Determination of several classes of elementary
                 functions by functional inequalities. ({Chinese})",
  journal =      "Hunan Jiaoyu Xueyuan Xuebao (Ziran Kexue)",
  volume =       "11",
  number =       "2",
  pages =        "30--35, 12",
  year =         "1993",
  ISSN =         "1001-6074",
  MRclass =      "26A09 (39B72)",
  MRnumber =     "94g:26003",
  MRreviewer =   "Ling Yau Chan",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Louie:1993:DRS,
  author =       "M. E. Louie and M. D. Ercegovac",
  booktitle =    "Proceedings of the {IEEE} Workshop on {FPGAs} for
                 Custom Computing Machines, 5--7 April 1993",
  title =        "A digit-recurrence square root implementation for
                 field programmable gate arrays",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "178--183",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Creating efficient arithmetic processors requires a
                 pairing of high speed arithmetic algorithms with
                 optimal mapping strategies for a given technology. The
                 authors propose bit reduction as key to an efficient
                 pairing process for lookup table based \ldots{}",
}

@InProceedings{Lozier:1993:ABF,
  author =       "Daniel W. Lozier and F. W. J. Olver",
  title =        "{Airy} and {Bessel} Functions by Parallel Integration
                 of {ODEs}",
  crossref =     "Sincovec:1993:PSS",
  pages =        "530--538",
  year =         "1993",
  bibdate =      "Fri Jul 09 06:36:27 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Book{Mathai:1993:HGS,
  author =       "A. M. Mathai",
  title =        "A handbook of generalized special functions for
                 statistical and physical sciences",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "xi + 235",
  year =         "1993",
  ISBN =         "0-19-853595-3",
  ISBN-13 =      "978-0-19-853595-9",
  LCCN =         "QA351 .M35 1993",
  bibdate =      "Sat Oct 30 18:57:40 MDT 2010",
  bibsource =    "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Oxford science publications",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0635/92036065-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0635/92036065-t.html",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Handbooks, manuals, etc",
  tableofcontents = "I Mathematical preliminaries \\
                 1.1 The gamma function 1 \\
                 1.2 Bernoulli polynomials 6 \\
                 1.3 Asymptotic expansions of gamma functions 9 \\
                 1.4 The psi function 11 \\
                 1.5 The generalized zeta functions 12 \\
                 1.6 The beta function 15 \\
                 1.7 Calculation of residues for gamma functions 16 \\
                 1.8 The Mellin transform 23 \\
                 1.9 Density functions 24 \\
                 1.10 Methods of deriving distributions 49 \\
                 2 The G-function \\
                 2.1 The G-function 60 \\
                 2.2 Some basic properties of the G-function 69 \\
                 2.3 The Mellin transform of a G-function 78 \\
                 2.4 Properties connected with the derivatives of a
                 G-function 94 \\
                 2.5 Series representations for a G-function 96 \\
                 2.6 G-functions as multiple integrals or as solutions
                 of integral equations 106 \\
                 2.7 Differential equation for a G-function 111 \\
                 2.8 Asymptotic expansions for a G-function 112 \\
                 3 Elementary special functions and the G-function \\
                 3.1 Gamma and related functions: notations and
                 definitions 117 \\
                 3.2 Hypergeometric functions: notations and special
                 cases 118 \\
                 3.3 Confluent hypergeometric function and related
                 functions 119 \\
                 3.4 Exponential integral and related functions 121 \\
                 3.5 Bessel functions and associated functions 121 \\
                 3.6 Other special functions 122 \\
                 3.7 Orthogonal polynomials 124 \\
                 3.8 Elementary special functions expressed in terms of
                 G-functions 127 \\
                 3.9 G-functions expressed in terms of elementary
                 special functions 129 \\
                 3.10 Some integrals involving G-functions 132 \\
                 3.11 The H-function 140 \\
                 3.12 Computational aspects of G- and H-functions 144
                 \\
                 3.13 Orders of the special functions for small and
                 large values of the argument 145 \\
                 4 Generalizations to matrix variables \\
                 4.1 Scalar functions of a symmetric positive definite
                 matrix 152 \\
                 4.2 Scalar functions of matrix arguments 158 \\
                 4.3 Laplace transform 160 \\
                 4.4 Hypergeometric functions of matrix arguments 171
                 \\
                 4.5 Generalized matrix transform or M-transform 177 \\
                 4.6 Zonal polynomial 194 \\
                 4.7 Matrix variate Dirichlet distribution 197 \\
                 4.8 Hypergeometric functions of many scalar variables
                 205 \\
                 4.9 Hypergeometric functions of many matrix arguments
                 215 \\
                 4.10 G- and H-functions of two variables 217 \\
                 Bibliography 227 \\
                 Glossary of symbols 231 \\
                 Author index 233 \\
                 Subject index 234",
}

@Article{Mazenc:1993:CFU,
  author =       "Christophe Mazenc and Xavier Merrheim and Jean-Michel
                 Muller",
  title =        "Computing functions $ \cos^{-1} $ and $ \sin^{-1} $
                 using {Cordic}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "1",
  pages =        "118--122",
  month =        jan,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.192222",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:47 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192222",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{McQuillan:1993:NAV,
  author =       "S. E. McQuillan and J. V. McCanny and R. Hamill",
  booktitle =    "Proceedings of the 11th Symposium on Computer
                 Arithmetic, 2 July 1993",
  title =        "New algorithms and {VLSI} architectures for {SRT}
                 division and square root",
  crossref =     "Swartzlander:1993:SCA",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "80--86",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_McQuillan.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-11",
  summary =      "Radix two algorithms for SRT division and
                 square-rooting are developed. For these schemes, the
                 result digits and the residuals are computed
                 concurrently and the computations in adjacent rows are
                 overlapped. Consequently, their performance should
                 \ldots{}",
}

@Article{Montuschi:1993:RIT,
  author =       "P. Montuschi and L. Ciminiera",
  title =        "Reducing iteration time when result digit is zero for
                 radix $2$ {SRT} division and square root with redundant
                 remainders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "2",
  pages =        "239--246",
  month =        feb,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.204797",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Montuschi:1995:RRI}.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A new architecture is presented for shared radix 2
                 division and square root whose main characteristic is
                 the ability to avoid any addition/subtraction, when the
                 digit 0 has been selected. The solution presented uses
                 a redundant representation of the \ldots{}",
}

@TechReport{Morris:1993:NLM,
  author =       "Alfred H. {Morris, Jr.}",
  title =        "{NSWC} Library of Mathematics Subroutines",
  type =         "Report",
  number =       "NSWCDD/TR-92/425",
  institution =  "Naval Surface Warfare Center",
  address =      "Dahlgren, VA 22448-5000, USA; Silver Spring, MD
                 20903-5000, USA",
  pages =        "464",
  month =        jan,
  year =         "1993",
  bibdate =      "Tue Jun 13 08:47:19 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran2.bib",
  note =         "See also earlier edition \cite{Morris:1990:NLM}.",
  URL =          "https://ntrl.ntis.gov/NTRL/dashboard/searchResults/titleDetail/ADA261511.xhtml",
  abstract =     "The NSWC library is a library of general purpose
                 Fortran subroutines that provide a basic computational
                 capability for a variety of mathematical activities.
                 Emphasis has been placed on the transportability of the
                 codes. Subroutines are available in the following
                 areas: elementary operations, geometry, special
                 functions, polynomials, vectors, matrices, large dense
                 systems of linear equations, banded matrices, sparse
                 matrices, eigenvalues and eigenvectors, l1 solution of
                 linear equations, least-squares solution of linear
                 equations, optimization, transforms, approximation of
                 functions, curve fitting, surface fitting, manifold
                 fitting, numerical integration, integral equations,
                 ordinary differential equations, partial differential
                 equations, and random number generation.",
  acknowledgement = ack-nhfb,
  remark =       "[13-Jun-2023] Despite several Web searches, a
                 machine-readable freely downloadable copy of this
                 report, and its associated software, has not yet been
                 located. The entry for the earlier edition
                 [Morris:1993:NLM] has links to a PDF file and the
                 Fortran 90 source code. Another entry [Miller:2004:AMF]
                 has links to some of the source code, without
                 indication of software version dates.",
}

@Article{Muller:1993:NAC,
  author =       "J{\"u}rgen M{\"u}ller",
  title =        "On numerical analytic continuation and convergence
                 acceleration by summability methods",
  journal =      "Analysis",
  volume =       "13",
  number =       "3",
  pages =        "279--291",
  year =         "1993",
  ISSN =         "0174-4747",
  MRclass =      "40G10 (40A30 41A25 65B10)",
  MRnumber =     "1245757 (94j:40013)",
  MRreviewer =   "S. Sridhar",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Analysis. International Mathematical Journal of
                 Analysis and its Applications",
  keywords =     "convergence acceleration",
}

@Article{Perger:1993:NEG,
  author =       "Warren F. Perger and Atul Bhalla and Mark Nardin",
  title =        "A numerical evaluator for the generalized
                 hypergeometric series",
  journal =      j-COMP-PHYS-COMM,
  volume =       "77",
  number =       "2",
  pages =        "249--254",
  month =        oct,
  year =         "1993",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(93)90008-Z",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Dec 01 09:22:29 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  remark =       "Uses extended precision complex arithmetic.",
}

@Article{Petkovic:1993:SII,
  author =       "Miodrag S. Petkovi{\'c} and Carsten Carstensen",
  title =        "Some improved inclusion methods for polynomial roots
                 with {Weierstrass}' corrections",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "25",
  number =       "3",
  pages =        "59--67",
  month =        feb,
  year =         "1993",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:11:11 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219390143J",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Book{Povolotskii:1993:OFR,
  author =       "A. I. Povolotski{\u\i} and G. A. Sviridyuk",
  title =        "{{\cyr Odnomerny{\u\i} matematicheski{\u\i} analiz
                 {\`e}lementarnykh funktsi{\u\i}}}. ({Russian})
                 [One-dimensional mathematical analysis of elementary
                 functions] {{\cyr Nepreryvnye funktsii.
                 Differentsiruemye funktsii. Integriruemye funktsii}}.
                 [Continuous functions. Differentiable functions.
                 Integrable functions]",
  publisher =    "Chelyabinsk. Gos. Univ.",
  address =      "Chelyabinsk, USSR",
  pages =        "92",
  year =         "1993",
  ISBN =         "5-230-17764-0",
  ISBN-13 =      "978-5-230-17764-7",
  MRclass =      "26-01 (00A05)",
  MRnumber =     "94e:26001",
  MRreviewer =   "J{\'o}zef Kalinowski",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Ratis:1993:CCH,
  author =       "Yu. L. Ratis and P. Fern{\'a}ndez de C{\'o}rdoba",
  title =        "A code to calculate (high order) {Bessel} functions
                 based on the continued fractions method",
  journal =      j-COMP-PHYS-COMM,
  volume =       "76",
  number =       "3",
  pages =        "381--388",
  month =        aug,
  year =         "1993",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(93)90062-H",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:29:39 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/001046559390062H",
  abstract =     "We have developed a fast code to calculate Bessel
                 functions of integer and fractional order based on the
                 continued fractions method. This algorithm is specially
                 useful in the case of Bessel functions of high order
                 because it does not require any recalculation using
                 normalization relations.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Book{Saurer:1993:BSF,
  author =       "Josef Saurer",
  title =        "Bases of special functions and their domains of
                 convergence",
  volume =       "73",
  publisher =    "Akademie Verlag GmbH",
  address =      "Berlin, Germany",
  pages =        "158",
  year =         "1993",
  ISBN =         "3-05-501613-0",
  ISBN-13 =      "978-3-05-501613-4",
  ISSN =         "0138-3019",
  LCCN =         "QA351 .S28 1993",
  bibdate =      "Sat Oct 30 18:53:24 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Mathematical research",
  acknowledgement = ack-nhfb,
  remark =       "Revised version of the author's
                 thesis--Universit{\"a}t Essen, 1992.",
  subject =      "Functions, Special; Analytic functions; Eigenfunction
                 expansions; Convergence; Mathematical physics",
  tableofcontents = "Introduction 9 \\
                 1 Foundations of the theory 15 \\
                 1.1 Holomorphic operator functions in Frechet spaces 15
                 \\
                 1.2 Floquet eigenvalue problems (with a regular
                 singular point) 22 \\
                 1.3 Relationships between differential operators
                 corresponding to Floquet eigenvalue problems for
                 systems of differential equations and scalar
                 differential equations 26 \\
                 1.4 Biholomorphic images of functions 30 \\
                 1.5 An expansion theorem 37 \\
                 2 First order differential systems with a regular
                 singular point 43 \\
                 2.1 Fundamental properties 44 \\
                 2.2 Construction of fundamental systems depending
                 holomorphically on parameters 46 \\
                 2.3 A family of second order differential equations 55
                 \\
                 2.4 Differential equations and special functions of
                 mathematical physics 57 \\
                 2.4.1 Bessel equation, Bessel function 57 \\
                 2.4.2 Whittaker equation, Whittaker function 58 \\
                 2.4.3 Hypergeometric equation, hypergeometric function
                 60 \\
                 2.4.4 Generalised spherical function 61 \\
                 3 Floquet eigenvalue problems for first order
                 differential systems with a regular singular point 63
                 \\
                 3.1 Construction of biorthogonal canonical systems of
                 eigen- and associated vectors of the operator functions
                 $T$ and $T^*$ 67 \\
                 3.2 A general expansion theorem 73 \\
                 3.3 Floquet eigenvalue problems and expansion theorems
                 for a family of second order differential equations 75
                 \\
                 4 Domains of convergence of the eigenfunction
                 expansions 83 \\
                 4.1 The Bessel and Whittaker case 85 \\
                 4.2 The hypergeometric case 95 \\
                 4.3 Typical domains of convergence 105 \\
                 5 Examples of expansions in series of special functions
                 109 \\
                 5.1 Expansions in series of Bessel functions 109 \\
                 5.2 Expansions in series of Whittaker functions 115 \\
                 5.3 Expansions in series of hypergeometric functions
                 119 \\
                 6 First order differential systems for products of
                 vector-valued functions 127 \\
                 6.1 Products of vectors and sums of matrices of
                 different dimensions 128 \\
                 6.2 Construction of the first order differential system
                 132 \\
                 7 Floquet eigenvalue problems and expansions in series,
                 of m - fold products of special functions 135 \\
                 7.1 Construction of biorthogonal canonical systems of
                 eigen- and associated vectors of the operator functions
                 $T$ and $T^*$ 142 \\
                 7.2 Application 145 \\
                 References 151 \\
                 Notation index 154 \\
                 Index 157",
}

@InProceedings{Schulte:1993:ERC,
  author =       "M. Schulte and E. Swartzlander",
  title =        "Exact rounding of certain elementary functions",
  crossref =     "Swartzlander:1993:SCA",
  bookpages =    "xii + 284",
  pages =        "138--145",
  year =         "1993",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1993-01.pdf",
  abstract =     "An algorithm is described which produces exactly
                 rounded results for the functions of reciprocal, square
                 root, 2/sup x/, and log 2/sup x/. Hardware designs
                 based on this algorithm are presented for floating
                 point numbers with 16- and 24-b significands. These
                 designs use a polynomial approximation in which
                 coefficients are originally selected based on the
                 Chebyshev series approximation and are then adjusted to
                 ensure exactly rounded results for all inputs. To
                 reduce the number of terms in the approximation, the
                 input interval is divided into subintervals of equal
                 size and different coefficients are used for each
                 subinterval. For floating point numbers with 16-b
                 significands, the exactly rounded value of the function
                 can be computed in 51 ns on a 20-mm/sup 2/ chip. For
                 floating point numbers with 24-b significands, the
                 functions can be computed in 80 ns on a 98-mm/sup 2/
                 chip.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Electr. and Comput. Eng., Texas Univ.,
                 Austin, TX, USA",
  classification = "C4120 (Functional analysis); C5230 (Digital
                 arithmetic methods)",
  confdate =     "29 June--2 July 1993",
  conflocation = "Windsor, Ont., Canada",
  confsponsor =  "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
                 Natural Sci. and Eng. Res.; Council of Canada",
  keywords =     "Elementary functions; Exact rounding; Floating point
                 numbers; Polynomial approximation; Reciprocal; Rounded
                 results; Square root",
  thesaurus =    "Floating point arithmetic; Function evaluation",
}

@Article{Schulte:1993:PHD,
  author =       "Michael J. Schulte and Earl E. {Swartzlander, Jr.}",
  title =        "Parallel hardware designs for correctly rounded
                 elementary functions",
  journal =      j-INTERVAL-COMP,
  volume =       "4",
  pages =        "65--88",
  year =         "1993",
  ISSN =         "0135-4868",
  MRclass =      "65G10 (65C20)",
  MRnumber =     "1 305 859",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the International Conference on
                 Numerical Analysis with Automatic Result Verification
                 (Lafayette, LA, 1993)",
  acknowledgement = ack-nhfb,
  fjournal =     "Interval Computations = Interval'nye vychisleniia",
}

@TechReport{Schwarz:1993:HRAa,
  author =       "E. Schwarz",
  title =        "High-radix algorithms for high-order arithmetic
                 operations",
  type =         "Technical Report",
  number =       "CSL-TR-93-559",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        jan,
  year =         "1993",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@PhdThesis{Schwarz:1993:HRAb,
  author =       "Eric Mark Schwarz",
  title =        "High-radix algorithms for high-order arithmetic
                 operations",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Electrical Engineering, Stanford
                 University",
  address =      "Stanford, CA, USA",
  pages =        "224",
  month =        apr,
  year =         "1993",
  bibdate =      "Mon Jan 07 22:38:06 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Many common algorithms for high-order arithmetic
                 operations require an initial approximation. The
                 Newton--Raphson algorithm starts with an approximation
                 and then quadratically converges on the solution. The
                 initial approximation determines the number of
                 iterations of the algorithm and is typically
                 implemented as a look-up table in the form of a ROM or
                 PLA. A novel method is suggested which describes
                 high-order arithmetic operations with a partial product
                 array. This method applies to the operations of
                 division, reciprocal, square root, natural logarithm,
                 exponential, and trigonometric functions. The partial
                 product array of Boolean elements which describes the
                 operation can be summed on an existing floating-point
                 multiplier. The hardware needed is only the logic gates
                 to create the Boolean elements in the array and a
                 multiplexor, and the latency is that of the multiplier.
                 Thus, by reusing a floating-point multiplier, a
                 high-precision approximation to a high-order arithmetic
                 operation can be implemented with a low marginal
                 cost.\par

                 This dissertation describes the implementation and
                 shows a method for deriving partial product arrays to
                 approximate arithmetic operations. Then the proposed
                 method is applied and evaluated for several operations.
                 The proposed method yields a minimum approximation of
                 twelve bits correct for the reciprocal operation and
                 sixteen bits for the square root operation. The
                 proposed method is shown to be as small as 0.05\% the
                 size (in gates) of an equivalent precision look-up
                 table and has up to four times the accuracy (in bits)
                 as an equivalent latency polynomial approximation.
                 Also, three new iterative algorithms to increase the
                 precision of the approximations and a theoretical
                 analysis of the partial product array representation
                 are detailed. Thus, high-radix algorithms of many
                 arithmetic operations are possible at low cost.",
  acknowledgement = ack-nhfb,
  keywords =     "division; elementary functions; exponential;
                 logarithm; PPA (partial product array); reciprocal
                 square root; square root",
  remark =       "AAT 9317816. ProQuest document ID 746798521.",
}

@InProceedings{Schwarz:1993:HSA,
  author =       "E. M. Schwarz and M. J. Flynn",
  booktitle =    "Proceedings of the 11th Symposium on Computer
                 Arithmetic, 2 July 1993",
  title =        "Hardware starting approximation for the square root
                 operation",
  crossref =     "Swartzlander:1993:SCA",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "103--111",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  summary =      "A method for obtaining high-precision approximations
                 of high-order arithmetic operations is presented. These
                 approximations provide an accurate starting
                 approximation for high-precision iterative algorithms,
                 which translates into few iterations and \ldots{}",
}

@TechReport{Schwarz:1993:UFM,
  author =       "Eric Mark Schwarz and M. J. (Michael J.) Flynn",
  title =        "Using a floating-point multiplier's internals for
                 high-radix division and square root",
  type =         "Technical report",
  number =       "CSL-TR-93-554",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "iv + 45",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic.",
  remark =       "``January 1993.'' Abstract: ``A method for obtaining
                 high-precision approximations of high-order arithmetic
                 operations at low-cost is presented in this study.
                 Specifically, high-precision approximations of the
                 reciprocal (12 bits worst case) and square root (16
                 bits) operations are obtained using the internal
                 hardware of a floating-point multiplier without the use
                 of look-up tables. The additional combinatorial logic
                 necessary is very small due to the reuse of existing
                 hardware. These low-cost high-precision approximations
                 are used by iterative algorithms to perform the
                 operations of division and square root. The method
                 presented also applies to several other high-order
                 arithmetic operations. Thus, high-radix algorithms for
                 high-order arithmetic operations such as division and
                 square root are possible at low-cost.''",
}

@Article{Sellers:1993:CDC,
  author =       "H. Sellers",
  title =        "The {C$^2$-DIIS} Convergence Acceleration Algorithm",
  journal =      j-IJQC,
  volume =       "45",
  number =       "1",
  pages =        "31--??",
  year =         "1993",
  CODEN =        "IJQCB2",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Wed Jan 3 14:24:13 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  keywords =     "convergence acceleration",
}

@Article{Shishkov:1993:RDB,
  author =       "Dimit{\cdprime}r Shishkov",
  title =        "Reduction of domains of basic elementary functions to
                 arbitrary small intervals",
  journal =      "Annuaire Univ. Sofia Fac. Math. Inform.",
  volume =       "87",
  number =       "1--2",
  pages =        "3--32 (1999)",
  year =         "1993",
  ISSN =         "0205-0808",
  MRclass =      "65D20",
  MRnumber =     "MR1745336",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Godishnik na Sofi\u\i skiya Universitet ``Sv. Kliment
                 Okhridski''. Fakultet po Matematika i Informatika.
                 Annuaire de l'Universit\'e de Sofia ``St. Kliment
                 Ohridski''. Facult\'e de Math\'ematiques et
                 Informatique",
}

@Article{Snyder:1993:AFI,
  author =       "W. Van Snyder",
  title =        "{Algorithm 723}: {Fresnel} Integrals",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "452--456",
  month =        dec,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/168173.168193",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 29 15:24:56 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remarks \cite{Snyder:1996:RAF,Snyder:2021:CRA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p452-van_snyder/",
  abstract =     "An implementation of approximations for Fresnel
                 integrals and associated functions is described. The
                 approximations were originally developed by W. J. Cody,
                 but a Fortran implementation using them has not
                 previously been published.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; special functions",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Rational approximation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing.",
}

@Article{Thompson:1993:CCQ,
  author =       "William J. Thompson",
  title =        "Cutting Corners: Quick Square Roots and Trig
                 Functions",
  journal =      j-COMPUT-PHYS,
  volume =       "7",
  number =       "1",
  pages =        "18--??",
  month =        jan,
  year =         "1993",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.4823136",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:45:39 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.4823136",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}

@Article{Vedder:1993:IAN,
  author =       "John D. Vedder",
  title =        "An invertible approximation to the normal distribution
                 function",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "16",
  number =       "1",
  pages =        "119--123",
  month =        jun,
  year =         "1993",
  CODEN =        "CSDADW",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  bibdate =      "Fri Feb 6 11:39:39 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computstatdataanal1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/016794739390248R",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
}

@Article{Zaitsev:1993:IMM,
  author =       "A. V. Zaitsev",
  title =        "Implementation of {Miller}'s method for evaluation of
                 {Bessel} functions of first kind",
  journal =      j-J-SOV-MATH,
  volume =       "63",
  number =       "5",
  pages =        "558--560",
  month =        feb,
  year =         "1993",
  CODEN =        "JSOMAR",
  DOI =          "https://doi.org/10.1007/bf01142530",
  ISSN =         "0090-4104 (print), 2376-5798 (electronic)",
  ISSN-L =       "0090-4104",
  bibdate =      "Wed Mar 1 09:29:38 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Soviet Mathematics",
  journal-URL =  "http://link.springer.com/journal/10958",
}

@Article{Anonymous:1994:C,
  author =       "Anonymous",
  title =        "Corrigenda",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "553--553",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 14 16:17:03 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Hull:1994:ICE}",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bajard:1994:BNH,
  author =       "Jean-Claude Bajard and Sylvanus Kla and Jean-Michel
                 Muller",
  title =        "{BKM}: a new hardware algorithm for complex elementary
                 functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "955--963",
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295857",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "68M07",
  MRnumber =     "1 294 301",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Bender:1994:DAS,
  author =       "Carl M. Bender and Stefan Boettcher",
  title =        "Determination of $ f(\infty) $ from the asymptotic
                 series for $ f(x) $ about $ x = 0 $",
  journal =      j-J-MATH-PHYS,
  volume =       "35",
  number =       "4",
  pages =        "1914--1921",
  month =        apr,
  year =         "1994",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.530577",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  MRclass =      "41A60 (41A21 65D15 81Q15)",
  MRnumber =     "95d:41063",
  bibdate =      "Tue Nov 1 08:58:10 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1990.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v35/i4/p1914_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  pagecount =    "8",
}

@Article{Brown:1994:CAS,
  author =       "Barry W. Brown and Lawrence Levy",
  title =        "Certification of {Algorithm 708}: Significant Digit
                 Computation of the Incomplete Beta",
  journal =      j-TOMS,
  volume =       "20",
  number =       "3",
  pages =        "393--397",
  month =        sep,
  year =         "1994",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 12:53:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{DiDonato:1992:ASD}.",
  URL =          "http://doi.acm.org/10.1145/192115.192155;
                 http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p393-brown/",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; continued fractions; F-distribution",
  subject =      "G.1.2 [Numerical Analysis]: Approximation",
}

@Article{Carlson:1994:AAS,
  author =       "B. C. Carlson and J. L. Gustafson",
  title =        "Asymptotic Approximations for Symmetric Elliptic
                 Integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "25",
  number =       "2",
  pages =        "288--303",
  month =        mar,
  year =         "1994",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33E05 (41A60)",
  MRnumber =     "95b:33056",
  MRreviewer =   "Bruce C. Berndt",
  bibdate =      "Sat Dec 5 18:14:13 MST 1998",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/25/2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/22847",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@Article{Chaudhry:1994:GIG,
  author =       "M. Aslam Chaudhry and S. M. Zubair",
  title =        "Generalized incomplete gamma functions with
                 applications",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "55",
  number =       "1",
  pages =        "99--123",
  day =          "31",
  month =        oct,
  year =         "1994",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:33 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042794901872",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Chen:1994:ABB,
  author =       "Yang Chen and Mourad E. H. Ismail and K. A. Muttalib",
  title =        "Asymptotics of basic {Bessel} functions and
                 $q$-{Laguerre} polynomials",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "54",
  number =       "3",
  pages =        "263--272",
  day =          "20",
  month =        oct,
  year =         "1994",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:33 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279200128V",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Chen:1994:EDU,
  author =       "Sau-Gee Chen and Chieh-Chih Li",
  booktitle =    "{Proceedings of TENCON '94. IEEE Region 10's Ninth
                 Annual International Conference. Theme: `Frontiers of
                 Computer Technology'}",
  title =        "Efficient designs of unified $2$'s complement division
                 and square root algorithm and architecture",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "943--947",
  year =         "1994",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Efficient unified 2's complement division and square
                 root algorithm, and their architectures are proposed in
                 this work. The designs are high speed, small area and
                 high compatibility. The architectures provide bit level
                 pipelined operation, as well \ldots{}",
}

@Article{Cortadella:1994:HRD,
  author =       "J. Cortadella and T. Lang",
  title =        "High-Radix Division and Square-Root with Speculation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "919--931",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295854",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected revised and extended papers from ARITH'11
                 \cite{Swartzlander:1993:SCA}.",
  summary =      "The speed of high-radix digit-recurrence dividers and
                 square-root units is mainly determined by the
                 complexity of the result-digit selection. We present a
                 scheme in which a simpler function speculates the
                 result digit, and, when this speculation is \ldots{}",
}

@Article{Damnjanovic:1994:EFL,
  author =       "Zlatan Damnjanovic",
  title =        "Elementary functions and loop programs",
  journal =      j-NOTRE-DAME-J-FORM-LOG,
  volume =       "35",
  number =       "4",
  pages =        "496--522",
  year =         "1994",
  CODEN =        "NDJFAM",
  ISSN =         "0029-4527 (print), 1939-0726 (electronic)",
  ISSN-L =       "0029-4527",
  MRclass =      "03D20 (68Q15)",
  MRnumber =     "96i:03036",
  MRreviewer =   "John P. Helm",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Notre Dame journal of formal logic",
  journal-URL =  "http://projecteuclid.org/all/euclid.ndjfl",
}

@Article{Das:1994:ATE,
  author =       "Mrinal Kanti Das",
  title =        "Analysis of two elementary functions",
  journal =      j-INT-J-MATH-EDU-SCI-TECH,
  volume =       "25",
  number =       "1",
  pages =        "17--24",
  year =         "1994",
  CODEN =        "IJMEBM",
  ISSN =         "0020-739X (print), 1464-5211 (electronic)",
  ISSN-L =       "0020-739X",
  MRclass =      "26-01 (33B10)",
  MRnumber =     "1 257 731",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematical Education in
                 Science and Technology",
  journal-URL =  "http://www.tandfonline.com/loi/tmes20",
}

@TechReport{Dunham:1994:PMAa,
  author =       "Charles B. Dunham",
  title =        "Provably Monotone Approximations, {IV}",
  type =         "Technical report",
  number =       "TR-417",
  institution =  "Department of Computer Science, University of Western
                 Ontario",
  address =      "London, Ontario, Canada",
  day =          "8",
  month =        mar,
  year =         "1994",
  bibdate =      "Tue Apr 12 11:26:47 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.csd.uwo.ca/tech-reports/",
  acknowledgement = ack-nhfb,
}

@TechReport{Dunham:1994:PMAb,
  author =       "Charles B. Dunham",
  title =        "Provably Monotone Approximations, {IV}, Revised",
  type =         "Technical report",
  number =       "TR-422",
  institution =  "Department of Computer Science, University of Western
                 Ontario",
  address =      "London, Ontario, Canada",
  day =          "4",
  month =        apr,
  year =         "1994",
  bibdate =      "Tue Apr 12 11:26:47 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.csd.uwo.ca/tech-reports/",
  acknowledgement = ack-nhfb,
}

@Article{Dunkl:1994:AHI,
  author =       "Charles F. Dunkl and Donald E. Ramirez",
  title =        "{Algorithm 736}: Hyperelliptic Integrals and the
                 Surface Measure of Ellipsoids",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "427--435",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/198429.198431",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30",
  MRnumber =     "1 368 025",
  bibdate =      "Tue Mar 14 16:16:51 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p427-dunkl/",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "elliptic integral; expected radius; Lauricella's
                 hypergeometric function; optimal designs; surface
                 measure",
  subject =      "G.1.4 [Numerical Analysis]: Quadrature and Numerical
                 Differentiation -- multiple quadrature; G.3
                 [Mathematics of Computing]: Probability and
                 Statistics",
}

@Article{Dunkl:1994:CHI,
  author =       "Charles F. Dunkl and Donald E. Ramirez",
  title =        "Computing Hyperelliptic Integrals for Surface Measure
                 of Ellipsoids",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "413--426",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/198429.198430",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30",
  MRnumber =     "1 368 024",
  bibdate =      "Tue Mar 14 16:16:49 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p413-dunkl/",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "elliptic integral; expected radius; Lauricella's
                 hypergeometric function; optimal designs; surface
                 measure",
  subject =      "G.1.4 [Numerical Analysis]: Quadrature and Numerical
                 Differentiation -- multiple quadrature; G.3
                 [Mathematics of Computing]: Probability and
                 Statistics",
}

@Book{Ercegovac:1994:DSR,
  author =       "Milo{\v{s}} D. (Dragutin) Ercegovac and Tomas Lang",
  title =        "Division and square root: digit-recurrence algorithms
                 and implementations",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "x + 230",
  year =         "1994",
  ISBN =         "0-7923-9438-0",
  ISBN-13 =      "978-0-7923-9438-9",
  LCCN =         "QA76.9.C62 E73 1994",
  bibdate =      "Fri Mar 27 09:46:24 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Everitt:1994:GBF,
  author =       "W. N. Everitt and C. Markett",
  title =        "On a generalization of {Bessel} functions satisfying
                 higher-order differential equations",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "54",
  number =       "3",
  pages =        "325--349",
  day =          "20",
  month =        oct,
  year =         "1994",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:33 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042794902550",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Fukushima:1994:NCI,
  author =       "Toshio Fukushima and Hideharu Ishizaki",
  title =        "Numerical computation of incomplete elliptic integrals
                 of a general form",
  journal =      j-CELEST-MECH-DYN-ASTR,
  volume =       "59",
  number =       "3",
  pages =        "237--251",
  month =        jul,
  year =         "1994",
  CODEN =        "CLMCAV",
  DOI =          "https://doi.org/10.1007/BF00692874",
  ISSN =         "0923-2958 (print), 1572-9478 (electronic)",
  ISSN-L =       "0923-2958",
  MRclass =      "33E05 65R20 65D32 (33E30 70-08 70E15)",
  MRnumber =     "1285916 (95c:65041)",
  bibdate =      "Wed Oct 20 21:26:45 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/content/0923-2958/",
  ZMnumber =     "Zbl 0818.33013",
  abstract =     "We present an algorithm to compute the incomplete
                 elliptic integral of a general form. The algorithm
                 efficiently evaluates some linear combinations of
                 incomplete elliptic integrals of all kinds to a high
                 precision. Some numerical examples are given as
                 illustrations. This enables us to numerically calculate
                 the values and the partial derivatives of incomplete
                 elliptic integrals of all kinds, which are essential
                 when dealing with many problems in celestial mechanics,
                 including the analytic solution of the torque-free
                 rotational motion of a rigid body around its
                 barycenter.",
  acknowledgement = ack-nhfb,
  fjournal =     "Celestial Mechanics \& Dynamical Astronomy. An
                 International Journal of Space Dynamics",
  keywords =     "Incomplete elliptic integrals; numerical computation",
}

@Article{Hahn:1994:UDF,
  author =       "H. Hahn and D. Timmermann and B. J. Hosticka and B.
                 Rix",
  title =        "A unified and division-free {CORDIC} argument
                 reduction method with unlimited convergence domain
                 including inverse hyperbolic functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "11",
  pages =        "1339--1344",
  month =        nov,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.324568",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:58 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=324568",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Homeier:1994:NCA,
  author =       "Herbert H. H. Homeier",
  editor =       "Ralf Gruber and Marco Tomassini",
  booktitle =    "Proceedings of the 6th {Joint EPS-APS International
                 Conference} on {Physics Computing, Physics Computing}
                 '94",
  title =        "Nonlinear convergence acceleration for orthogonal
                 series",
  publisher =    "European Physical Society, Boite Postale 69, CH-1213
                 Petit-Lancy, Geneva, Switzerland",
  address =      "Lugano",
  pages =        "47--50",
  year =         "1994",
  ISBN =         "2-88270-011-3",
  ISBN-13 =      "978-2-88270-011-7",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA942",
  keywords =     "convergence acceleration",
  tech =         "Technical Report TC-NA-94-2, Institut f{\"u}r
                 {Physikalische} und {Theoretische Chemie,
                 Universit{\"a}t Regensburg, D-93040 Regensburg}, 1994",
}

@Article{Hull:1994:ICE,
  author =       "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter
                 Tang",
  title =        "Implementing Complex Elementary Functions Using
                 Exception Handling",
  journal =      j-TOMS,
  volume =       "20",
  number =       "2",
  pages =        "215--244",
  month =        jun,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/178365.178404",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 21 15:10:29 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See correction \cite{Anonymous:1994:C}, and improved
                 analysis, tightened bounds, and exhibition of worst
                 cases for complex square roots
                 \cite{Jeannerod:2017:REC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-2/p215-hull/",
  abstract =     "Algorithms are developed for reliable and accurate
                 evaluations of the complex elementary functions
                 required in Fortran 77 and Fortran 90, namely cabs,
                 csqrt, cexp, clog, csin, and ccos. The algorithms are
                 presented in a pseudocode that has a convenient
                 exception-handling facility. A tight error bound is
                 derived for each algorithm. Corresponding Fortran
                 programs for an IEEE environment have also been
                 developed to illustrate the practicality of the
                 algorithms, and these programs have been tested very
                 carefully to help confirm the correctness of the
                 algorithms and their error bounds. The results are of
                 these tests are included in the paper, but the Fortran
                 programs are not; the programs are available from
                 Fairgrieve, (tff@cs.toronto.edu).",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; complex elementary functions; design;
                 implementation",
  subject =      "G.1.0 [Numerical Analysis]: General--error analysis;
                 numerical algorithms; G.1.2 [Numerical Analysis]:
                 Approximation--elementary function approximation; G.4
                 [Mathematics of Computing]: Mathematical
                 Software--algorithm analysis; reliability and
                 robustness; verification",
}

@Article{Iserles:1994:CAD,
  author =       "A. Iserles",
  title =        "Convergence acceleration as a dynamical system",
  journal =      j-APPL-NUM-MATH,
  volume =       "15",
  number =       "2",
  pages =        "101--121",
  day =          "13",
  month =        sep,
  year =         "1994",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "58F23 (30D05 58F08 65D99 65H99)",
  MRnumber =     "95i:58155",
  MRreviewer =   "Peter M. Makienko",
  bibdate =      "Wed Jul 28 14:35:48 MDT 1999",
  bibsource =    "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1994&volume=15&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Innovative methods in numerical analysis (Bressanone,
                 1992).",
  URL =          "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1994&volume=15&issue=2&aid=496",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}

@Article{Jablonski:1994:NES,
  author =       "Aleksander Jablonski",
  title =        "Numerical Evaluation of Spherical {Bessel} Functions
                 of the First Kind",
  journal =      j-J-COMPUT-PHYS,
  volume =       "111",
  number =       "2",
  pages =        "256--259",
  month =        apr,
  year =         "1994",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1006/jcph.1994.1060",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:54:54 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0021999184710606",
  abstract =     "Calculations of cross sections for elastic scattering
                 of electrons require frequent evaluations of the
                 spherical Bessel functions, $ j_l(x) $ and $ n_l(x) $,
                 in a wide range of the argument $x$ and the order $l$.
                 It turns out that the usual algorithms providing the
                 values of the spherical Bessel function of the first
                 kind, $ j_l(x) $, have a rather limited range of
                 stability. It is shown that there is no algorithm
                 implementing a single method which can be used in
                 calculations associated with the theory of elastic
                 scattering of electrons. An attempt is made to select
                 different areas of stability from different algorithms
                 in order to create a relatively fast and universal
                 algorithm.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@InProceedings{Jain:1994:SRR,
  author =       "V. K. Jain and Lei Lin",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP-94, 19--22} April 1994",
  title =        "Square-root, reciprocal, sine\slash cosine, arctangent
                 cell for signal and image processing",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II/521--II/524",
  year =         "1994",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper discusses an efficient interpolation method
                 for nonlinear function generation. Based on this, a 24
                 bit VLSI cell, capable of computing the (1) square
                 root, (2) reciprocal, (3) sine/cosine, and (4)
                 arctangent functions, is presented for \ldots{}",
}

@Misc{Karp:1994:FPA,
  author =       "Alan H. Karp and Peter Markstein and Dennis
                 Brzezinski",
  title =        "Floating point arithmetic unit using modified
                 {Newton--Raphson} technique for division and square
                 root",
  howpublished = "US Patent 5,341,321",
  day =          "23",
  month =        aug,
  year =         "1994",
  bibdate =      "Thu Oct 17 10:20:52 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Patent filed 5 May 1993, granted to Hewlett-Packard
                 Company on 23 August 1994. Patent expired 5-May-2013.
                 See criticism in \cite{Zimmermann:2005:XXX}.",
  URL =          "http://patft.uspto.gov/netahtml/PTO/search-bool.html;
                 https://patents.google.com/patent/US5341321A",
  abstract =     "A floating point processing system which uses a
                 multiplier unit and an adder unit to perform floating
                 point division and square root operations using both a
                 conventional and a modified form of the Newton--Raphson
                 method. The modified form of the Newton--Raphson method
                 is used in place of the final iteration of the
                 conventional Newton--Raphson so as to compute high
                 precision approximated results with a substantial
                 improvement in speed. The invention computes
                 approximated results faster and simplifies hardware
                 requirements because no multiplications of numbers of
                 the precision of the result are required.",
  acknowledgement = ack-nhfb,
}

@Article{Kearfott:1994:AIP,
  author =       "R. B. Kearfott and M. Dawande and K. Du and C. Hu",
  title =        "Algorithm 737: {INTLIB}: a Portable {Fortran}-77
                 Elementary Function Library",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "447--459",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat May 20 15:54:18 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  accepted =     "December 1993",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "BLAS; Fortran 77; Fortran 90; interval arithmetic;
                 operator overloading; standard functions",
  subject =      "D.2.2 [Software Engineering]: Tools and Techniques --
                 software libraries; D.2.7 [Software Engineering]:
                 Distribution and Maintenance -- documentation;
                 portability; G.1.0 [Numerical Analysis]: General --
                 computer arithmetic; G.1.2 [Numerical Analysis]:
                 Approximation -- elementary function approximation",
}

@Article{Khajah:1994:UHP,
  author =       "H. G. Khajah and E. L. Ortiz",
  title =        "Ultra-high precision computations",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "27",
  number =       "7",
  pages =        "41--57",
  month =        apr,
  year =         "1994",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(94)90148-1",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Mon Jun 13 22:03:39 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122194901481",
  abstract =     "We describe a machine independent Fortran subroutine
                 which performs the four basic arithmetic operations
                 with a degree of accuracy prescribed by the user.
                 Tables of Chebyshev expansions of orders 48 and 50 for
                 some basic mathematical functions are obtained as a
                 result of applying this subroutine in conjunction with
                 the recursive formulation of the Tau Method. A recently
                 devised technique for the sharp determination of upper
                 and lower error bounds for Tau Method approximations
                 enables us to find the degree $n$ required to achieve a
                 prescribed accuracy $ \epsilon $ over a given interval
                 $ [a, b] $. A number of practical illustrations are
                 given.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Math., Imperial Coll. of Sci., Technol. and
                 Med., London, UK",
  classification = "C6140D (High level languages); C7310 (Mathematics)",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "$\cos(\pi x)$; $\erf(x) / x$; $\exp(-x^2)$; $\exp(x)$;
                 $\sin(\pi x)$; $x \exp(x^2) erfc(x)$; $z \exp(z)
                 \Ei(-z)$; Arithmetic operations; Chebyshev expansions;
                 Lower error bounds; Machine independent Fortran
                 subroutine; Mathematical functions; Tau method; Upper
                 error bounds",
  pubcountry =   "UK",
  thesaurus =    "FORTRAN; Mathematics computing",
}

@Article{Lewanowicz:1994:SAS,
  author =       "Stanis{\l}aw Lewanowicz",
  title =        "A simple approach to the summation of certain slowly
                 convergent series",
  journal =      j-MATH-COMPUT,
  volume =       "63",
  number =       "208",
  pages =        "741--745",
  month =        oct,
  year =         "1994",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65B10",
  MRnumber =     "95a:65010",
  MRreviewer =   "Thomas A. Atchison",
  bibdate =      "Sat Jan 11 13:29:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Litvinov:1994:ACR,
  author =       "Grigori L. Litvinov",
  title =        "Approximate construction of rational approximations
                 and the effect of error autocorrection",
  journal =      j-RUSS-J-MATH-PHYS,
  volume =       "1",
  number =       "3",
  pages =        "313--352",
  month =        "????",
  year =         "1994",
  CODEN =        "RJMPEL",
  ISSN =         "1061-9208 (print), 1555-6638 (electronic)",
  ISSN-L =       "1061-9208",
  bibdate =      "Tue Mar 24 20:54:11 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arxiv.org/abs/math/0101042",
  abstract =     "Several construction methods for rational
                 approximations to functions of one real variable are
                 described in the present paper; the computational
                 results that characterize the comparative accuracy of
                 these methods are presented; an effect of error
                 autocorrection is considered. This effect occurs in
                 efficient methods of rational approximation (e.g.,
                 Pad{\'e} approximations, linear and nonlinear Pad{\'e}
                 Chebyshev approximations) where very significant errors
                 in the coefficients do not affect the accuracy of the
                 approximation. The matter of import is that the errors
                 in the numerator and the denominator of a fractional
                 rational approximant compensate each other. This effect
                 is related to the fact that the errors in the
                 coefficients of a rational approximant are not
                 distributed in an arbitrary way but form the
                 coefficients of a new approximant to the approximated
                 function. Understanding of the error autocorrection
                 mechanism allows to decrease this error by varying the
                 approximation procedure depending on the form of the
                 approximant. Some applications are described in the
                 paper. In particular, a method of implementation of
                 basic calculations on decimal computers that uses the
                 technique of rational approximations is described in
                 the Appendix.\par

                 To a considerable extent the paper is a survey and the
                 exposition is as elementary as possible.",
  acknowledgement = ack-nhfb,
  fjournal =     "Russian Journal of Mathematical Physics",
}

@TechReport{Lozier:1994:NESa,
  author =       "D. W. Lozier and F. W. J. Olver",
  title =        "Numerical evaluation of special functions",
  type =         "Report",
  number =       "NISTIR 5383",
  institution =  "Computing and Applied Mathematics Laboratory, U. S.
                 Department of Commerce",
  address =      "Washington, DC, USA",
  pages =        "47",
  month =        mar,
  year =         "1994",
  MRclass =      "65D20 (33-00)",
  bibdate =      "Thu Nov 16 07:52:34 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib",
  URL =          "https://math.nist.gov/~DLozier/publications/nistir5383.pdf",
  abstract =     "Higher transcendental functions continue to play
                 varied and important roles in investigations by
                 engineers, mathematicians, scientists and
                 statisticians. The purpose of this paper is to assist
                 in locating useful approximations and software for the
                 numerical generation of these functions, and to offer
                 some suggestions for future developments in this
                 field.",
  acknowledgement = ack-nhfb,
  author-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
  tableofcontents = "1. Introduction / 3 \\
                 2. Mathematical Developments / 5 \\
                 3. Packages, Libraries and Systems / 6 \\
                 3.1. Software Packages / 6 \\
                 3.2. Intermediate Libraries / 8 \\
                 3.3. Comprehensive Libraries / 8 \\
                 3.4. Interactive Systems / 12 \\
                 4. Functions of One Variable / 15 \\
                 4.1. Airy Functions / 15 \\
                 4.2. Error Functions, Dawson's Integral, Fresnel
                 Integrals, Goodwin--Staton Integral / 15 \\
                 4.3. Exponential Integrals, Logarithmic Integral, Sine
                 and Cosine Integrals / 16 \\
                 4.4. Gamma, Psi, and Polygamma Functions / 16 \\
                 4.5. Landau Density and Distribution Functions / 16 \\
                 4.6. Polylogarithms, Clausen Integral / 16 \\
                 4.7. Zeta Function / 17 \\
                 4.8. Additional Functions of One Variable / 17 \\
                 5. Functions of Two or More Variables / 17 \\
                 5.1. Bessel Functions / 17 \\
                 5.2. Coulomb Wave Functions / 18 \\
                 5.3. Elliptic Integrals and Functions / 18 \\
                 5.4. Fermi--Dirac, Bose--Einstein, and Debye Integrals
                 / 19 \\
                 5.5. Hypergeometric and Concuent Hypergeometric
                 Functions / 19 \\
                 5.6. Incomplete Bessel Functions, Incomplete Beta
                 Function / 19 \\
                 5.7. Incomplete Gamma Functions, Generalized
                 Exponential Integrals / 20 \\
                 5.8. Legendre Functions and Associated Legendre
                 Functions / 20 \\
                 5.9. Mathieu, Lam{\'e}, and Spheroidal Wave Functions /
                 20 \\
                 5.10. Orthogonal Polynomials / 21 \\
                 5.11. Polylogarithms (Generalized) / 21 \\
                 5.12. Struve and Anger--Weber Functions / 21 \\
                 5.13. Weber Parabolic Cylinder Functions / 21 \\
                 5.14. Zeta Function (Generalized) / 21 \\
                 5.15. Additional Functions of Two or More Variables /
                 21 \\
                 6. Testing and Library Construction / 22 \\
                 7. Future Trends / 22 \\
                 Acknowledgments / 23 \\
                 A Note on the Reference Acronyms / 23 \\
                 References / 23--47",
}

@InProceedings{Lozier:1994:NESb,
  author =       "D. W. Lozier and F. W. J. Olver",
  title =        "Numerical evaluation of special functions",
  crossref =     "Gautschi:1994:MCH",
  volume =       "48",
  pages =        "79--125",
  year =         "1994",
  DOI =          "https://doi.org/10.1090/psapm/048/1314844",
  MRclass =      "65D20 (30-04 33-04 41-04)",
  MRnumber =     "95m:65036 (1314844)",
  MRreviewer =   "John P. Coleman",
  bibdate =      "Fri Jul 9 05:44:10 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  series =       "Proc. Sympos. Appl. Math.",
  URL =          "http://math.nist.gov/mcsd/Reports/2001/nesf/",
  abstract =     "Higher transcendental functions continue to play
                 varied and important roles in investigations by
                 engineers, mathematicians, scientists, and
                 statisticians. The purpose of this paper is to assist
                 in locating useful approximations and software for the
                 numerical generation of these functions, and to offer
                 some suggestions for future developments in the
                 field.",
  acknowledgement = ack-nhfb,
  remark =       "The references list contains about 400 entries which
                 should ultimately be incorporated in this BibTeX
                 bibliography collection.",
  author-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
}

@TechReport{Lozier:1994:SNS,
  author =       "Daniel W. Lozier",
  title =        "Software Needs in Special Functions",
  type =         "Technical Report",
  number =       "NISTIR 5490",
  institution =  pub-NIST,
  address =      pub-NIST:adr,
  pages =        "16",
  month =        aug,
  year =         "1994",
  bibdate =      "Fri Jul 09 05:47:26 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Published in \cite{Lozier:1996:SNS}.",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5490.ps",
  acknowledgement = ack-nhfb,
}

@Article{MacLeod:1994:CIA,
  author =       "Allan J. MacLeod",
  title =        "Computation of inhomogeneous {Airy} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "53",
  number =       "1",
  pages =        "109--116",
  day =          "29",
  month =        jul,
  year =         "1994",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:31 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042794901961",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{MacLeod:1994:TBT,
  author =       "Allan J. MacLeod",
  title =        "Table-based tests for {Bessel} function software",
  journal =      j-ADV-COMPUT-MATH,
  volume =       "2",
  number =       "2",
  pages =        "251--260",
  month =        mar,
  year =         "1994",
  CODEN =        "ACMHEX",
  DOI =          "https://doi.org/10.1007/BF02521111",
  ISSN =         "1019-7168 (print), 1572-9044 (electronic)",
  ISSN-L =       "1019-7168",
  MRclass =      "65-04 (33-04 33C10 65D20)",
  MRnumber =     "1269384",
  bibdate =      "Sat Feb 3 18:21:41 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02521111",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in Computational Mathematics",
  journal-URL =  "http://link.springer.com/journal/10444",
}

@InProceedings{Magnus:1994:ASA,
  author =       "Alphonse P. Magnus",
  title =        "Asymptotics and super asymptotics of best rational
                 approximation error norms for the exponential function
                 (the `$ 1 / 9 $' problem) by the
                 {Carath{\'e}odory--Fej{\'e}r} method",
  crossref =     "Cuyt:1994:NNM",
  pages =        "173--185",
  year =         "1994",
  bibdate =      "Mon Nov 24 21:30:41 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "809.41015",
  acknowledgement = ack-nhfb,
}

@Article{Marsaglia:1994:REI,
  author =       "George Marsaglia and Arif Zaman and John C. W.
                 Marsaglia",
  title =        "Rapid evaluation of the inverse of the normal
                 distribution function",
  journal =      j-STAT-PROB-LETT,
  volume =       "19",
  number =       "4",
  pages =        "259--266",
  day =          "15",
  month =        mar,
  year =         "1994",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/0167-7152(94)90174-0",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "65U05",
  MRnumber =     "1 278 658",
  bibdate =      "Thu Dec 22 07:42:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 MathSciNet database",
  ZMnumber =     "0798.65132",
  abstract =     "This is an interesting article with direct application
                 in generating normal random variable by computer
                 programs. The suggested applications are related to
                 Monte Carlo simulation based on massively parallel
                 systems or supercomputers. The idea is to replace
                 larger programs with complicated computations and with
                 difficulties in accuracy controlling by simpler
                 arithmetic programs that use tabled constants. These
                 seem to be the normal evolution since memory becomes
                 cheaper and cheaper.\par

                 The authors compute the inverse of the cPhi function $$
                 c P h i(x) = (2 / \pi)^{1 / 2} \int^\infty_x \exp ( -
                 t^2 / 2) d t = u, $$ using a uniform random variable as
                 input and the truncated Taylor series development of
                 it. In order to increase the speed the coefficients of
                 the truncated Taylor series $$ x(u_0 + h) = x(u_0) +
                 x'(u_0) \cdot h + {1 \over 2} x''(u_0) \cdot h^2 + {1
                 \over 6} x'''(u_0) \cdot h^3, $$ are predetermined for
                 1024 points. And here comes another bright idea: the
                 1024 points are chosen based on the representation of
                 the uniform random variable in modern computers as
                 floating point variable of the form: $ u = 2^{-k} ((1 /
                 2) + (j / 64)) + 2^{-k} \cdot (m / 2^{24}) $ with $ 0
                 \le k & l t; 32 $, $ 0 \le j & l t; 32 $ and $ 0 \le m
                 & l t; 2^{18} $ and considering 32 bit
                 representation.\par

                 With this assumptions and the truncation to the third
                 power of $h$ of the Taylor series, the authors show
                 that the error does not exceed the limit of single
                 precision accuracy. Furthermore the calculations are
                 speeded up based on reducing multiplications. A number
                 of FORTRAN programs are also presented in order to
                 evaluate the complementary normal distribution function
                 cPhi (several versions) with great accuracy, create the
                 constant tables, and generate the normal distribution
                 variable. These simple programs give the user the
                 possibility to completely control the accuracy.",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "cPhi function; FORTRAN programs; massive parallel
                 systems; Monte Carlo simulation; normal distribution
                 function; normal random variable; supercomputers;
                 truncated Taylor series",
  ZMclass =      "*65C99 Numerical simulation 65C05 Monte Carlo methods
                 60-04 Machine computation, programs (probability
                 theory) 60E05 General theory of probability
                 distributions 62E17 Approximations to statistical
                 distributions (nonasymptotic)",
  ZMreviewer =   "A. Pasculescu (Bucuresti)",
}

@Article{Merrheim:1994:CEF,
  author =       "X. Merrheim",
  title =        "The computation of elementary functions in radix $ 2^p
                 $",
  journal =      j-COMPUTING,
  volume =       "53",
  number =       "3--4",
  pages =        "219--232",
  year =         "1994",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "68M07",
  MRnumber =     "95j:68028",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "International Symposium on Scientific Computing,
                 Computer Arithmetic and Validated Numerics (Vienna,
                 1993).",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Narayanaswami:1994:AE,
  author =       "Chandrasekhar Narayanaswami and William Luken",
  title =        "Approximating $ x^n $ efficiently",
  journal =      j-INFO-PROC-LETT,
  volume =       "50",
  number =       "4",
  pages =        "205--210",
  day =          "25",
  month =        may,
  year =         "1994",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "65D20 (41-04 65B99)",
  MRnumber =     "95b:65031",
  bibdate =      "Wed Nov 11 12:16:26 MST 1998",
  bibsource =    "Compendex database;
                 http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Advanced Workstations and Systems Div",
  affiliationaddress = "Austin, TX, USA",
  classification = "721.1; 723.2; 723.5; 741.2; 921.1; 921.6; B0290F
                 (Interpolation and function approximation); C4130
                 (Interpolation and function approximation); C6130B
                 (Graphics techniques)",
  corpsource =   "IBM Adv. Workstations and Syst. Div., Austin, TX,
                 USA",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  journalabr =   "Inf Process Lett",
  keywords =     "$x^n$ approximation; approximation theory;
                 Approximation theory; Color computer graphics;
                 Computational complexity; Computational methods;
                 computer graphics; elementary functions; floating-point
                 arithmetic; Function evaluation; graphics modeling;
                 Image quality; Light intensity computation; look-up
                 tables; performance requirements; Polynomial
                 evaluation; Polynomials; polynomials; power function;
                 scientific applications; Semiconducting silicon; Table
                 lookup",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Nishioka:1994:EFB,
  author =       "Keiji Nishioka",
  title =        "Elementary functions based on elliptic curves",
  journal =      j-TOKYO-J-MATH,
  volume =       "17",
  number =       "2",
  pages =        "439--446",
  year =         "1994",
  ISSN =         "0387-3870",
  MRclass =      "12H05",
  MRnumber =     "96b:12011",
  MRreviewer =   "Alexandru Buium",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tokyo journal of mathematics",
}

@Article{Ohta:1994:INP,
  author =       "Shigemi Ohta and Eiichi Goto and Weng Fai Wong and
                 Nobuaki Yoshida",
  title =        "Improvement and new proposal on fast evaluation of
                 elementary functions. ({Japanese})",
  journal =      j-TRANS-INFO-PROCESSING-SOC-JAPAN,
  volume =       "35",
  number =       "5",
  pages =        "926--933",
  month =        may,
  year =         "1994",
  CODEN =        "JSGRD5",
  ISSN =         "0387-5806",
  ISSN-L =       "0387-5806",
  MRclass =      "65D20",
  MRnumber =     "95f:65045",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Wong, Gore, and Yoshida (ibid., vol. 34, no. 7, pp.
                 1570-1579, 1993) introduced fast methods for numerical
                 evaluation of elementary functions based on table
                 lookup. They are called ATA (add/table-lookup/add) and
                 ATA-M (add/table-lookup/add and multiply) methods for
                 single- and double-precision calculations respectively.
                 In this paper, an improvement to these methods that
                 shrinks the size of the table by a factor of about 3/16
                 is presented. Another method called the `split parallel
                 multiplication method', which is characterized by
                 simpler table lookup than ATA-M and by split and
                 parallel use of double-precision floating point
                 circuitry, is also introduced, These new methods fit on
                 to integrated circuits of a size comparable with
                 commercially available floating-point accelerators.
                 Methods for accelerating double-precision division,
                 generating uniform pseudo-random numbers in
                 double-precision, and accelerating the multiplication
                 of single-precision complex numbers using the same
                 circuitry are proposed.",
  acknowledgement = ack-nhfb,
  affiliation =  "RIKEN, Inst. of Phys. and Chem. Res., Saitama, Japan",
  classification = "C4120 (Functional analysis); C5230 (Digital
                 arithmetic methods); C6130 (Data handling techniques)",
  fjournal =     "Transactions of the Information Processing Society of
                 Japan",
  keywords =     "Add/table-lookup/add method;
                 Add/table-lookup/add/multiply method; ATA method; ATA-M
                 method; Double-precision calculations; Double-precision
                 division; Double-precision floating point circuitry;
                 Elementary functions evaluation; Floating-point
                 accelerators; Integrated circuits; Numerical
                 evaluation; Single-precision calculations;
                 Single-precision complex number multiplication; Split
                 parallel multiplication method; Table size; Uniform
                 pseudo-random number generation",
  language =     "Japanese",
  pubcountry =   "Japan",
  thesaurus =    "Digital arithmetic; Function evaluation; Random number
                 generation; Table lookup",
}

@InProceedings{Olver:1994:GEI,
  author =       "F. W. J. Olver",
  title =        "The generalized exponential integral",
  crossref =     "Zahar:1994:ACF",
  pages =        "497--510",
  year =         "1994",
  MRclass =      "33B20 (34E05 41A60)",
  MRnumber =     "1333639",
  MRreviewer =   "Richard B. Paris",
  bibdate =      "Sat Feb 18 15:02:52 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "International Series of Numerical Mathematics",
  acknowledgement = ack-nhfb,
}

@Article{Osada:1994:CAM,
  author =       "Naoki Osada",
  title =        "Convergence acceleration methods",
  journal =      "S\=urikaisekikenky\=usho K\=oky\=uroku",
  volume =       "880",
  number =       "??",
  pages =        "28--43",
  month =        "????",
  year =         "1994",
  MRclass =      "65B05",
  MRnumber =     "1366233",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "The state of the art of scientific computing and its
                 prospects (Japanese) (Kyoto, 1993)",
  acknowledgement = ack-nhfb,
  fjournal =     "S\=urikaisekikenky\=usho K\=oky\=uroku",
  keywords =     "convergence acceleration",
}

@InProceedings{Rappoport:1994:TMC,
  author =       "Juri M. Rappoport",
  title =        "The {Tau-Method} and the Computation of the {Bessel}
                 Functions of the Complex Order",
  crossref =     "Brown:1994:PCL",
  pages =        "353--355",
  year =         "1994",
  bibdate =      "Sat Jun 11 17:22:09 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
}

@Article{Schulte:1994:HDE,
  author =       "M. J. Schulte and E. E. {Swartzlander, Jr.}",
  title =        "Hardware Design for Exactly Rounded Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "964--973",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295858",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This paper presents hardware designs that produce
                 exactly rounded results for the functions of
                 reciprocal, square-root, 2/sup x/, and log/sub 2/(x).
                 These designs use polynomial approximation in which the
                 terms in the approximation are generated in parallel,
                 and then summed by using a multi-operand adder. To
                 reduce the number of terms in the approximation, the
                 input interval is partitioned into subintervals of
                 equal size, and different coefficients are used for
                 each subinterval. The coefficients used in the
                 approximation are initially determined based on the
                 Chebyshev series approximation. They are then adjusted
                 to obtain exactly rounded results for all inputs.
                 Hardware designs are presented, and delay and area
                 comparisons are made based on the degree of the
                 approximating polynomial and the accuracy of the final
                 result. For single-precision floating point numbers, a
                 design that produces exactly rounded results for all
                 four functions has an estimated delay of 80 ns and a
                 total chip area of 98 mm/sup 2/ in a 1.0-micron CMOS
                 technology. Allowing the results to have a maximum
                 error of one unit in the last place reduces the
                 computational delay by 5\% to 30\% and the area
                 requirements by 33\% to 77\%.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Dept. of Electr. and Comput. Eng., Texas Univ.,
                 Austin, TX, USA",
  classification = "B0290F (Interpolation and function approximation);
                 B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C4130 (Interpolation and function
                 approximation); C5120 (Logic and switching circuits);
                 C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "1 Micron; 1.0-Micron CMOS technology; Argument
                 reduction; Chebyshev series approximation; Chip area;
                 Computational delay; Computer arithmetic; Exact
                 rounding; Exactly rounded elementary functions;
                 Hardware designs; Multi-operand adder; Parallel
                 multiplier; Polynomial approximation; Reciprocal;
                 Single-precision floating point numbers;
                 Special-purpose hardware; Square-root",
  numericalindex = "Size 1.0E-06 m",
  pubcountry =   "USA",
  thesaurus =    "Approximation theory; Chebyshev approximation; CMOS
                 integrated circuits; Digital arithmetic; Multiplying
                 circuits; Polynomials; Summing circuits",
}

@InProceedings{Skaf:1994:LHI,
  author =       "Ali Skaf and Jean-Michel Muller and Alain Guyot",
  editor =       "Anonymous",
  booktitle =    "{ESSCIRC '94: Twentieth European Solid-State Circuits
                 Conference. Ulm, Germany. September 20--22, 1994}",
  title =        "On-Line Hardware Implementation for Complex
                 Exponential and Logarithm",
  publisher =    "{\'E}ditions Fronti{\`e}res",
  address =      "B. P. 33. 91192 Gif-sur-Yvette Cedex, France",
  pages =        "252--255",
  year =         "1994",
  ISBN =         "2-86332-160-9",
  ISBN-13 =      "978-2-86332-160-7",
  bibdate =      "Fri Sep 29 10:32:36 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sorenson:1994:TFG,
  author =       "J. Sorenson",
  title =        "Two Fast {GCD} Algorithms",
  journal =      j-J-ALG,
  volume =       "16",
  number =       "1",
  pages =        "110--144",
  month =        jan,
  year =         "1994",
  CODEN =        "JOALDV",
  DOI =          "https://doi.org/10.1006/jagm.1994.1006",
  ISSN =         "0196-6774 (print), 1090-2678 (electronic)",
  ISSN-L =       "0196-6774",
  bibdate =      "Tue Dec 11 09:15:38 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jalg.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0196677484710066",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Algorithms",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01966774",
}

@Article{Spouge:1994:CGD,
  author =       "John L. Spouge",
  title =        "Computation of the Gamma, Digamma, and Trigamma
                 Functions",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "31",
  number =       "3",
  pages =        "931--944",
  month =        jun,
  year =         "1994",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "33B15 (30E10 33-04 40-04 65D20)",
  MRnumber =     "95g:33002",
  MRreviewer =   "E. Kaucher",
  bibdate =      "Mon Jan 20 15:27:00 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}

@InProceedings{Temme:1994:CAI,
  author =       "N. M. Temme",
  title =        "Computational aspects of incomplete gamma functions
                 with large complex parameters",
  crossref =     "Zahar:1994:ACF",
  pages =        "551--562",
  year =         "1994",
  bibdate =      "Sat Feb 18 15:02:52 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "International Series of Numerical Mathematics",
  acknowledgement = ack-nhfb,
}

@Article{Temme:1994:SAI,
  author =       "N. M. Temme",
  title =        "A Set of Algorithms for the Incomplete Gamma
                 Functions",
  journal =      j-PROBAB-ENGRG-INFORM-SCI,
  volume =       "8",
  number =       "2",
  pages =        "291--307",
  month =        apr,
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1017/S0269964800003417",
  ISSN =         "0269-9648 (print), 1469-8951 (electronic)",
  ISSN-L =       "0269-9648",
  bibdate =      "Thu Aug 24 08:18:58 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/probab-engrg-inform-sci.bib",
  URL =          "https://www.cambridge.org/core/product/F5677268895A0805A0BDF31E4B20A106",
  acknowledgement = ack-nhfb,
  ajournal =     "Probab. Engrg. Inform. Sci.",
  fjournal =     "Probability in the Engineering and Informational
                 Sciences",
  journal-URL =  "http://www.journals.cambridge.org/jid_PES",
  onlinedate =   "01 July 2009",
}

@Article{Timmermann:1994:CFV,
  author =       "D. Timmermann and B. Rix and H. Hahn and B. J.
                 Hosticka",
  title =        "A {CMOS} floating-point vector-arithmetic unit",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "29",
  number =       "5",
  pages =        "634--639",
  month =        may,
  year =         "1994",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/4.284719",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This work describes a floating-point arithmetic unit
                 based on the CORDIC algorithm. The unit computes a full
                 set of high level arithmetic and elementary functions:
                 multiplication, division, (co)sine, hyperbolic
                 (co)sine, square root, natural logarithm, inverse
                 (hyperbolic) tangent, vector norm, and phase. The chip
                 has been integrated in 1.6 mu m double-metal n-well
                 CMOS technology and achieves a normalized peak
                 performance of 220 MFLOPS.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fraunhofer Inst. of Microelectron. Circuits and Syst.,
                 Duisburg, Germany",
  classification = "B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C5120 (Logic and switching circuits); C5220P
                 (Parallel architecture); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "1.6 Micron; 220 MFLOPS; CORDIC algorithm; Cosine;
                 Division; Double-metal n-well CMOS technology;
                 Floating-point vector-arithmetic unit; Hyperbolic sine;
                 Inverse tangent; Multiplication; Natural logarithm;
                 Phase; Sine; Square root; Vector norm",
  numericalindex = "Size 1.6E-06 m; Computer speed 2.2E+08 FLOPS",
  pubcountry =   "USA",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic;
                 Integrated logic circuits; Parallel architectures;
                 Pipeline processing; Vector processor systems",
}

@Article{Turner:1994:SRM,
  author =       "Stephen M. Turner",
  title =        "Square roots mod $p$",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "101",
  number =       "5",
  pages =        "443--449",
  month =        may,
  year =         "1994",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11A07",
  MRnumber =     "95c:11004",
  MRreviewer =   "David Lee Hilliker",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Book{Watanabe:1994:MSP,
  author =       "T. (Tsutomu) Watanabe and Makoto Natori and Tsutomu
                 Oguni",
  title =        "Mathematical Software for the {P.C.} and Work
                 Stations: a Collection of {Fortran 77} Programs",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "xiv + 387",
  month =        jun,
  year =         "1994",
  ISBN =         "0-444-82000-0",
  ISBN-13 =      "978-0-444-82000-6",
  LCCN =         "QA 76.73 F25 F6813 1994",
  bibdate =      "Sun Sep 28 10:42:07 MDT 1997",
  bibsource =    "http://www.amazon.com/exec/obidos/ISBN=0444820000/wholesaleproductA/;
                 http://www.cbooks.com/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Translation of: FORTRAN 77 ni yoru suchi keisan
                 sofutowea.",
  price =        "US\$178.50",
  URL =          "http://www.cbooks.com/sqlnut/SP/search/gtsumt?source=&isbn=0444820000",
  acknowledgement = ack-nhfb,
  alttitle =     "{Fortran 77} ni yoru suchi keisan sofutowea.
                 English.",
  keywords =     "Fortran 77 (computer program language); Numerical
                 analysis --- Use of --- Computers; {Fortran 77}
                 (Computer program language)",
}

@InProceedings{Wong:1994:FEE,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast evaluation of the elementary functions in double
                 precision",
  crossref =     "Mudge:1994:PTS",
  bookpages =    "xi + 621",
  pages =        "349--358",
  year =         "1994",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "One of the most spectacular development in computer
                 technology is the growth in memory density and speed.
                 It is with this development in mind that we intend to
                 tackle the old problem of computing the elementary
                 functions. Since the dawn of computing, the fast and
                 accurate computation of the elementary functions has
                 been a constant concern of numerical computing. It now
                 seems possible to use tables of sizes in the range of
                 megabits to aid in such computation. To this end, in
                 this paper, we propose a method called ATA-M (Add-Table
                 Lookup-Add with Multiplication) for evaluating
                 polynomials with the aid of tables. When applied to the
                 elementary functions, we obtained a set of algorithms
                 which computes the reciprocal, square root,
                 exponential, sine, cosine, logarithm, are tangent and
                 the hyperbolic functions in about 3 to 4 double
                 precision floating point multiplication time and
                 utilizing about 2 Mbyte of tables.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
                 Singapore, Singapore",
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods)",
  confdate =     "4-7 Jan. 1994",
  conflocation = "Wailea, HI, USA",
  confsponsor =  "IEEE; ACM; Univ. Hawaii; Univ. Hawaii Coll. Bus.
                 Admin",
  keywords =     "Add-Table Lookup-Add with Multiplication; ATA-M;
                 Double precision; Elementary functions; Floating point
                 multiplication time; Hyperbolic functions; Memory
                 density; Memory speed; Numerical computing;
                 Polynomials",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Polynomials; Table lookup",
}

@Article{Wong:1994:FHB,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast Hardware-Based Algorithms for Elementary Function
                 Computations Using Rectangular Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "3",
  pages =        "278--294",
  month =        mar,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.272429",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:54 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=272429",
  abstract =     "As the name suggests, elementary functions play a
                 vital role in scientific computations. Yet due to their
                 inherent nature, they are a considerable computing task
                 by themselves. Not surprisingly, since the dawn of
                 computing, the goal of speeding up elementary function
                 computation has been pursued. This paper describes new
                 hardware based algorithms for the computation of the
                 common elementary functions, namely division,
                 logarithm, reciprocal square root, arc tangent, sine
                 and cosine. These algorithms exploit microscopic
                 parallelism using specialized hardware with heavy use
                 of truncation based on detailed accuracy analysis. The
                 contribution of this work lies in the fact that these
                 algorithms are very fast and yet are accurate. If we
                 let the time to perform an IEEE Standard 754 double
                 precision floating point multiplication be $
                 \tau_\times $, our algorithms to achieve roughly $ 3.68
                 \tau_\times $, $ 4.56 \tau_\times $, $ 5.25 \tau_\times
                 $, $ 3.69 \tau_\times $, $ 7.06 \tau_\times $, and $
                 6.5 \tau_\times $, for division, logarithm, square
                 root, exponential, are tangent and complex exponential
                 (sine and cosine) respectively. The trade-off is the
                 need for tables and some specialized hardware. The
                 total amount of tables required, however, is less than
                 128 Kbytes. We discuss the hardware, algorithmic and
                 accuracy aspects of these algorithms.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
                 Singapore, Singapore",
  classification = "C4110 (Error analysis in numerical methods); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Arc tangent; Common elementary functions; Cosine;
                 Elementary function computations; Floating point
                 multiplication; Hardware-based algorithms; Microscopic
                 parallelism; Reciprocal square root; Rectangular
                 multipliers; Scientific computations; Sine",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Error analysis",
}

@Article{Xu:1994:VPC,
  author =       "Guo Liang Xu and Jia Kai Li",
  title =        "Variable precision computation of elementary
                 functions. ({Chinese})",
  journal =      j-J-NUMER-METHODS-COMPUT-APPL,
  volume =       "15",
  number =       "3",
  pages =        "161--171",
  year =         "1994",
  ISSN =         "1000-3266",
  MRclass =      "65D20 (65Y20)",
  MRnumber =     "MR1357336 (96i:65013)",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal on Numerical Methods and Computer
                 Applications. Shuzhi Jisuan yu Jisuanji Yingyong",
}

@Article{Abad:1995:CRC,
  author =       "Julio Abad and Javier Sesma",
  title =        "Computation of the Regular Confluent Hypergeometric
                 Function",
  journal =      j-MATHEMATICA-J,
  volume =       "5",
  number =       "4",
  pages =        "??--??",
  month =        "Fall",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "1047-5974 (print), 1097-1610 (electronic)",
  ISSN-L =       "1047-5974",
  bibdate =      "Sat Nov 6 13:34:06 MDT 2010",
  bibsource =    "http://www.mathematica-journal.com/issue/v5i4/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.mathematica-journal.com/issue/v5i4/article/abad/index.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematica Journal",
  journal-URL =  "http://www.mathematica-journal.com/",
}

@Article{Amos:1995:RAP,
  author =       "D. E. Amos",
  title =        "A Remark on {Algorithm 644}: a Portable Package for
                 {Bessel} Functions of a Complex Argument and
                 Nonnegative Order",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "388--393",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.212078",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:24:54 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Amos:1986:APP,Amos:1990:RPP,Kodama:2007:RA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p388-amos/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "complex Airy Functions; complex Bessel functions;
                 derivatives of Airy functions; H, I, J, K, and Y Bessel
                 functions; log gamma function",
  subject =      "G.1.0 [Numerical Analysis]: General -- numerical
                 algorithms; G.1.m [Numerical Analysis]: Miscellaneous;
                 G.m [Mathematics of Computing]: Miscellaneous",
}

@Article{Bagby:1995:CNP,
  author =       "Richard J. Bagby",
  title =        "Calculating normal probabilities",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "102",
  number =       "1",
  pages =        "46--48",
  month =        jan,
  year =         "1995",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "65D20",
  MRnumber =     "96f:65021",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Baratchart:1995:RIE,
  author =       "L. Baratchart and E. B. Saff and F. Wielonsky",
  title =        "Rational interpolation of the exponential function",
  journal =      j-CAN-J-MATH,
  volume =       "47",
  number =       "??",
  pages =        "1121--1147",
  month =        "????",
  year =         "1995",
  CODEN =        "CJMAAB",
  DOI =          "https://doi.org/10.4153/CJM-1995-058-6",
  ISSN =         "0008-414X (print), 1496-4279 (electronic)",
  ISSN-L =       "0008-414X",
  bibdate =      "Sat Sep 10 15:39:05 MDT 2011",
  bibsource =    "http://cms.math.ca/cjm/v47/;
                 https://www.math.utah.edu/pub/tex/bib/canjmath1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Canadian Journal of Mathematics = Journal canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cjm/",
}

@TechReport{Borwein:1995:EARa,
  author =       "Peter Borwein",
  title =        "An Efficient Algorithm for the {Riemann} Zeta
                 Function",
  type =         "Report",
  institution =  "Department of Mathematics \& Statistics, Simon Fraser
                 University",
  address =      "Burnaby, BC V5A 1S6, Canada",
  pages =        "9",
  day =          "20",
  month =        jan,
  year =         "1995",
  bibdate =      "Thu Sep 01 18:09:22 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/107",
  abstract =     "A very simple class of algorithms for the computation
                 of the Riemann-zeta function to arbitrary precision in
                 arbitrary domains is proposed. These algorithms out
                 perform the standard methods based on Euler--Maclaurin
                 summation, are easier to implement and are easier to
                 analyse.",
  acknowledgement = ack-nhfb,
  author-dates = "10 May 1953--23 August 2020",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}

@InProceedings{Borwein:1995:EARb,
  author =       "P. Borwein",
  editor =       "????",
  booktitle =    "{CMS} Conference Proceedings",
  title =        "An efficient algorithm for the {Riemann} zeta
                 function",
  volume =       "27",
  publisher =    "Canadian Mathematical Society",
  address =      "616 Cooper Street, Ottawa, ON, K1R 5J2, Canada",
  pages =        "29--34",
  month =        jan,
  year =         "1995",
  bibdate =      "Wed Jun 28 08:27:14 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://web.archive.org/web/20140602151514/http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf",
  acknowledgement = ack-nhfb,
  xxURL =        "http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf",
}

@Article{Carlson:1995:NCR,
  author =       "B. C. Carlson",
  title =        "Numerical computation of real or complex elliptic
                 integrals",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "10",
  number =       "1--2",
  pages =        "13--26",
  month =        jul,
  year =         "1995",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/BF02198293",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "33Exx (33-04 65D20)",
  MRnumber =     "1 345 407",
  bibdate =      "Fri Nov 6 18:06:29 MST 1998",
  bibsource =    "http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Special functions (Torino, 1993)",
  abstract =     "Algorithms for numerical computation of symmetric
                 elliptic integrals of all three kinds are improved in
                 several ways and extended to complex values of the
                 variables (with some restrictions in the case of the
                 integral of the third kind). Numerical check values,
                 consistency checks, and relations to Legendre's
                 integrals and Bulirsch's integrals are included.",
  acknowledgement = ack-nhfb,
  classification = "B0290R (Integral equations); C4180 (Integral
                 equations)",
  conflocation = "Torino, Italy; 14-15 Oct. 1993",
  conftitle =    "International Joint Symposium on Special Functions and
                 Artificial Intelligence",
  corpsource =   "Ames Lab., Iowa State Univ., Ames, IA, USA",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Bulirsch's integrals; complex elliptic integrals;
                 complex values; consistency checks; elliptic equations;
                 integral equations; Legendre's integrals; numerical
                 analysis; numerical check values; numerical computation
                 algorithms; real elliptic integrals",
  pubcountry =   "Switzerland",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Chaudhry:1995:DGI,
  author =       "M. Aslam Chaudhry and S. M. Zubair",
  title =        "On the decomposition of generalized incomplete gamma
                 functions with applications to {Fourier} transforms",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "59",
  number =       "3",
  pages =        "253--284",
  day =          "30",
  month =        may,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:37 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037704279400026W",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Chen:1995:UCA,
  author =       "San-Gee Chen and Chieh-Chih Li",
  booktitle =    "{IEEE} Signal Processing Society Workshop on {VLSI}
                 Signal Processing, {VIII, 1995}",
  title =        "A unified cellular array for multiplication, division
                 and square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "533--541",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "A unified fast, small-area processor capable of
                 executing multiplication, division and square-root
                 operations, all starting from MSD is proposed. Unlike
                 the existing designs which require both addition and
                 subtraction operations, and complicated \ldots{}",
}

@Article{Das:1995:IFC,
  author =       "D. Das and K. Mukhopadhyaya and B. P. Sinha",
  title =        "Implementation of four common functions on an {LNS}
                 co-processor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "1",
  pages =        "155--161",
  month =        jan,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.367997",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "We propose a scheme for evaluating four commonly used
                 functions namely, (1) inverse trigonometric functions,
                 (2) trigonometric functions, (3) the exponential
                 function, and (4) the logarithmic function with the
                 help of a logarithmic number system (\ldots{}).",
}

@Article{Daumas:1995:MRR,
  author =       "Marc Daumas and Christophe Mazenc and Xavier Merrheim
                 and Jean-Michel Muller",
  title =        "Modular range reduction: a new algorithm for fast and
                 accurate computation of the elementary functions",
  journal =      j-J-UCS,
  volume =       "1",
  number =       "3",
  pages =        "162--175 (electronic)",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  MRclass =      "68M07 (68Q20)",
  MRnumber =     "1 390 003",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}

@Article{Doman:1995:SAP,
  author =       "B. G. S. Doman and C. J. Pursglove and W. M. Coen",
  title =        "A Set of {Ada} Packages for High Precision
                 Calculations",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "416--431",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 14 09:57:55 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accuracy; Ada; arithmetic elementary-function
                 evaluation; floating-point; multiple-precision portable
                 software",
  subject =      "G.1.0 [Numerical Analysis]: General -- computer
                 arithmetic; G.1.2 [Numerical Analysis]: Approximation
                 -- elementary function approximation; G.4 [Mathematics
                 of Computing]: Mathematical Software -- algorithm
                 analysis; efficiency; portability",
}

@Article{Driver:1995:NQH,
  author =       "Kathy Driver",
  title =        "Nondiagonal quadratic {Hermite--Pad{\'e}}
                 approximation to the exponential function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "65",
  number =       "1--3",
  pages =        "125--134",
  day =          "29",
  month =        dec,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:02:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795001069",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Goano:1995:ACC,
  author =       "Michele Goano",
  title =        "{Algorithm 745}: Computation of the Complete and
                 Incomplete {Fermi--Dirac} Integral",
  journal =      j-TOMS,
  volume =       "21",
  number =       "3",
  pages =        "221--232",
  month =        sep,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210089.210090",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:19:43 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Goano:1997:RA7}",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p221-goano/",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "asymptotic expansions; confluent hypergeometric
                 functions; convergence acceleration; e[k] transforms;
                 epsilon algorithm; Euler transformation; Fermi--Dirac
                 integral; incomplete Fermi--Dirac integral; incomplete
                 gamma function; Levin's u transform; Riemann's zeta
                 function",
  subject =      "G.1.2 [Mathematics of Computing]: Approximation; G.4
                 [Mathematics of Computing]: Mathematical Software; J.2
                 [Computer Applications]: Physical Sciences and
                 Engineering",
}

@Article{Hobson:1995:EMR,
  author =       "R. F. Hobson and M. W. Fraser",
  title =        "An efficient maximum-redundancy radix-$8$ {SRT}
                 division and square-root method",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "30",
  number =       "1",
  pages =        "29--38",
  month =        jan,
  year =         "1995",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/4.350197",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "A new approach to integrating hardware multiplication,
                 division, and square-root is presented. We use a fully
                 integrated control path which simultaneously reduces
                 part of the redundant partial-remainder and performs a
                 truncated multiplication of the next quotient or
                 square-root digit by the divisor or square-root value.
                 A separate (parallel) full precision iterative
                 multiplier is used for partial remainder production.
                 Strategic details of a radix-8 implementation are
                 discussed. It is shown that a maximally redundant digit
                 set is a viable choice for high performance in this
                 case.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Comput. Sci., Simon Fraser Univ., Burnaby, BC,
                 Canada",
  classification = "B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "1.2 Mum; CMOS adder cell; CMOS divider; Division; IEEE
                 floating point algorithm; Integrated control path;
                 Maximally redundant digit set; Maximum-redundancy
                 radix-8 SRT algorithm; Multiplication; Parallel
                 iterative multiplier; Partial remainder production;
                 Redundant partial-remainder; Square-root method; Table
                 lookup",
  numericalindex = "Size 1.2E-06 m",
  pubcountry =   "USA",
  summary =      "A new approach to integrating hardware multiplication,
                 division, and square-root is presented. We use a fully
                 integrated control path which simultaneously reduces
                 part of the redundant partial-remainder and performs a
                 truncated multiplication of the \ldots{}",
  thesaurus =    "Adders; CMOS digital integrated circuits; Digital
                 arithmetic; Dividing circuits; Floating point
                 arithmetic; Multiplying circuits",
}

@InProceedings{Ito:1995:EIA,
  author =       "M. Ito and N. Takagi and S. Yajima",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, 19--21 July 1995",
  title =        "Efficient Initial Approximation and Fast Converging
                 Methods for Division and Square Root",
  crossref =     "Knowles:1995:PSC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2--9",
  month =        jul,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  summary =      "Efficient initial approximations and fast converging
                 algorithms are important to achieve the desired
                 precision faster at lower hardware cost in
                 multiplicative division and square root. In this paper,
                 a new initial approximation method for division,
                 \ldots{}",
}

@Article{Krattenthaler:1995:HHM,
  author =       "C. Krattenthaler",
  title =        "{HYP} and {HYPQ}: {Mathematica} packages for the
                 manipulation of binomial sums and hypergeometric
                 series, respectively $q$-binomial sums and basic
                 hypergeometric series",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "20",
  number =       "5--6",
  pages =        "737--744",
  month =        nov # "--" # dec,
  year =         "1995",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  MRclass =      "05Axx (11Bxx 33-04 33Cxx 33Dxx)",
  MRnumber =     "1 395 424",
  bibdate =      "Sat May 10 15:54:09 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Symbolic computation in combinatorics $ \Delta_1 $
                 (Ithaca, NY, 1993).",
  acknowledgement = ack-nhfb,
  classcodes =   "C7310 (Mathematics computing); C1100 (Mathematical
                 techniques)",
  corpsource =   "Inst. fur Math., Wien Univ., Austria",
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
  keywords =     "basic hypergeometric; binomial sums; HYP;
                 hypergeometric series; HYPQ; Mathematica packages;
                 mathematics computing; packages; q-binomial sums;
                 series; series (mathematics); software; symbol
                 manipulation",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Kwan:1995:CII,
  author =       "H. Kwan and R. L. {Nelson, Jr.} and E. E.
                 {Swartzlander, Jr.}",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, 19--21 July 1995",
  title =        "Cascaded Implementation of an Iterative
                 Inverse-Square-Root Algorithm, with Overflow
                 Lookahead",
  crossref =     "Knowles:1995:PSC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "115--122",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "We present an unconventional method of computing the
                 inverse of the square root. It implements the
                 equivalent of two iterations of a well-known
                 multiplicative method to obtain 24-bit mantissa
                 accuracy. We implement each ``iteration'' as a
                 \ldots{}",
}

@InProceedings{Lang:1995:VHR,
  author =       "T. Lang and P. Montuschi",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, 19--21 July 1995",
  title =        "Very-High Radix Combined Division and Square Root with
                 Prescaling and Selection by Rounding",
  crossref =     "Knowles:1995:PSC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "124--131",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "An algorithm for square root with prescaling is
                 developed and combined with a similar scheme for
                 division. An implementation is described, evaluated and
                 compared with other combined div/sqrt \ldots{}",
}

@Book{Lau:1995:NLC,
  author =       "H. T. (Hang Tong) Lau",
  title =        "A Numerical library in {C} for scientists and
                 engineers",
  publisher =    pub-CRC,
  address =      pub-CRC:adr,
  pages =        "xvii + 795",
  year =         "1995",
  ISBN =         "0-8493-7376-X",
  ISBN-13 =      "978-0-8493-7376-3",
  LCCN =         "QA76.73.C15 L38 1995",
  bibdate =      "Fri Sep 26 14:29:10 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0744/94037928-d.html",
  acknowledgement = ack-nhfb,
  subject =      "C (Computer program language)",
}

@InProceedings{Leeser:1995:VSR,
  author =       "M. Leeser and J. O'Leary",
  booktitle =    "Proceedings of the {IEEE} International Conference on
                 Computer Design: {VLSI} in Computers and Processors,
                 {ICCD '95}",
  title =        "Verification of a subtractive radix-$2$ square root
                 algorithm and implementation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "526--531",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Many modern microprocessors implement floating point
                 square root hardware using subtractive algorithms. Such
                 processors include the HP PA7200, the MIPS R4400, and
                 the Intel Pentium. The Intel Pentium division bug
                 highlights the importance of \ldots{}",
}

@Article{Lether:1995:MAZ,
  author =       "F. G. Lether and P. R. Wenston",
  title =        "Minimax approximations to the zeros of {$ P_n(x) $}
                 and {Gauss--Legendre} quadrature",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "59",
  number =       "2",
  pages =        "245--252",
  day =          "19",
  month =        may,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:37 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042794000305",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Lewanowicz:1995:AMC,
  author =       "Stanis{\l}aw Lewanowicz and Stefan Paszkowski",
  title =        "An analytic method for convergence acceleration of
                 certain hypergeometric series",
  journal =      j-MATH-COMPUT,
  volume =       "64",
  number =       "210",
  pages =        "691--713",
  month =        apr,
  year =         "1995",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2153446",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33C45 (65B10 65D20)",
  MRnumber =     "1277769 (95h:33006)",
  MRreviewer =   "Anton Hut'a",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Comput. Sci., Wroclaw Univ., Poland",
  classcodes =   "B0290 (Numerical analysis); C4100 (Numerical
                 analysis)",
  corpsource =   "Inst. of Comput. Sci., Wroclaw Univ., Poland",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "analytic method; convergence acceleration; convergence
                 of numerical methods; fast converging expansions;
                 hypergeometric; iterated transformation; mathematical
                 constants; series; series (mathematics)",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Liu:1995:SRV,
  author =       "S.-I. Liu",
  title =        "Square-rooting and vector summation circuits using
                 current conveyors",
  journal =      "IEE Proceedings on Circuits, Devices and Systems [see
                 also IEE Proceedings G - Circuits, Devices and
                 Systems]",
  volume =       "142",
  number =       "4",
  pages =        "223--226",
  month =        aug,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "New analogue squaring, square-rooting and vector
                 summation circuits using current conveyors (CCIIs) are
                 presented. They consist of MOS transistors biased in
                 the triode region, a buffered unity-gain inverting
                 amplifier, resistors and CCIIs. A general \ldots{}",
}

@Article{Louie:1995:VPS,
  author =       "Marianne E. Louie and Milo{\v{s}} D. Ercegovac",
  title =        "A Variable-Precision Square Root Implementation for
                 Field Programmable Gate Arrays",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "9",
  number =       "3",
  pages =        "315--336",
  month =        sep,
  year =         "1995",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/BF01212874",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Wed Jul 6 11:13:09 MDT 2005",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=9&issue=3;
                 http://www.wkap.nl/issuetoc.htm/0920-8542+9+3+1995;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=9&issue=3&spage=315;
                 http://www.wkap.nl/oasis.htm/95692",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Comput. Sci., California Univ., Los Angeles,
                 CA, USA",
  classification = "C5120 (Logic and switching circuits); C5230 (Digital
                 arithmetic methods)",
  corpsource =   "Dept. of Comput. Sci., California Univ., Los Angeles,
                 CA, USA",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
  keywords =     "digital arithmetic; field programmable gate arrays;
                 square root; square root implementation;
                 variable-precision; Xilinx XC4010",
  treatment =    "P Practical",
}

@Article{Lucas:1995:EII,
  author =       "S. K. Lucas and H. A. Stone",
  title =        "Evaluating infinite integrals involving {Bessel}
                 functions of arbitrary order",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "64",
  number =       "3",
  pages =        "217--231",
  year =         "1995",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(95)00142-5",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Thu Jul 8 13:22:49 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/B6TYH-4002HHC-J/2/54f1e67d9bea3e951acc3c39556ab452",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "$\varepsilon$-algorithm; Bessel functions; Bessel
                 zeros; infinite integration; mW transform; quadrature",
  remark =       "This paper examines several methods for accurately
                 integrating oscillatory functions, such as products of
                 $ f(x) $ with a trigonometric function or a Bessel
                 function. It also discusses finding zeros of Bessel
                 functions, and sequence acceleration techniques.",
}

@Article{Luther:1995:HAT,
  author =       "Wolfram Luther",
  title =        "Highly accurate tables for elementary functions",
  journal =      j-BIT-NUM-MATH,
  volume =       "35",
  number =       "3",
  pages =        "352--360",
  month =        sep,
  year =         "1995",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01732609",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65D20 (68U05)",
  MRnumber =     "97h:65024",
  bibdate =      "Wed Jan 4 18:52:24 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=35&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit35.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=35&issue=3&spage=352",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "elementary functions",
}

@InProceedings{Lynch:1995:KTF,
  author =       "T. Lynch and A. Ahmed and M. Schulte and T. Callaway",
  title =        "The {K5} Transcendental Functions",
  crossref =     "Knowles:1995:PSC",
  pages =        "163--171",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1995-04.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Maroni:1995:IRB,
  author =       "P. Maroni",
  title =        "An integral representation for the {Bessel} form",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "57",
  number =       "1--2",
  pages =        "251--260",
  day =          "20",
  month =        feb,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042793E0249L",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Matsubara:1995:NBS,
  author =       "G. Matsubara and N. Ide and H. Tago and S. Suzuki and
                 N. Goto",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, 19--21 July 1995",
  title =        "30-ns 55-b Shared Radix $2$ Division and Square Root
                 Using a Self-Timed Circuit",
  crossref =     "Knowles:1995:PSC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "98--105",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "A shared radix 2 division and square root
                 implementation using a self-timed circuit is presented.
                 The same execution time for division and square root is
                 achieved by using an on-the-fly digit decoding and a
                 root multiple generation technique. Most \ldots{}",
}

@Article{Miller:1995:RCF,
  author =       "A. R. Miller and I. S. Moskowitz",
  title =        "Reduction of a class of {Fox--Wright} psi functions
                 for certain rational parameters",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "30",
  number =       "11",
  pages =        "73--82",
  month =        dec,
  year =         "1995",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219500165U",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  remark =       "From the abstract: ``The Fox--Wright Psi function is a
                 special case of Fox's $H$-function and a generalization
                 of the generalized hypergeometric function. In the
                 present paper, we show that the Psi function reduces to
                 a single generalized hypergeometric function when
                 certain of its parameters are integers and to a finite
                 sum of generalized hypergeometric functions when these
                 parameters are rational numbers.''",
}

@Article{Montuschi:1995:RRI,
  author =       "P. Montuschi and L. Ciminiera",
  title =        "A remark on {``Reducing iteration time when result
                 digit is zero for radix-$2$ SRT division and square
                 root with redundant remainders''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "1",
  pages =        "144--146",
  month =        jan,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.368000",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Montuschi:1993:RIT}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "In a previous paper by P. Montuschi and L. Ciminiera
                 (ibid., vol. 42, no.2 p239-246, Feb 1993), an
                 architecture for shared radix 2 division and square
                 root has been presented whose main characteristic is
                 the ability to avoid any addition/subtraction,
                 \ldots{}",
}

@Article{Muldoon:1995:EZB,
  author =       "Martin E. Muldoon",
  title =        "Electrostatics and zeros of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "65",
  number =       "1--3",
  pages =        "299--308",
  day =          "29",
  month =        dec,
  year =         "1995",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:02:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795001182",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{OLeary:1995:NRI,
  author =       "J. O'Leary and M. Leeser and J. Hickey and M.
                 Aagaard",
  title =        "Non-Restoring Integer Square Root: a Case Study in
                 Design by Principled Optimization",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "901",
  pages =        "52--??",
  year =         "1995",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat May 11 13:45:32 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Paszkowski:1995:QHS,
  author =       "S. Paszkowski",
  title =        "Quasipower and hypergeometric series---construction
                 and evaluation",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "10",
  number =       "3--4",
  pages =        "337--361",
  month =        oct,
  year =         "1995",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "41A58 (33-04 65B99)",
  MRnumber =     "96k:41042",
  MRreviewer =   "Walter Schempp",
  bibdate =      "Fri Nov 6 18:06:29 MST 1998",
  bibsource =    "http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 B0290Z (Other numerical methods); C4130 (Interpolation
                 and function approximation); C4190 (Other numerical
                 methods)",
  corpsource =   "Inst. for Low Temp. and Structure Res., Polish Acad.
                 of Sci., Wroclaw, Poland",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "approximation theory; Euler's dilogarithm;
                 Hermite-Pade approximation; hypergeometric series;
                 Levin's transforms; Pade approximants; power series;
                 quasipower; recurrence relations; series (mathematics);
                 transforms",
  pubcountry =   "Switzerland",
  treatment =    "P Practical; T Theoretical or Mathematical",
}

@InProceedings{Prabhu:1995:MRD,
  author =       "J. A. Prabhu and G. B. Zyner",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, 19--21 July 1995",
  title =        "{167 MHz} Radix-$8$ Divide and Square Root Using
                 Overlapped Radix-$2$ Stages",
  crossref =     "Knowles:1995:PSC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "155--162",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "UltraSPARC's IEEE-754 compliant floating point divide
                 and square root implementation is presented. Three
                 overlapping stages of SRT radix-$2$ quotient selection
                 logic enable an effective radix-$8$ calculation at 167
                 MHz while only a single radix-$2$ \ldots{}",
}

@InProceedings{Schwarz:1995:RQC,
  author =       "E. M. Schwarz",
  booktitle =    "Conference Record of the Twenty-Ninth Asilomar
                 Conference on Signals, Systems and Computers, 1995",
  title =        "Rounding for quadratically converging algorithms for
                 division and square root",
  crossref =     "Singh:1995:CRT",
  volume =       "1",
  pages =        "600--603",
  month =        oct,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  summary =      "Exactly rounded results are necessary for many
                 architectures such as IEEE 754 standard. For division
                 and square root, rounding is easy to perform if a
                 remainder is available. But for quadratically
                 converging algorithms, the remainder is not \ldots{}",
}

@Article{Sidhu:1995:EIF,
  author =       "Satinder S. Sidhu",
  title =        "Elliptic Integrals and Functions",
  journal =      j-COMPUT-PHYS,
  volume =       "9",
  number =       "3",
  pages =        "268--276",
  month =        may # "\slash " # jun,
  year =         "1995",
  CODEN =        "CPHYE2",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Thu Feb 02 18:05:53 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers in Physics",
}

@Article{Smith:1995:CFA,
  author =       "Roger Alan Smith",
  title =        "A Continued-Fraction Analysis of Trigonometric
                 Argument Reduction",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "11",
  pages =        "1348--1351",
  month =        nov,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.475133",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Dec 08 10:21:28 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The calculation of a trigonometric function of a large
                 argument x is effectively carried out by finding the
                 integer $N$ and $ 0 \leq \alpha < 1 $ such that $ x =
                 (N + \alpha) \pi / 4 $. This reduction modulo $ \pi / 4
                 $ makes it possible to calculate a trigonometric
                 function of a reduced argument, either $ \alpha \pi / 4
                 $ or $ (1 - \alpha) \pi / 4 $, which lies in the
                 interval $ (0, \pi / 4) $. Payne and Hanek [1]
                 described an efficient algorithm for computing $ \alpha
                 $ to a predetermined level of accuracy. They noted that
                 if $x$ differs only slightly from an integral multiple
                 $ \pi / 2 $, the reduction must be carried out quite
                 accurately to avoid loss of significance in the reduced
                 argument. We present a simple method using continued
                 fractions for determining, for all numbers $x$ for
                 which the greatest number of insignificant leading bits
                 occur. Applications are made IEEE single-precision and
                 double-precision formats and two extended-precision
                 formats.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "argument reduction; computer arithmetic; continued
                 fractions; nonlinear optimization; Payne/Hanek radian
                 reduction; range reduction; trigonometric functions",
}

@InProceedings{Soderquist:1995:APC,
  author =       "Peter Soderquist and Miriam Leeser",
  title =        "An Area\slash Performance Comparison of Subtractive
                 and Multiplicative Divide\slash Square Root
                 Implementations",
  crossref =     "Knowles:1995:PSC",
  pages =        "132--139",
  month =        jul,
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
                 Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Soderquist.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-12",
}

@Book{Varchenko:1995:MHF,
  author =       "A. N. (Aleksandr Nikolaevich) Varchenko",
  title =        "Multidimensional hypergeometric functions and
                 representation theory of {Lie} algebras and quantum
                 groups",
  volume =       "21",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "ix + 371",
  year =         "1995",
  ISBN =         "981-02-1880-X",
  ISBN-13 =      "978-981-02-1880-5",
  LCCN =         "QA353.H9 V37 1995",
  bibdate =      "Sat Oct 30 21:12:24 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Advanced series in mathematical physics",
  acknowledgement = ack-nhfb,
  subject =      "Hypergeometric functions; Kac-Moody algebras;
                 Representations of Lie algebras; Representations of
                 quantum groups",
}

@Book{Vilenkin:1995:RLG,
  author =       "N. Ja. (Naum Jakovlevich) Vilenkin and A. U. (Anatolii
                 Ulsianovich) Klimyk",
  title =        "Representation of {Lie} groups and special functions:
                 recent advances",
  volume =       "316",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "xvi + 497",
  year =         "1995",
  ISBN =         "0-7923-3210-5",
  ISBN-13 =      "978-0-7923-3210-7",
  LCCN =         "QA176 .V55 1995",
  bibdate =      "Sat Oct 30 16:43:03 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Mathematics and its applications",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0823/95108075-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0823/95108075-t.html",
  acknowledgement = ack-nhfb,
  remark =       "Translated to English from Russian by V. A. Groza and
                 A. A. Groza.",
  subject =      "Representations of Lie groups; Functions, Special;
                 Integral transforms",
}

@Article{Vrahatis:1995:RPP,
  author =       "M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A.
                 Zafiropoulos and T. N. Grapsa",
  title =        "{RFSFNS}: a portable package for the numerical
                 determination of the number and the calculation of
                 roots of {Bessel} functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "92",
  number =       "2--3",
  pages =        "252--266",
  month =        dec,
  year =         "1995",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(95)00115-9",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:01 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See erratum \cite{Vrahatis:1999:ESP}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465595001159",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Book{Watson:1995:TTB,
  author =       "G. N. (George Neville) Watson",
  title =        "A Treatise on the Theory of {Bessel} Functions",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Second",
  pages =        "vi + 804",
  year =         "1995",
  ISBN =         "0-521-48391-3 (paperback), 0-521-06743-X (hardcover)",
  ISBN-13 =      "978-0-521-48391-9 (paperback), 978-0-521-06743-0
                 (hardcover)",
  LCCN =         "QA408 .W2 1995",
  bibdate =      "Sat Apr 19 09:15:26 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Cambridge mathematical library",
  URL =          "http://www.loc.gov/catdir/description/cam028/96139881.html;
                 http://www.loc.gov/catdir/toc/cam029/96139881.html",
  acknowledgement = ack-nhfb,
  remark =       "First published 1922. Second edition 1944. Reprinted
                 1966.",
  subject =      "Bessel functions",
  tableofcontents = "1. Bessel functions before 1826 \\
                 2. The Bessel coefficients \\
                 3. Bessel functions \\
                 4. Differential equations \\
                 5. Miscellaneous properties of Bessel functions \\
                 6. Integral representations of Bessel functions \\
                 7. Asymptotic expansions of Bessel functions \\
                 8. Bessel functions of large order \\
                 9. Polynomials associated with Bessel functions \\
                 10. Functions associated with Bessel functions \\
                 11. Addition theorems \\
                 12. Definite integrals \\
                 13. Infinitive integrals \\
                 14. Multiple integrals \\
                 15. The zeros of Bessel functions \\
                 16. Neumann series and Lommel's functions of two
                 variables \\
                 17. Kapteyn series \\
                 18. Series of Fourier-Bessel and Dini \\
                 19. Schl{\"o}mlich series \\
                 20. The tabulation of Bessel functions \\
                 Tables of Bessel functions \\
                 Bibliography \\
                 Indices",
  xxauthor =     "G. N. Watson",
}

@Article{Wong:1995:EHS,
  author =       "W. F. Wong and Yoshio Oyanagi and Eiichi Goto",
  title =        "Evaluation of the {Hitachi S-3800} Supercomputer Using
                 Six Benchmarks",
  journal =      j-IJSAHPC,
  volume =       "9",
  number =       "1",
  pages =        "58--70",
  month =        "Spring",
  year =         "1995",
  CODEN =        "IJSAE9",
  ISSN =         "0890-2720",
  bibdate =      "Tue Feb 18 09:07:32 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The S-3000 series is the third generation of Hitachi's
                 supercomputers. It is claimed to be currently the
                 fastest single processor supercomputer. In this paper,
                 we introduce the S-3000 and, using six benchmarks we
                 designed, evaluate a member of this series of
                 supercomputer, the top of the range S-3800, against its
                 predecessor, the Hitachi HITAC S-820. Our purpose is to
                 determine in what areas the S-3800 is an improvement
                 over its predecessor. The suite of benchmarks include
                 kernels for random number generation, elementary
                 function computation, FFT, dense matrix operations,
                 SOR, and list vector (scatter\slash gather) operations.
                 The use of small-to medium-sized kernels, as opposed to
                 large application benchmarks, help to better understand
                 the behavior of the machine. Our findings support the
                 claim that the S-3000 series is at least twice as fast
                 as the previous generation of Hitachi supercomputers.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
                 Singapore",
  affiliationaddress = "Singapore",
  classification = "722.4; 921.3; 921.6; 922.2",
  fjournal =     "International Journal of Supercomputer Applications
                 and High Performance Computing",
  journal-URL =  "http://hpc.sagepub.com/content/by/year",
  journalabr =   "Int J Supercomput Appl High Perform Comput",
  keywords =     "Benchmarks; Computer selection and evaluation;
                 Computer testing; Fast Fourier transforms; Fastest
                 single processor; Hitachi supercomputer; Matrix
                 algebra; Medium sized kernels; Performance; Random
                 number generation; Supercomputers; Vectors",
}

@Article{Wong:1995:FEE,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast evaluation of the elementary functions in single
                 precision",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "3",
  pages =        "453--457",
  month =        mar,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.372037",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "In this paper we introduce a new method for the fast
                 evaluation of the elementary functions in single
                 precision based on the evaluation of truncated Taylor
                 series using a difference method. We assume the
                 availability of large and fast (at least for read
                 purposes) memory. We call this method the ATA
                 (Add-Table lookup-Add) method. As the name implies, the
                 hardware required for the method are adders (both two/
                 and multi/operand adders) and fast tables. For IEEE
                 single precision numbers our initial estimates indicate
                 that we can calculate the basic elementary functions,
                 namely reciprocal, square root, logarithm, exponential,
                 trigonometric and inverse trigonometric functions,
                 within the latency of two to four floating point
                 multiplies.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. of Inf. Syst. and Comput. Sci., Nat. Univ. of
                 Singapore, Singapore",
  classification = "C4110 (Error analysis in numerical methods); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; Difference method; Elementary functions; Fast
                 evaluation; Floating point multiplies; Inverse
                 trigonometric functions; Logarithm functions;
                 Reciprocal; Single precision; Square root; Truncated
                 Taylor series",
  pubcountry =   "USA",
  thesaurus =    "Error analysis; Floating point arithmetic",
}

@Article{Ypma:1995:HDN,
  author =       "Tjalling J. Ypma",
  title =        "Historical Development of the {Newton--Raphson}
                 Method",
  journal =      j-SIAM-REVIEW,
  volume =       "37",
  number =       "4",
  pages =        "531--551",
  month =        dec,
  year =         "1995",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1037125",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "01A05 (65-03)",
  MRnumber =     "97b:01003",
  MRreviewer =   "M. Z. Nashed",
  bibdate =      "Sat Mar 29 09:55:35 MDT 2014",
  bibsource =    "Compendex database;
                 http://epubs.siam.org/toc/siread/37/4;
                 http://www.siam.org/journals/sirev/sirev374.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://epubs.siam.org/23425.htm;
                 http://link.aip.org/link/?SIR/37/531/1",
  abstract =     "This expository paper traces the development of the
                 Newton--Raphson method for solving nonlinear algebraic
                 equations through the extant notes, letters, and
                 publications of Isaac Newton, Joseph Raphson, and
                 Thomas Simpson. It is shown how Newton's formulation
                 differed from the iterative process of Raphson, and
                 that Simpson was the first to give a general
                 formulation, in terms of fluxional calculus, applicable
                 to nonpolynomial equations. Simpson's extension of the
                 method to systems of equations is exhibited.",
  acknowledgement = ack-nhfb,
  affiliation =  "Western Washington Univ",
  affiliationaddress = "Bellingham, WA, USA",
  classification = "921.1; 921.2; 921.6",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "Algebra; Algorithms; Approximation theory;
                 Differentiation (calculus); Finite difference method;
                 Fluxional calculus; Isaac Newton; Iterative methods;
                 Joseph Raphson; Linearization; Newton--Raphson method;
                 Nonlinear algebraic equations; Nonlinear equations;
                 Nonpolynomial equation; Polynomials; Secant method;
                 Thomas Simpson",
  onlinedate =   "December 1995",
}

@Article{Zhang:1995:TMAa,
  author =       "J. Zhang and J. A. Belward",
  title =        "Tau-method approximations for the {Bessel} function {$
                 Y_0 (z) $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "30",
  number =       "7",
  pages =        "5--14",
  month =        oct,
  year =         "1995",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(95)00120-N",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Sun Jun 12 08:33:42 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219500120N",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Zhang:1995:TMAb,
  author =       "J. Zhang",
  title =        "Tau-method approximations for the {Bessel} function {$
                 Y_1 (z) $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "30",
  number =       "7",
  pages =        "15--19",
  month =        oct,
  year =         "1995",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(95)00121-E",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Sun Jun 12 09:26:01 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219500121E",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  remark =       "From p. 18 (conclusions section), ``We may use this
                 method to approximate the Bessel functions of other
                 integer orders. \ldots{} It is therefore advisable to
                 use the recurrence relations of the Bessel functions to
                 compute function values for $ n > 1 $ \ldots''. [This
                 is a similar limitation as with Chebyshev and minimax
                 polynomial approximations: they are valid only for a
                 single order the Bessel function.]",
}

@InProceedings{Ahrendt:1996:FHC,
  author =       "Timm Ahrendt",
  title =        "Fast High-Precision Computations of Complex Square
                 Roots",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "142--149",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p142-ahrendt/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; measurement;
                 SIGNUM; SIGSAM; symbolic computation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 F.1.1} Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Models of Computation, Bounded-action devices.
                 {\bf G.1.5} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Iterative
                 methods. {\bf G.1.2} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation.",
  xxtitle =      "Fast high-precision computation of complex square
                 roots",
}

@Article{Balla:1996:SCB,
  author =       "K. Balla and V. H. Linh",
  title =        "The simultaneous computation of {Bessel} functions of
                 first and second kind",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "31",
  number =       "4--5",
  pages =        "87--97",
  month =        feb # "\slash " # mar,
  year =         "1996",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:26 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122195002200",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Cappuccino:1996:DDH,
  author =       "G. Cappuccino and P. Corsonello and G. Cocorullo",
  title =        "Design and demonstration of high throughput square
                 rooting circuit",
  journal =      j-ELECT-LETTERS,
  volume =       "32",
  number =       "5",
  pages =        "434",
  month =        "????",
  year =         "1996",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "Not \ldots{}",
}

@Article{Chaudhry:1996:ACF,
  author =       "M. A. Chaudhry and N. M. Temme and E. J. M. Veling",
  title =        "Asymptotics and closed form of a generalized
                 incomplete gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "67",
  number =       "2",
  pages =        "371--379",
  day =          "29",
  month =        mar,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:27:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795000186",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Guyot:1996:STD,
  author =       "A. Guyot and M. Renaudin and B. {El Hassan} and V.
                 Levering",
  booktitle =    "Proceedings of the Ninth International Conference on
                 {VLSI} Design, 1996",
  title =        "Self timed division and square-root extraction",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "376--381",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper describes a self-timed integrated circuit
                 for division and square-root extraction. First it
                 concentrates on the development and the proof of a new
                 mathematical algorithm. Then the design methodology and
                 the architecture of a self-timed \ldots{}",
}

@Article{Heinrich:1996:AAF,
  author =       "Peter Heinrich",
  title =        "Algorithm Alley: a Fast Integer Square Root",
  journal =      j-DDJ,
  volume =       "21",
  number =       "4",
  pages =        "113--114, 130",
  month =        apr,
  year =         "1996",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@TechReport{Hickey:1996:FSP,
  author =       "Timothy J. Hickey and Qun Ju",
  title =        "Fast, Sound, and Precise Narrowing of the Exponential
                 Function",
  type =         "Technical report",
  institution =  "Computer Science Department, Brandeis University",
  address =      "Waltham, MA, USA 02254",
  month =        mar,
  year =         "1996",
  bibdate =      "Sat Nov 05 15:42:23 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz",
  acknowledgement = ack-nhfb,
}

@Article{Homeier:1996:CAI,
  author =       "H. H. H. Homeier",
  title =        "On Convergence Acceleration for the Iterative Solution
                 of the Inverse {Dyson} Equation",
  journal =      j-J-MOL-STRUCT-THEOCHEM,
  volume =       "368",
  pages =        "81--91",
  year =         "1996",
  CODEN =        "THEODJ",
  ISSN =         "0166-1280 (print), 1872-7999 (electronic)",
  ISSN-L =       "0166-1280",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the 2nd {Electronic Computational
                 Chemistry Conference}.",
  URL =          "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM954",
  fjournal =     "Journal of molecular structure. Theochem",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01661280",
  keywords =     "convergence acceleration",
  tech =         "Technical Report TC-QM-95-4, Institut f{\"u}r
                 {Physikalische} und {Theoretische Chemie,
                 Universit{\"a}t Regensburg, D-93040 Regensburg}, 1995",
}

@TechReport{Homeier:1996:KMP,
  author =       "H. H. H. Homeier",
  title =        "{Zur Konvergenzverbesserung der M{\o}ller--Plesset
                 St{\"o}rungsreihe} ({English}: {On} Convergence
                 Acceleration of the {M{\o}ller--Plesset} Perturbation
                 Series)",
  number =       "Homeier:1996:KMP",
  institution =  inst-IPTC,
  address =      inst-IPTC:adr,
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Poster CP 14.77, {Fr{\"u}hjahrstagung des
                 Arbeitskreises Festk{\"o}rperphysik bei der DPG,
                 Regensburg 1996}. Abstract: Verhandl. DPG (VI) 31,
                 2165-2166 (1996).",
  URL =          "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM962",
  keywords =     "convergence acceleration",
}

@Article{Ito:1996:SRI,
  author =       "Masayuki Ito and Naofumi Takagi and Shuzo Yajima",
  title =        "Square rooting by iterative multiply-additions",
  journal =      j-INFO-PROC-LETT,
  volume =       "60",
  number =       "5",
  pages =        "267--269",
  day =          "8",
  month =        dec,
  year =         "1996",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68M07",
  MRnumber =     "97i:68014",
  bibdate =      "Wed Nov 11 12:16:26 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods)",
  corpsource =   "Dept. of Inf. Sci., Kyoto Univ., Japan",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "computer arithmetic; convergence of numerical methods;
                 digital arithmetic; iterative methods; iterative
                 multiply-additions; linear converging ratio;
                 multiplicative methods; Newton--Raphson method;
                 read-only storage; ROM sizes; square root algorithm",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Jeffrey:1996:UBL,
  author =       "D. J. Jeffrey and D. E. G. Hare and Robert M.
                 Corless",
  title =        "Unwinding the branches of the {Lambert $W$} function",
  journal =      j-MATH-SCI,
  volume =       "21",
  number =       "1",
  pages =        "1--7",
  month =        jun,
  year =         "1996",
  ISSN =         "0312-3685 (print), 1475-6080 (electronic)",
  ISSN-L =       "0312-3685",
  bibdate =      "Sat Oct 06 09:02:19 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.appliedprobability.org/data/files/TMS%20articles/21_1_1.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematical Scientist",
  journal-URL =  "http://www.appliedprobability.org/content.aspx?Group=tms&Page=allissues",
}

@Unpublished{Kahan:1996:TCR,
  author =       "W. Kahan",
  title =        "A Test for Correctly Rounded {SQRT}",
  pages =        "4",
  year =         "1996",
  bibdate =      "Mon Apr 25 05:47:38 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Lecture notes.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/SQRTest.ps",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; rounding errors",
}

@Article{Kalantari:1996:HOI,
  author =       "B. Kalantari and I. Kalantari",
  title =        "High order iterative methods for approximating square
                 roots",
  journal =      j-BIT-NUM-MATH,
  volume =       "36",
  number =       "2",
  pages =        "395--399",
  month =        jun,
  year =         "1996",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01731991",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65D15 (65H99)",
  MRnumber =     "97k:65039",
  bibdate =      "Wed Jan 4 18:52:24 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit36.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=395",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Kantabutra:1996:HCE,
  author =       "V. Kantabutra",
  title =        "On hardware for computing exponential and
                 trigonometric functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "3",
  pages =        "328--339",
  month =        mar,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.485571",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485571",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kolbig:1996:PF,
  author =       "K. S. K{\"o}lbig",
  title =        "The polygamma function $ \psi^{(k)}(x) $ for $ x = 1 /
                 4 $ and $ x = 3 / 4 $",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "75",
  number =       "1",
  pages =        "43--46",
  day =          "12",
  month =        nov,
  year =         "1996",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(96)00055-6",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796000556",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Lang:1996:BPU,
  author =       "T. Lang and R. Wong",
  title =        "``{Best} possible'' upper bounds for the first two
                 positive zeros of the {Bessel} function {$ J_v(x) $}:
                 the infinite case",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "71",
  number =       "2",
  pages =        "311--329",
  day =          "27",
  month =        jul,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:56 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795002200",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Lehoucq:1996:CEU,
  author =       "R. B. Lehoucq",
  title =        "The Computation of Elementary Unitary Matrices",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "393--400",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The construction of elementary unitary matrices that
                 transform a complex vector to a multiple of $ e_1 $,
                 the first column of the identity matrix, is studied. We
                 present four variants and their software
                 implementation, including a discussion on the {LAPACK}
                 subroutine {CLARFG}. Comparisons are also given.",
  accepted =     "June 1996",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf F.2}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices. {\bf G.1.3}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis.",
}

@Article{Lether:1996:RAF,
  author =       "Frank G. Lether",
  title =        "Rational approximation formulas for computing the
                 positive zeros of {$ J_0 (x) $}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "67",
  number =       "1",
  pages =        "167--172",
  day =          "20",
  month =        feb,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:27:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795002197",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Li:1996:NNR,
  author =       "Yamin Li and Wanming Chu",
  booktitle =    "Proceedings of the {IEEE} International Conference on
                 Computer Design: {VLSI} in Computers and Processors:
                 {ICCD '96}",
  title =        "A new non-restoring square root algorithm and its
                 {VLSI} implementations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "538--544",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present a new non-restoring square root algorithm
                 that is very efficient to implement. The new algorithm
                 presented here has the following features unlike other
                 square root algorithms. First, the focus of the
                 ``non-restoring'' is on the {\&} \ldots{}",
}

@Article{Lorch:1996:BPU,
  author =       "Lee Lorch and Riccardo Uberti",
  title =        "``{Best} possible'' upper bounds for the first
                 positive zeros of {Bessel} functions --- the finite
                 part",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "75",
  number =       "2",
  pages =        "249--258",
  day =          "28",
  month =        nov,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796000659",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@TechReport{Lozier:1996:PST,
  author =       "Daniel W. Lozier",
  title =        "A Proposed Software Test Service for Special
                 Functions",
  type =         "Technical Report",
  number =       "NISTIR 5916",
  institution =  pub-NIST,
  address =      pub-NIST:adr,
  pages =        "11",
  month =        oct,
  year =         "1996",
  bibdate =      "Fri Jul 09 06:02:16 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Published in \cite{Lozier:1997:PST}.",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5916.ps",
  acknowledgement = ack-nhfb,
}

@Article{Lozier:1996:SNS,
  author =       "Daniel W. Lozier",
  title =        "Software Needs in Special Functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "66",
  number =       "??",
  pages =        "345--358",
  month =        "????",
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Fri Jul 09 05:51:55 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  remark =       "See preprint \cite{Lozier:1994:SNS}.",
}

@Article{Macleod:1996:AMS,
  author =       "Allan J. Macleod",
  title =        "{Algorithm 757}: {MISCFUN}, a software package to
                 compute uncommon special functions",
  journal =      j-TOMS,
  volume =       "22",
  number =       "3",
  pages =        "288--301",
  month =        sep,
  year =         "1996",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/232826.232846;
                 http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p288-macleod/",
  abstract =     "MISCFUN (MISCellaneous FUNctions) is a Fortran package
                 for the evaluation of several special functions, which
                 are not used often enough to have been included in the
                 standard libraries or packages. The package uses
                 Chebyshev expansions as the underlying method of
                 approximation, with the Chebyshev coefficients given to
                 20D. A wide variety of functions are included, and the
                 package is designed so that other functions can be
                 added in a standard manner.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev
                 approximation and theory. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Certification and
                 testing.",
}

@Article{Oleksy:1996:CAM,
  author =       "Cz. Oleksy",
  title =        "A convergence acceleration method of {Fourier}
                 series",
  journal =      j-COMP-PHYS-COMM,
  volume =       "96",
  number =       "1",
  pages =        "17--26",
  year =         "1996",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(96)00044-6",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  MRclass =      "65B05",
  MRnumber =     "1396682 (97c:65012)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  keywords =     "convergence acceleration",
}

@Article{Panteliou:1996:DII,
  author =       "S. D. Panteliou and A. D. Dimarogonas and I. N. Katz",
  title =        "Direct and inverse interpolation for {Jacobian}
                 elliptic functions, zeta function of {Jacobi} and
                 complete elliptic integrals of the second kind",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "32",
  number =       "8",
  pages =        "51--57",
  month =        oct,
  year =         "1996",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:33 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122196001666",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Book{Patel:1996:HND,
  author =       "Jagdish K. Patel and Campbell B. Read",
  title =        "Handbook of the Normal Distribution",
  volume =       "150",
  publisher =    pub-DEKKER,
  address =      pub-DEKKER:adr,
  edition =      "Second revised and expanded",
  pages =        "ix + 431",
  year =         "1996",
  ISBN =         "0-8247-9342-0 (hardcover)",
  ISBN-13 =      "978-0-8247-9342-5 (hardcover)",
  LCCN =         "QA273.6 .P373 1996",
  bibdate =      "Sat Dec 16 17:22:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Statistics, textbooks and monographs",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0647/95049404-d.html",
  acknowledgement = ack-nhfb,
  subject =      "Gaussian distribution",
}

@Article{Plofker:1996:ESM,
  author =       "Kim Plofker",
  title =        "An Example of the Secant Method of Iterative
                 Approximation in a {Fifteenth-Century Sanskrit} Text",
  journal =      j-HIST-MATH,
  volume =       "23",
  number =       "3",
  pages =        "246--256",
  month =        aug,
  year =         "1996",
  CODEN =        "HIMADS",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Jun 26 06:19:07 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0315086096900269",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
}

@Article{Qiu:1996:SEC,
  author =       "S.-L. Qiu and M. K. Vamanamurthy",
  title =        "Sharp Estimates for Complete Elliptic Integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "27",
  number =       "3",
  pages =        "823--834",
  month =        may,
  year =         "1996",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33E05",
  MRnumber =     "97f:33033",
  MRreviewer =   "G. D. Anderson",
  bibdate =      "Sat Dec 5 18:14:13 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@InProceedings{Rao:1996:RTS,
  author =       "V. M. Rao and B. Nowrouzian",
  booktitle =    "Canadian Conference on Electrical and Computer
                 Engineering. 26--29 May 1996",
  title =        "Rounding techniques for signed binary arithmetic",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "294--297",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This paper is concerned with the derivation of the
                 relationship that exists between the number truncation
                 in two's complement (TC) arithmetic and the
                 corresponding truncation in signed-binary (SB)
                 arithmetic. The resulting relationship is subsequently
                 exploited and applied to the development of a pair of
                 novel techniques for SB rounding. These techniques are
                 then translated into algorithm suitable for two-level
                 logic implementation. Finally, the resulting algorithms
                 are applied to the design and implementation of a
                 high-speed SB-kernel based TC multiply-accumulate
                 arithmetic architecture.",
  acknowledgement = ack-nhfb,
}

@Article{Schwarz:1996:HSA,
  author =       "Eric M. Schwarz and Michael J. Flynn",
  title =        "Hardware Starting Approximation Method and Its
                 Application to the Square Root Operation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "12",
  pages =        "1356--1369",
  month =        dec,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.545966",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "Quadratically converging algorithms for high-order
                 arithmetic operations typically are accelerated by a
                 starting approximation. The higher the precision of the
                 starting approximation, the less number of iterations
                 required for convergence. \ldots{}",
}

@Article{Sinclair:1996:ORS,
  author =       "R. Sinclair",
  title =        "Optimization of reciprocals and square roots on the
                 {i860} microprocessor",
  journal =      j-INT-J-HIGH-SPEED-COMPUTING,
  volume =       "8",
  number =       "1",
  pages =        "57--64",
  year =         "1996",
  CODEN =        "IHSCEZ",
  ISSN =         "0129-0533",
  bibdate =      "Mon Feb 25 11:19:22 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
                 Article1st database",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of High Speed Computing
                 (IJHSC)",
  journal-URL =  "http://www.worldscientific.com/worldscinet/ijhsc",
}

@Article{Snyder:1996:RAF,
  author =       "W. Van Snyder",
  title =        "Remark on {Algorithm 723}: {Fresnel} Integrals",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "498--500",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235825",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Snyder:1993:AFI}.",
  abstract =     "{\it Algorithm 723: Fresnel Integrals} has been
                 improved to provide more precise results for $ x \gg 0
                 $.",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Rational
                 approximation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing.",
}

@Book{Temme:1996:SFI,
  author =       "N. M. Temme",
  title =        "Special Functions: an Introduction to the Classical
                 Functions of Mathematical Physics",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xii + 374",
  year =         "1996",
  ISBN =         "0-471-11313-1",
  ISBN-13 =      "978-0-471-11313-3",
  LCCN =         "QC20.7.F87 T46 1996",
  bibdate =      "Mon Nov 24 21:41:54 MST 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.bibsys.no:2100/BIBSYS;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "functions, special; mathematical physics; boundary
                 value problems",
}

@Article{Temme:1996:UAI,
  author =       "N. M. Temme",
  title =        "Uniform asymptotics for the incomplete gamma functions
                 starting from negative values of the parameters",
  journal =      j-METHODS-APPL-ANAL,
  volume =       "3",
  number =       "3",
  pages =        "335--344",
  year =         "1996",
  DOI =          "https://doi.org/10.4310/MAA.1996.v3.n3.a3",
  ISSN =         "1073-2772 (print), 1945-0001 (electronic)",
  ISSN-L =       "1073-2772",
  MRclass =      "33B20 (41A60)",
  MRnumber =     "1421474",
  MRreviewer =   "Richard B. Paris",
  bibdate =      "Sat Feb 18 15:19:00 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Methods and Applications of Analysis",
  journal-URL =  "http://www.intlpress.com/MAA/",
}

@Article{Waissi:1996:SAS,
  author =       "Gary R. Waissi and Donald F. Rossin",
  title =        "A sigmoid approximation of the standard normal
                 integral",
  journal =      j-APPL-MATH-COMP,
  volume =       "77",
  number =       "1",
  pages =        "91--95",
  month =        jun,
  year =         "1996",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/0096-3003(95)00190-5",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Nov 20 21:02:39 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0096300395001905",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Book{Walz:1996:AE,
  author =       "Guido Walz",
  title =        "Asymptotics and extrapolation",
  volume =       "88",
  publisher =    pub-AKADEMIE-VERLAG,
  address =      pub-AKADEMIE-VERLAG:adr,
  pages =        "330",
  year =         "1996",
  ISBN =         "3-05-501732-3",
  ISBN-13 =      "978-3-05-501732-2",
  LCCN =         "QA281 .W349 1996",
  bibdate =      "Thu Dec 1 10:25:13 MST 2011",
  bibsource =    "catalog.princeton.edu:7090/voyager;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Mathematical research",
  acknowledgement = ack-nhfb,
  subject =      "Extrapolation; Asymptotic expansions",
}

@Article{Weniger:1996:CWF,
  author =       "Ernst Joachim Weniger",
  title =        "Computation of the {Whittaker} function of the second
                 kind by summing its divergent asymptotic series with
                 the help of nonlinear sequence transformations",
  journal =      j-COMPUT-PHYS,
  volume =       "10",
  number =       "5",
  pages =        "496--??",
  month =        sep,
  year =         "1996",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168579",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:46:03 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168579",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}

@Article{Williams:1996:TMF,
  author =       "K. B. Williams",
  title =        "Testing Math Functions: When requirements are tight,
                 we must carefully examine all potential sources of
                 error. {Make} sure your math library isn't the weak
                 link in the chain",
  journal =      j-CCCUJ,
  volume =       "14",
  number =       "12",
  pages =        "49--54, 58--65",
  month =        dec,
  year =         "1996",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Thu Nov 14 06:34:33 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Describes a package that extends the
                 Cody-Waite-Plauger work on the ELEFUNT package for the
                 testing of the elementary functions, including the
                 inverse hyperbolic functions, cube root, and Bessel
                 functions of the first and second kinds. The C++
                 package implements 192-bit extended precision versions
                 of all of the functions, so that accurate results are
                 available for comparison with the normal
                 double-precision results.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}

@Article{Zahle:1996:FDW,
  author =       "M. Z{\"a}hle and H. Ziezold",
  title =        "Fractional derivatives of {Weierstrass}-type
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "76",
  number =       "1--2",
  pages =        "265--275",
  day =          "17",
  month =        dec,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796001100",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Book{Zhang:1996:CSF,
  author =       "Shanjie Zhang and Jianming Jin",
  title =        "Computation of Special Functions",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xxvi + 717",
  year =         "1996",
  ISBN =         "0-471-11963-6",
  ISBN-13 =      "978-0-471-11963-0",
  LCCN =         "QA351.C45 1996",
  bibdate =      "Wed Mar 22 14:39:04 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  price =        "US\$94.00",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Preface / xi \\
                 Acknowledgments / xvii \\
                 List of Computer Programs / xix \\
                 1: Bernoulli and Euler Numbers / 1 \\
                 2: Orthogonal Polynomials / 12 \\
                 3: Gamma, Beta, and Psi Functions / 44 \\
                 4: Legendre Functions / 77 \\
                 5: Bessel Functions / 126 \\
                 6: Modified Bessel Functions / 202 \\
                 7: Integrals of Bessel Functions / 252 \\
                 8: Spherical Bessel Functions / 273 \\
                 9: Kelvin Functions / 307 \\
                 10: Airy Functions / 325 \\
                 11: Struve Functions / 341 \\
                 12: Hypergeometric and Confluent Hypergeometric / 366
                 \\
                 13: Parabolic Cylinder Functions / 425 \\
                 14: Mathieu Functions / 475 \\
                 15: Spheroidal Wave Functions / 536 \\
                 16: Error Function and Fresnel Integrals / 620 \\
                 17: Cosine and Sine Integrals / 644 \\
                 18: Elliptic Integrals and Jacobian Elliptic Functions
                 19: Exponential Integrals / 680 \\
                 20: Summary of Methods for Computing Special Functions
                 Appendix A: Derivation of Some Special Differential
                 Appendix B: Root-Finding Methods / 704 \\
                 Reference / 706 \\
                 Appendix C: About the Software / 707 \\
                 Index / 709 \\
                 Index of Computer Programs / 715",
  tableofcontents = "Preface / xi \\
                 Acknowledgments / xvii \\
                 List of Computer Programs / xix \\
                 1: Bernoulli and Euler Numbers / 1 \\
                 1.1 Bernoulli Numbers / 1 \\
                 1.2 Euler Numbers / 6 \\
                 1.3 Mathematical Table / 10 \\
                 References / 11 \\
                 2: Orthogonal Polynomials / 12 \\
                 2.1 Introduction / 12 \\
                 2.2 Chebyshev Polynomials / 13 \\
                 2.3 Laguerre Polynomials / 18 \\
                 2.4 Hermite Polynomials / 20 \\
                 2.5 Numerical Computation / 23 \\
                 2.6 Application in Numerical Integration / 27 \\
                 References / 43 \\
                 3: Gamma, Beta, and Psi Functions / 44 \\
                 3.1 Gamma Function / 44 \\
                 3.2 Beta Function / 53 \\
                 3.3 Psi Function / 55 \\
                 3.4 Incomplete Gamma Function / 61 \\
                 3.5 Incomplete Beta Function / 64 \\
                 3.6 Mathematical Tables / 66 \\
                 References and Further Reading / 76 \\
                 4: Legendre Functions / 77 \\
                 4.1 Introduction / 77 \\
                 4.2 Legendre Functions of the First Kind / 78 \\
                 4.3 Legendre Functions of the Second Kind / 83 \\
                 4.4 Associated Legendre Functions of the First Kind /
                 89 \\
                 4.5 Associated Legendre Functions of the Second Kind /
                 96 \\
                 4.6 Legendre Functions with an Arbitrary Degree / 104
                 \\
                 4.7 Mathematical Tables / 113 \\
                 References and Further Reading / 125 \\
                 5: Bessel Functions / 126 \\
                 5.1 Introduction / 126 \\
                 5.2 Computation of $J_0(x)$, $J_1(x)$, $Y_0(x)$, and
                 $Y_1(x)$ / 131 \\
                 5.3 Computation of $J_n(x)$ and $Y_n(x)$ with Real
                 Arguments / 140 \\
                 5.4 Computation of $Y_n(z)$ and$ Y_n(z)$ with Complex
                 Arguments / 149 \\
                 5.5 Computation of $J_\nu(z)$ and $J_\nu(z)$ with an
                 Arbitrary Order / 161 \\
                 5.6 Assessment of Validity and Accuracy of Computation
                 / 175 \\
                 5.7 Zeros of Bessel Functions / 180 \\
                 5.8 Lambda Functions / 182 \\
                 5.9 Mathematical Tables / 184 \\
                 References and Further Reading / 201 \\
                 6: Modified Bessel Functions / 202 \\
                 6.1 Introduction / 202 \\
                 6.2 Computation of $I_0(x)$, $I_1(x)$, $K_0(x)$, and
                 $K_1(x)$ / 207 \\
                 6.3 Computation of $I_n(x)$ and $K_n(x)$ with Real
                 Arguments / 213 \\
                 6.4 Computation of $I_n(z)$ and $K_n(z)$ with Complex
                 Arguments / 217 \\
                 6.5 Computation of $I_\nu(z)$ and $K_\nu(z)$ with an
                 Arbitrary Order / 225 \\
                 6.6 Computation of $H_\nu^{(1)}(z)$ and
                 $H_\nu^{(2)}(z)$ for Complex Arguments / 235 \\
                 6.7 Mathematical Tables / 239 \\
                 References and Further Reading / 251 \\
                 7: Integrals of Bessel Functions / 252 \\
                 7.1 Simple Integrals of Bessel Functions / 252 \\
                 7.2 Simple Integrals of Modified Bessel Functions / 261
                 \\
                 7.3 Curves and Tables / 268 \\
                 References / 272 \\
                 8: Spherical Bessel Functions / 273 \\
                 8.1 Spherical Bessel Functions / 273 \\
                 8.2 Riccati--Bessel Functions / 283 \\
                 8.3 Modified Spherical Bessel Functions / 286 \\
                 8.4 Mathematical Tables / 295 \\
                 References and Further Reading / 306 \\
                 9: Kelvin Functions / 307 \\
                 9.1 Introduction / 307 \\
                 9.2 Mathematical Properties / 311 \\
                 9.3 Asymptotic Expansions / 312 \\
                 9.4 Numerical Computation / 315 \\
                 9.5 Zeros of Kelvin Functions / 321 \\
                 9.6 Mathematical Tables / 321 \\
                 Reference / 324 \\
                 10: Airy Functions / 325 \\
                 10.1 Introduction / 325 \\
                 10.2 Numerical Computation / 329 \\
                 10.3 Mathematical Tables / 336 \\
                 References / 340 \\
                 11: Struve Functions / 341 \\
                 11.1 Struve Functions / 341 \\
                 11.2 Modified Struve Functions / 353 \\
                 11.3 Mathematical Tables / 362 \\
                 References / 365 \\
                 12: Hypergeometric and Confluent Hypergeometric
                 Functions / 366 \\
                 12.1 Definition of Hypergeometric Functions / 366 \\
                 12.2 Properties of Hypergeometric Functions / 368 \\
                 12.3 Linear Transformation Formulas / 369 \\
                 12.4 Recurrence Relations for Hypergeometric Functions
                 / 372 \\
                 12.5 Special Functions Expressed as Hypergeometric
                 Functions / 373 \\
                 12.6 Numerical Computation of Hypergeometric Functions
                 / 374 \\
                 12.7 Definition of Confluent Hypergeometric Functions /
                 385 \\
                 12.8 Properties of Confluent Hypergeometric Functions /
                 387 \\
                 12.9 Recurrence Relations for Confluent Hypergeometric
                 Functions / 389 \\
                 12.10 Special Functions Expressed as Confluent
                 Hypergeometric Functions / 394 \\
                 12.11 Definition of Whittaker Functions / 395 \\
                 12.12 Numerical Computation of Confluent Hypergeometric
                 Functions / 398 \\
                 12.13 Mathematical Tables / 411 \\
                 References and Further Reading / 424 \\
                 13: Parabolic Cylinder Functions / 425 \\
                 13.1 Introduction / 425 \\
                 13.2 Definitions of Parabolic Cylinder Functions / 428
                 \\
                 13.3 Basic Properties / 432 \\
                 13.4 Series and Asymptotic Expansions / 437 \\
                 13.5 Numerical Computation / 438 \\
                 13.6 Mathematical Tables / 455 \\
                 References and Further Reading / 474 \\
                 14: Mathieu Functions / 475 \\
                 14.1 Definition of Mathieu Functions / 475 \\
                 14.2 Determination of Expansion Coefficients and
                 Characteristic Values / 477 \\
                 14.3 Approximate Calculation of Characteristic Values /
                 482 \\
                 14.4 Expansion of Mathieu Functions When $|q| < 1$ /
                 485 \\
                 14.5 Properties of Mathieu Functions / 487 \\
                 14.6 Definition of Modified Mathieu Functions / 489 \\
                 14.7 Properties of Modified Mathieu Functions / 496 \\
                 14.8 Numerical Computation: Algorithms and Computer
                 Programs / 501 \\
                 14.9 Mathematical Tables / 520 \\
                 References and Further Reading / 535 \\
                 15: Spheroidal Wave Functions / 536 \\
                 15.1 Spheroidal Coordinate Systems / 536 \\
                 15.2 Wave Equation and Its Solution in Spheroidal
                 Coordinates / 540 \\
                 15.3 Definitions of Angular and Radial Prolate
                 Spheroidal Wave Functions / 542 \\
                 15.4 Determination of Characteristic Values and
                 Expansion Coefficients / 550 \\
                 15.5 Evaluation of Prolate Radial Wave Functions of the
                 Second Kind for Small $c \xi$ / 556 \\
                 15.6 Definitions of Angular and Radial Oblate
                 Spheroidal Wave Functions / 559 \\
                 15.7 Evaluation of Oblate Radial Wave Functions of the
                 Second Kind for Small $c \xi$ / 561 \\
                 15.8 Numerical Computation: Algorithms and Computer
                 Programs / 569 \\
                 15.9 Mathematical Tables / 594 \\
                 References / 619 \\
                 16: Error Function and Fresnel Integrals / 620 \\
                 16.1 Introduction to Error Function / 620 \\
                 16.2 Numerical Computation of Error Function / 621 \\
                 16.3 Gaussian Probability Integral / 624 \\
                 16.4 Introduction to Fresnel Integrals / 625 \\
                 16.5 Series and Asymptotic Expansions of Fresnel
                 Integrals / 629 \\
                 16.6 Numerical Computation of Fresnel Integrals / 630
                 \\
                 16.7 Zeros of Error Function and Fresnel Integrals /
                 635 \\
                 16.8 Mathematical Tables / 636 \\
                 References and Further Reading / 643 \\
                 17: Cosine and Sine Integrals / 644 \\
                 17.1 Introduction / 644 \\
                 17.2 Series and Asymptotic Expansions / 646 \\
                 17.3 Numerical Computation / 647 \\
                 17.4 Mathematical Table / 651 \\
                 References and Further Readings / 653 \\
                 18: Elliptic Integrals and Jacobian Elliptic Functions
                 / 654 \\
                 18.1 Introduction to Elliptic Integrals / 654 \\
                 18.2 Series Expansion of Elliptic Integrals / 659 \\
                 18.3 Numerical Computation of Elliptic Integrals / 661
                 \\
                 18.4 Introduction to Jacobian Elliptic Functions / 666
                 \\
                 18.5 Numerical Computation of Jacobian Elliptic
                 Functions / 670 \\
                 18.6 Mathematical Tables / 672 \\
                 References and Further Reading / 679 \\
                 19: Exponential Integrals / 680 \\
                 19.1 Introduction / 680 \\
                 19.2 Series, Asymptotic, and Continued Fraction
                 Expressions / 682 \\
                 19.3 Rational Approximations / 683 \\
                 19.4 Numerical Computation / 684 \\
                 19.5 Mathematical Tables / 688 \\
                 References / 693 \\
                 20: Summary of Methods for Computing Special Functions
                 / 694 \\
                 Appendix A: Derivation of Some Special Differential
                 Equations / 697 \\
                 A.1 Helmholtz Equation and Separation of Variables /
                 697 \\
                 A.2 Circular Cylindrical Coordinates / 698 \\
                 A.3 Elliptic Cylindrical Coordinates / 700 \\
                 A.4 Parabolic Cylindrical Coordinates / 700 \\
                 A.5 Spherical Coordinates / 701 \\
                 A.6 Prolate Spheroidal Coordinates / 701 \\
                 A.7 Oblate Spheroidal Coordinates / 702 \\
                 A.8 Parabolic Coordinates / 703 \\
                 References / 703 \\
                 Appendix B: Root-Finding Methods / 704 \\
                 B.1 Newton's Method / 704 \\
                 B.2 Modified Newton's Method / 706 \\
                 B.3 Secant Method / 706 \\
                 Reference / 706 \\
                 Appendix C: About the Software / 707 \\
                 Index / 709 \\
                 Index of Computer Programs / 715",
  xxauthor =     "Shan-chieh Chang and Shanjie Zhang and Jianming Jin",
  xxnote =       "There is online bookstore and library catalog
                 confusion over the authors of this book. The
                 publisher's Web page at
                 http://catalog.wiley.com/remsrch.cgi has Shan-jie Zhang
                 (Nanjing Univ., China) / Jianming Jin (Univ. of
                 Illinois at Urbana-Champaign), and a price of
                 US\$125.00. It looks like Shan-chieh Chang is merely a
                 different English transcription of Shanjie Zhang.
                 http://www.fatbrain.com/ lists this book for US\$99.95.
                 My copy of the book lists the authors as Shanjie Zhang
                 and Jianming Jin in four places.",
}

@Article{Zhang:1996:NTM,
  author =       "J. Zhang",
  title =        "A note on the tau-method approximations for the
                 {Bessel} functions {$ Y_0 (z) $} and {$ Y_1 (z) $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "31",
  number =       "9",
  pages =        "63--70",
  month =        may,
  year =         "1996",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(96)00043-0",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Sun Jun 12 08:43:36 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122196000430",
  abstract =     "This paper is to complete and improve the work
                 reported in [1,2], using the Lanczos $ \tau $-method
                 (in Coleman's version) to approximate the Bessel
                 functions $ Y_0 (z) $ and $ Y_1 (z) $. We introduce
                 symbolic representations of the scaled Faber
                 polynomials on any fan-shaped section of the complex
                 plane. These Faber polynomials are used as the
                 perturbation terms in the $ \tau $-method. Numerical
                 comparison among the power series, the Chebyshev series
                 and the $ \tau $-method are conducted to show the
                 accuracy improvement achieved by this new version of
                 the $ \tau $-method. Some concluding remarks and
                 suggestions on future research are given.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "Automated $\tau$-method; Bessel functions; Chebyshev
                 series; Symbolic Faber polynomials",
}

@Article{Zhang:1996:SNC,
  author =       "Jun Zhang",
  title =        "Symbolic and numerical computation on {Bessel}
                 functions of complex argument and large magnitude",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "75",
  number =       "1",
  pages =        "99--118",
  day =          "12",
  month =        nov,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796000635",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Abad:1997:NEC,
  author =       "Julio Abad and Javier Sesma",
  title =        "A new expansion of the confluent hypergeometric
                 function in terms of modified {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "78",
  number =       "1",
  pages =        "97--101",
  day =          "3",
  month =        feb,
  year =         "1997",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:59 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796001331",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Alzer:1997:HMI,
  author =       "Horst Alzer",
  title =        "A harmonic mean inequality for the gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "87",
  number =       "2",
  pages =        "195--198",
  day =          "23",
  month =        dec,
  year =         "1997",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:06 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  note =         "See corrigendum \cite{Alzer:1998:CHM}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796001811",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Alzer:1997:SIG,
  author =       "Horst Alzer",
  title =        "On some inequalities for the gamma and psi functions",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "217",
  pages =        "373--389",
  month =        jan,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33B15 (26D07)",
  MRnumber =     "97e:33004",
  MRreviewer =   "Peter Schroth",
  bibdate =      "Fri Jul 16 10:38:40 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1997-66-217;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00807-7&u=/mcom/1997-66-217/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Alzer:1997:SII,
  author =       "Horst Alzer",
  title =        "On some inequalities for the incomplete gamma
                 function",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "218",
  pages =        "771--778",
  month =        apr,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33B20 (26D07)",
  MRnumber =     "97h:33004",
  bibdate =      "Fri Jul 16 10:38:42 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1997-66-218;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00814-4&u=/mcom/1997-66-218/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Bailey:1997:RCV,
  author =       "David Bailey and Peter Borwein and Simon Plouffe",
  title =        "On the rapid computation of various polylogarithmic
                 constants",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "218",
  pages =        "903--913",
  month =        apr,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Yxx",
  MRnumber =     "1 415 794",
  bibdate =      "Fri Jul 16 10:38:42 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1997-66-218;
                 http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  URL =          "http://www.ams.org/journals/mcom/1997-66-218/S0025-5718-97-00856-9/S0025-5718-97-00856-9.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "BBP formula",
  xxnote =       "See \cite{Adamchik:1997:SF}.",
}

@Article{Blinn:1997:JBC,
  author =       "James F. Blinn",
  title =        "{Jim Blinn}'s Corner: Floating-Point Tricks",
  journal =      j-IEEE-CGA,
  volume =       "17",
  number =       "4",
  pages =        "80--84",
  month =        jul # "\slash " # aug,
  year =         "1997",
  CODEN =        "ICGADZ",
  DOI =          "https://doi.org/10.1109/38.595279",
  ISSN =         "0272-1716 (print), 1558-1756 (electronic)",
  ISSN-L =       "0272-1716",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Discusses use of IEEE 754 single-precision
                 floating-point bit patterns as integers for
                 implementations of fast, but low-accuracy, functions
                 useful in computer graphics.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Computer Graphics and Applications",
  journal-URL =  "http://www.computer.org/portal/web/csdl/magazines/cga",
  summary =      "The author discusses IEEE floating point
                 representation that stores numbers in what amounts to
                 scientific notation. He considers the sign bit, the
                 logarithm function, function approximations, errors and
                 refinements \ldots{}",
}

@InCollection{Borwein:1997:AGMa,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  crossref =     "Berggren:1997:PSB",
  pages =        "537--552",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-1-4757-2736-4_56",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprint of \cite{Borwein:1984:AGM}.",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_56",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}

@Article{Bshouty:1997:TBA,
  author =       "Nader H. Bshouty and Yishay Mansour and Baruch
                 Schieber and Prasoon Tiwari",
  title =        "A tight bound for approximating the square root",
  journal =      j-INFO-PROC-LETT,
  volume =       "63",
  number =       "4",
  pages =        "211--213",
  day =          "10",
  month =        sep,
  year =         "1997",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68Q25 (65B15 68Q40)",
  MRnumber =     "1 477 306",
  bibdate =      "Sat Nov 7 17:55:54 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@Article{El-Gabali:1997:MTA,
  author =       "Magdi A. El-Gabali",
  title =        "Multiple-term approximations for {Appell}'s {$ F_1 $}
                 function",
  journal =      j-J-AUSTRAL-MATH-SOC-SER-B,
  volume =       "39",
  number =       "1",
  pages =        "135--148",
  month =        jul,
  year =         "1997",
  CODEN =        "JAMMDU",
  DOI =          "https://doi.org/10.1017/S0334270000009267",
  ISSN =         "0334-2700",
  ISSN-L =       "0334-2700",
  bibdate =      "Fri Apr 26 16:13:39 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/anziamj.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.cambridge.org/core/journals/anziam-journal/article/multipleterm-approximations-for-appells-f1-function/8E218109899D68FD0DC15B6E9D61E8BD",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Austral Math. Soc. Ser. B",
  fjournal =     "Journal of the Australian Mathematical Society. Series
                 B, Applied Mathematics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
  onlinedate =   "17 February 2009",
}

@Article{Fdil:1997:SRC,
  author =       "A. Fdil",
  title =        "Some results of convergence acceleration for a general
                 {$ \Theta $}-type algorithm",
  journal =      j-APPL-NUM-MATH,
  volume =       "23",
  number =       "2",
  pages =        "219--240",
  day =          "21",
  month =        mar,
  year =         "1997",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65B10 (65D32)",
  MRnumber =     "1 437 884",
  bibdate =      "Wed Jul 28 14:36:42 MDT 1999",
  bibsource =    "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1997&volume=23&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.com/cas/tree/store/apnum/sub/1997/23/2/738.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}

@Article{Forrey:1997:CHF,
  author =       "Robert C. Forrey",
  title =        "Computing the hypergeometric function",
  journal =      j-J-COMPUT-PHYS,
  volume =       "137",
  number =       "1",
  pages =        "79--100",
  month =        oct,
  year =         "1997",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1006/jcph.1997.5794",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  MRclass =      "33C05 (33-04 65D20)",
  MRnumber =     "MR1481885 (99g:33004)",
  bibdate =      "Thu Dec 01 09:06:55 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
  remark =       "The author gives a FORTRAN program for computing $_2
                 F_1$ for real variable and parameters, using
                 rapidly-convergent power series in six separate
                 intervals.",
}

@Article{Ghanem:1997:SBF,
  author =       "Riadh Ben Ghanem and Cl{\'e}ment Frappier",
  title =        "Spherical {Bessel} functions and explicit quadrature
                 formula",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "217",
  pages =        "289--296",
  month =        jan,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33C10 (41A55 65D32)",
  MRnumber =     "97c:33005",
  MRreviewer =   "N. Hayek Calil",
  bibdate =      "Fri Jul 16 10:38:40 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1997-66-217;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00794-1&u=/mcom/1997-66-217/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Goano:1997:RA7,
  author =       "Michele Goano",
  title =        "Remark on {Algorithm 745}",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "295--295",
  month =        jun,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/264029.643581",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 9 10:19:38 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Goano:1995:ACC}.",
  acknowledgement = ack-rfb # " and " # ack-kr # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hare:1997:CPB,
  author =       "D. E. G. Hare",
  title =        "Computing the Principal Branch of {log-Gamma}",
  journal =      j-J-ALG,
  volume =       "25",
  number =       "2",
  pages =        "221--236",
  month =        nov,
  year =         "1997",
  CODEN =        "JOALDV",
  DOI =          "https://doi.org/10.1006/jagm.1997.0881",
  ISSN =         "0196-6774 (print), 1090-2678 (electronic)",
  ISSN-L =       "0196-6774",
  bibdate =      "Tue Dec 11 09:16:52 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jalg.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0196677497908816",
  abstract =     "The log-Gamma function is an important special
                 function of mathematics, and its principal branch is
                 required in many applications. We develop here the
                 mathematics required to evaluate the principal branch
                 to arbitrary precision, including a new bound for the
                 error in Stirling's asymptotic series. We conclude with
                 a discussion of the implementation of the principal
                 branch of the log-Gamma function in the Maple symbolic
                 algebra system, starting with version Maple V, Release
                 3.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Algorithms",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01966774",
}

@Article{Harris:1997:NAC,
  author =       "Frank E. Harris",
  title =        "New Approach to Calculation of the Leaky Aquifer
                 Function",
  journal =      j-IJQC,
  volume =       "63",
  number =       "5",
  pages =        "913--916",
  month =        "????",
  year =         "1997",
  CODEN =        "IJQCB2",
  DOI =          "https://doi.org/10.1002/(SICI)1097-461X(1997)63:5<913::AID-QUA1>3.0.CO%3B2-Z",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Tue Oct 4 06:59:09 MDT 2011",
  bibsource =    "Compendex database;
                 http://www.interscience.wiley.com/jpages/0020-7608;
                 http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib",
  URL =          "http://www3.interscience.wiley.com/cgi-bin/abstract?ID=42641;
                 http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=42641&PLACEBO=IE.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Quantum Chem.",
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  journalabr =   "Int J Quant Chem",
  onlinedate =   "6 Dec 1998",
}

@Article{Ito:1997:EIA,
  author =       "M. Ito and N. Takagi and S. Yajima",
  title =        "Efficient initial approximation for multiplicative
                 division and square root by a multiplication with
                 operand modification",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "4",
  pages =        "495--498",
  month =        apr,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.588066",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588066",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "An efficient initial approximation method for
                 multiplicative division and square root is proposed. It
                 is a modification of the piecewise linear
                 approximation. The multiplication and the addition
                 required for the linear approximation are replaced by
                 \ldots{}",
}

@Article{Karp:1997:HPD,
  author =       "Alan H. Karp and Peter Markstein",
  title =        "High-Precision Division and Square Root",
  journal =      j-TOMS,
  volume =       "23",
  number =       "4",
  pages =        "561--589",
  month =        dec,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/279232.279237",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Nov 8 14:50:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/articles/journals/toms/forthcoming/a0-karp/a0-karp.ps;
                 http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p561-karp/",
  abstract =     "We present division and square root algorithms for
                 calculation with more bits than are handled by the
                 floating-point hardware. These algorithms avoid the
                 need to multiply two high-precision numbers, speeding
                 up the last iteration by as much as a factor of 10. We
                 also show how to produce the floating-point number
                 closest to the exact result with relatively few
                 additional operations.",
  accepted =     "June 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance, division, quad precision,
                 square root.",
  subject =      "G.1.0 [Numerical Analysis]: General -- computer
                 arithmetic. G.4 [Mathematics of Computing]:
                 Mathematical Software.",
}

@Article{Kolbig:1997:TEH,
  author =       "K. S. K{\"o}lbig",
  title =        "Table errata: {{\booktitle{Handbook of elliptic
                 integrals for engineers and scientists}} [Second
                 edition, Springer, New York, 1971, MR {\bf 43} \#3506]
                 by P. F. Byrd and M. D. Friedman}",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "220",
  pages =        "1767--1767",
  month =        oct,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "44-00 (33-00)",
  MRnumber =     "1 434 945",
  bibdate =      "Tue Dec 2 11:25:56 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Lee:1997:PRF,
  author =       "M. Howard Lee",
  title =        "Polylogarithms and {Riemann}'s $ \zeta $ function",
  journal =      j-PHYS-REV-E,
  volume =       "56",
  number =       "4",
  pages =        "3909--3912",
  month =        oct,
  year =         "1997",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/physreve.56.3909",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://doi.org/10.1103/physreve.56.3909",
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  remark =       "The paper presents increasingly complicated closed
                 forms of $ \Li_n(x) $ for negative $n$ to $ n = - 8$,
                 and reports that no general form for negative $n$ is
                 apparent. See https://oeis.org/A131758 for related
                 functions and sequences. Maple and Mathematica can
                 produce such formulas with code like
                 simplify(expand(polylog(-13,x))) and PolyLog[-13, x].",
}

@Article{Lether:1997:CNM,
  author =       "Frank G. Lether",
  title =        "Constrained near-minimax rational approximations to
                 {Dawson}'s integral",
  journal =      j-APPL-MATH-COMP,
  volume =       "88",
  number =       "2--3",
  pages =        "267--274",
  day =          "30",
  month =        dec,
  year =         "1997",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/S0096-3003(96)00330-X",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Nov 20 21:02:59 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S009630039600330X",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@InProceedings{Li:1997:ISP,
  author =       "Yamin Li and Wanming Chu",
  booktitle =    "Proceedings of the 5th Annual {IEEE} Symposium on
                 {FPGAs} for Custom Computing Machines, 16--18 April
                 1997",
  title =        "Implementation of single precision floating point
                 square root on {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "226--232",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The square root operation is hard to implement on
                 FPGAs because of the complexity of the algorithms. In
                 this paper, we present a non-restoring square root
                 algorithm and two very simple single precision floating
                 point square root implementations \ldots{}",
}

@InProceedings{Li:1997:PAI,
  author =       "Yamin Li and Wanming Chu",
  booktitle =    "Proceedings of the 1997 {IEEE} International
                 Conference on Computer Design: {VLSI} in Computers and
                 Processors: {ICCD '97}",
  title =        "Parallel-array implementations of a non-restoring
                 square root algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "690--695",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "In this paper we present a parallel-array
                 implementation of a new non-restoring square root
                 algorithm (PASQRT). The carry-save adder (CSA) is used
                 in the parallel array. The PASQRT has several features
                 unlike other implementations. First, it does \ldots{}",
}

@InCollection{Lozier:1997:PST,
  author =       "Daniel W. Lozier",
  title =        "A Proposed Software Test Service for Special
                 Functions",
  crossref =     "Boisvert:1997:QNS",
  pages =        "167--178",
  year =         "1997",
  bibdate =      "Fri Jul 09 06:00:46 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "See preprint \cite{Lozier:1996:PST}.",
}

@TechReport{Lozier:1997:TRN,
  author =       "Daniel W. Lozier",
  title =        "Toward a Revised {NBS} Handbook of Mathematical
                 Functions",
  type =         "Technical Report",
  number =       "NISTIR 6072",
  institution =  pub-NIST,
  address =      pub-NIST:adr,
  pages =        "8",
  month =        sep,
  year =         "1997",
  bibdate =      "Fri Jul 09 06:35:07 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir6072.ps.gz",
  acknowledgement = ack-nhfb,
}

@Article{MacLeod:1997:AEE,
  author =       "Allan J. MacLeod",
  title =        "Accurate and efficient evaluation of the
                 {Bose--Einstein} functions $ g_{3 / 2} $ and $ g_{5 /
                 2} $",
  journal =      j-COMPUT-PHYS,
  volume =       "11",
  number =       "4",
  pages =        "385--??",
  month =        jul,
  year =         "1997",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168609",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:46:08 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168609",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}

@InProceedings{Matsubara:1997:LPZ,
  author =       "G. Matsubara and N. Ide",
  booktitle =    "Proceedings of the Third International Symposium on
                 Advanced Research in Asynchronous Circuits and Systems,
                 7--10 April 1997",
  title =        "A low power zero-overhead self-timed division and
                 square root unit combining a single-rail static circuit
                 with a dual-rail dynamic circuit",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "198--209",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "An asynchronous pipeline scheme that combines a low
                 power static circuit with a high-speed dual-rail
                 dynamic circuit is proposed. The scheme utilizes a
                 dual-rail circuit only in the critical path of an SRT
                 division and square root calculation unit. \ldots{}",
}

@Book{Muller:1997:EFA,
  author =       "Jean-Michel Muller",
  title =        "Elementary functions: algorithms and implementation",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "xv + 204",
  year =         "1997",
  ISBN =         "0-8176-3990-X",
  ISBN-13 =      "978-0-8176-3990-7",
  LCCN =         "QA331.M866 1997",
  bibdate =      "Fri Jul 25 12:00:55 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  price =        "US\$59.95",
  URL =          "http://www.birkhauser.com/cgi-win/ISBN/0-8176-3990-X;
                 http://www.ens-lyon.fr/~jmmuller/book_functions.html",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schulte:1997:AFA,
  author =       "M. J. Schulte and James E. Stine",
  title =        "Accurate Function Approximations by Symmetric Table
                 Lookup and Addition",
  crossref =     "Thiele:1997:IIC",
  pages =        "144--153",
  year =         "1997",
  bibdate =      "Sun Mar 04 10:55:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1997-02.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schulte:1997:SBT,
  author =       "M. Schulte and J. Stine",
  title =        "Symmetric Bipartite Tables for Accurate Function
                 Approximation",
  crossref =     "Lang:1997:ISC",
  pages =        "175--183",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1997-01.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Segura:1997:CEM,
  author =       "J. Segura and P. Fern{\'a}ndez de C{\'o}rdoba and Yu.
                 L. Ratis",
  title =        "A code to evaluate modified {Bessel} functions based
                 on the continued fraction method",
  journal =      j-COMP-PHYS-COMM,
  volume =       "105",
  number =       "2--3",
  pages =        "263--272",
  day =          "1",
  month =        oct,
  year =         "1997",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(97)00069-6",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:19 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465597000696",
  abstract =     "We present an algorithm to evaluate the modified
                 Bessel functions $ I \_ n u $ and $ K_\nu $ of integral
                 and half-integral order based on the calculation of the
                 continued fraction for the $ I \_ n u $'s, the
                 Wronskian and the application of forward recurrence
                 relations for the $ K_\nu $'s and backward recurrence
                 for the $ I \_ n u $'s. The main feature of the
                 algorithm is that it does not require recalculations
                 using normalization relations nor trial values to start
                 the recurrences; the code evaluates in each step
                 (already normalized) Bessel functions. The accuracy of
                 the method ($ 10^{-16} $ for half-integral order and
                 better than $ 2 \times 10^{-7} $ for integral order in
                 our code) is limited only by the precision in the
                 initial values for the recurrence and the maximum order
                 available for a given value of the argument is
                 restricted only by the maximum real number available in
                 the computer.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Soderquist:1997:DSR,
  author =       "Peter Soderquist and Miriam Leeser",
  title =        "Division and Square Root: Choosing the Right
                 Implementation: Exploring the major design choices for
                 microprocessor implementations of floating-point
                 division and square root",
  journal =      j-IEEE-MICRO,
  volume =       "17",
  number =       "4",
  pages =        "56--66",
  month =        jul # "\slash " # aug,
  year =         "1997",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.612224",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
                 Science Citation Index database (1980--2000)",
  URL =          "http://pascal.computer.org/mi/books/mi1997/pdf/m4056.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@Book{Thompson:1997:ACMa,
  author =       "William J. (William Jackson) Thompson",
  title =        "Atlas for computing mathematical functions: an
                 illustrated guidebook for practitioners: with programs
                 in {C} and {Mathematica}",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiv + 903",
  year =         "1997",
  ISBN =         "0-471-00260-7 (cloth)",
  ISBN-13 =      "978-0-471-00260-4 (cloth)",
  LCCN =         "QA331.T385 1997",
  bibdate =      "Fri May 21 07:11:19 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  annote =       "A Wiley-Interscience publication. Includes CD-ROM.",
  keywords =     "C (Computer program language); Functions -- Computer
                 programs; Mathematica (Computer program language);
                 Science -- Mathematics -- Computer programs",
}

@Book{Thompson:1997:ACMb,
  author =       "William J. (William Jackson) Thompson",
  title =        "Atlas for computing mathematical functions: an
                 illustrated guide for practitioners with programs in
                 {Fortran 90} and {Mathematica}",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiv + 888",
  year =         "1997",
  ISBN =         "0-471-18171-4 (cloth)",
  ISBN-13 =      "978-0-471-18171-2 (cloth)",
  LCCN =         "QA331.T386 1997",
  bibdate =      "Fri May 21 07:11:19 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Includes CD-ROM.",
  acknowledgement = ack-nhfb,
  annote =       "A Wiley-Interscience publication. System requirements
                 for accompanying computer disc: Windows; Macintosh
                 compatible.",
  keywords =     "FORTRAN (Computer program language); Functions --
                 Computer programs; Mathematica (Computer program
                 language); Science -- Mathematics -- Computer
                 programs",
}

@Book{Yoshida:1997:HFM,
  author =       "Masaaki Yoshida",
  title =        "Hypergeometric functions, my love: modular
                 interpretations of configuration spaces",
  volume =       "E 32",
  publisher =    pub-VIEWEG,
  address =      pub-VIEWEG:adr,
  pages =        "xvi + 292",
  year =         "1997",
  ISBN =         "3-528-06925-2",
  ISBN-13 =      "978-3-528-06925-4",
  ISSN =         "0179-2156",
  LCCN =         "QA353.H9 Y67 1997",
  bibdate =      "Sat Oct 30 21:12:24 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Aspects of mathematics",
  acknowledgement = ack-nhfb,
  subject =      "Hypergeometric functions; Configuration space",
}

@Article{Yousif:1997:BFF,
  author =       "Hashim A. Yousif and Richard Melka",
  title =        "{Bessel} function of the first kind with complex
                 argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "106",
  number =       "3",
  pages =        "199--206",
  month =        nov,
  year =         "1997",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(97)00087-8",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:21 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465597000878",
  abstract =     "A new method of computing integral order Bessel
                 functions of the first kind $ J_n(z) $ when either the
                 absolute value of the real part or the imaginary part
                 of the argument $ z = x + i y $ is small, is described.
                 This method is based on computing the Bessel functions
                 from asymptotic expressions when $ x \sim 0 $ (or $ y
                 \sim 0 $ ). These expansions are derived from the
                 integral definition of Bessel functions. This method is
                 necessary because some existing algorithms and methods
                 fail to give correct results for small $x$ or small
                 $y$. In addition, our overall method of computing
                 Bessel functions of any order and argument is discussed
                 and the logarithmic derivative is used in computing
                 these functions. The starting point of the backward
                 recurrence relations needed to evaluate the Bessel
                 function and their logarithmic derivatives are
                 investigated in order to obtain accurate numerical
                 results. Our numerical method, together with
                 established techniques of computing the Bessel
                 functions, is easy to implement, efficient, and
                 produces reliable results for all $z$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Zhang:1997:CSA,
  author =       "Jun Zhang and John A. Belward",
  title =        "{Chebyshev} series approximations for the {Bessel}
                 function {$ Y_n(z) $} of complex argument",
  journal =      j-APPL-MATH-COMP,
  volume =       "88",
  number =       "2--3",
  pages =        "275--286",
  day =          "30",
  month =        dec,
  year =         "1997",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/S0096-3003(96)00335-9",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Nov 20 21:02:59 MST 2012",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300396003359",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Aberbour:1998:PMF,
  author =       "M. Aberbour and A. Houelle and H. Mehrez and N.
                 Vaucher and A. Guyot",
  title =        "On portable macrocell {FPU} generators for division
                 and square root operators complying to the full
                 {IEEE-754} standard",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "6",
  number =       "1",
  pages =        "114--121",
  month =        mar,
  year =         "1998",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/92.661253",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  summary =      "In this paper, we investigate the design of macrocell
                 generators of division and square root floating-point
                 operators. The number representation used in our
                 operators is the IEEE-754-1985 standard for binary
                 floating-point numbers. The design and \ldots{}",
}

@Article{Adamchik:1998:PFN,
  author =       "Victor S. Adamchik",
  title =        "{Polygamma} functions of negative order",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "100",
  number =       "2",
  pages =        "191--199",
  day =          "21",
  month =        dec,
  year =         "1998",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:39:42 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042798001927",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Alzer:1998:CHM,
  author =       "Horst Alzer",
  title =        "Corrigendum: {A harmonic mean inequality for the gamma
                 function [J. Comput. Appl. Math. {\bf 87} (1997)
                 195--198]}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "90",
  number =       "2",
  pages =        "265--265",
  day =          "17",
  month =        apr,
  year =         "1998",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(98)00040-5",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:08 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  note =         "See \cite{Alzer:1997:HMI}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042798000405",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Book{Andrews:1998:SFM,
  author =       "Larry C. Andrews",
  title =        "Special functions of mathematics for engineers",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  edition =      "Second",
  pages =        "xvii + 479",
  year =         "1998",
  ISBN =         "0-19-856558-5 (Oxford hardcover), 0-8194-2616-4 (SPIE
                 Press hardcover)",
  ISBN-13 =      "978-0-19-856558-1 (Oxford hardcover),
                 978-0-8194-2616-1 (SPIE Press)",
  LCCN =         "QA351 .A75 1998",
  bibdate =      "Sat Oct 30 16:44:00 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 library.ox.ac.uk:210/ADVANCE;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Originally published: New York : McGraw-Hill, c1992.",
  subject =      "Functions, Special",
  tableofcontents = "Preface to the Second Edition \\
                 Preface to the First Edition \\
                 Notation for Special Functions \\
                 Infinite Series, Improper Integrals, and Infinite
                 Products \\
                 The Gamma Function and Related Functions \\
                 Other Functions Defined by Integrals \\
                 Legendre Polynomials and Related Functions \\
                 Other Orthogonal Polynomials \\
                 Bessel Functions \\
                 Bessel Functions of Other Kinds \\
                 Applications Involving Bessel Functions \\
                 The Hypergeometric Function \\
                 The Confluent Hypergeometric Functions \\
                 Generalized Hypergeometric Functions \\
                 Applications Involving Hypergeometric-Type Functions
                 \\
                 Bibliography \\
                 Appendix: A List of Special Function Formulas \\
                 Selected Answers to Exercises \\
                 Index",
}

@Book{Anonymous:1998:AMS,
  editor =       "Anonymous",
  title =        "Analytical methods and special functions",
  publisher =    "Gordon and Breach Science Publishers",
  address =      "Amsterdam, The Netherlands",
  pages =        "????",
  year =         "1998",
  ISSN =         "1027-0264",
  LCCN =         "A299.6 A533 v. 1 1998",
  bibdate =      "Sat Oct 30 19:02:18 2010",
  bibsource =    "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Antelo:1998:CVH,
  author =       "E. Antelo and T. Lang and J. D. Bruguera",
  title =        "Computation of $ \sqrt {(x / d)} $ in a very high
                 radix combined division\slash square-root unit with
                 scaling and selection by rounding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "2",
  pages =        "152--161",
  month =        feb,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.663761",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:53 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663761",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A very-high radix digit-recurrence algorithm for the
                 operation {\surd}(x/d) is developed, with residual
                 scaling and digit selection by rounding. This is an
                 extension of the division and square-root algorithms
                 presented previously, and for which a \ldots{}",
}

@Article{BenGhanem:1998:QFU,
  author =       "Riadh {Ben Ghanem}",
  title =        "Quadrature formulae using zeros of {Bessel} functions
                 as nodes",
  journal =      j-MATH-COMPUT,
  volume =       "67",
  number =       "221",
  pages =        "323--336",
  month =        jan,
  year =         "1998",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D32",
  MRnumber =     "98c:65031",
  MRreviewer =   "Kai Diethelm",
  bibdate =      "Fri Jul 16 10:38:50 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1998-67-221;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00882-5&u=/mcom/1998-67-221/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@TechReport{Borwein:1998:CSR,
  author =       "Jonathan M. Borwein and David M. Bradley and Richard
                 E. Crandall",
  title =        "Computational Strategies for the {Riemann} Zeta
                 Function",
  type =         "Report",
  number =       "CECM-98-118",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "68",
  day =          "30",
  month =        oct,
  year =         "1998",
  bibdate =      "Mon Oct 24 11:29:15 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Published in \cite{Borwein:2000:CSR}.",
  URL =          "http://docserver.carma.newcastle.edu.au/211;
                 http://people.reed.edu/~crandall/papers/attach01.pdf",
  abstract =     "We provide a compendium of evaluation methods for the
                 Riemann zeta function, presenting formulae ranging from
                 historical attempts to recently found convergent series
                 to curious oddities old and new. We concentrate
                 primarily on practical computational issues, such
                 issues depending on the domain of the argument, the
                 desired speed of computation, and the incidence of what
                 we call ``value recycling.''",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August 2016);
                 Richard Eugene Crandall (29 December 1947--20 December
                 2012)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}

@InCollection{Buhring:1998:ACG,
  author =       "Wolfgang B{\"u}hring and H. M. Srivastava",
  editor =       "Themistocles M. Rassias",
  booktitle =    "Approximation theory and applications",
  title =        "Analytic Continuation of the Generalized
                 Hypergeometric Series Near Unit Argument with Emphasis
                 on the Zero-Balanced Series",
  publisher =    "Hadronic Press",
  address =      "Palm Harbor, FL, USA",
  bookpages =    "v + 193",
  pages =        "17--35",
  year =         "1998",
  ISBN =         "1-57485-041-5",
  ISBN-13 =      "978-1-57485-041-3",
  LCCN =         "QA297.5 .A685 1998",
  MRclass =      "33C20; 41-06 (00B15)",
  MRnumber =     "MR1924838 (2003i:33006); MR1924835 (2003c:41003)",
  bibdate =      "Thu Dec 01 10:08:00 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://catalog.hathitrust.org/api/volumes/oclc/42786578.html",
  acknowledgement = ack-nhfb,
  remark =       "The paper treats $_{p + 1F}_p(z)$ for $ z \approx 1 $.
                 Available as arxiv:math/0102032.",
}

@Article{Carsky:1998:IGF,
  author =       "Petr C{\'a}rsky and Martin Pol{\'a}sek",
  title =        "Incomplete Gamma {$ F_m(x) $} Functions for Real
                 Negative and Complex Arguments",
  journal =      j-J-COMPUT-PHYS,
  volume =       "143",
  number =       "1",
  pages =        "259--265",
  day =          "10",
  month =        jun,
  year =         "1998",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1006/jcph.1998.5975",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:55:26 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0021999198959757",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Cornea-Hasegan:1998:PIC,
  author =       "Marius Cornea-Hasegan",
  title =        "Proving the {IEEE} Correctness of Iterative
                 Floating-Point Square Root, Divide, and Remainder
                 Algorithms",
  journal =      j-INTEL-TECH-J,
  volume =       "Q2",
  number =       "Q2",
  pages =        "11",
  year =         "1998",
  ISSN =         "1535-766X",
  bibdate =      "Fri Jun 01 06:02:08 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://developer.intel.com/technology/itj/q21998/articles/art_3.htm;
                 http://developer.intel.com/technology/itj/q21998/pdf/ieee.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Crenshaw:1998:ISR,
  author =       "Jack W. Crenshaw",
  title =        "Integer Square Roots",
  journal =      j-EMBED-SYS-PROG,
  volume =       "11",
  number =       "2",
  pages =        "15--32",
  month =        feb,
  year =         "1998",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Fri Nov 28 16:31:58 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.embedded.com/98/9802fe2.htm",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Embedded Systems Programming",
}

@Article{Dattoli:1998:GBF,
  author =       "G. Dattoli and A. Torre and S. Lorenzutta and G.
                 Maino",
  title =        "Generalized {Bessel} functions and {Kapteyn} series",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "35",
  number =       "8",
  pages =        "117--125",
  month =        apr,
  year =         "1998",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122198000509",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Deleglise:1998:C,
  author =       "Marc Del{\'e}glise and Jo{\"e}l Rivat",
  title =        "Computing $ \psi (x) $",
  journal =      j-MATH-COMPUT,
  volume =       "67",
  number =       "224",
  pages =        "1691--1696",
  month =        oct,
  year =         "1998",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y35 (11N56)",
  MRnumber =     "1 474 649",
  bibdate =      "Fri Jul 16 10:38:58 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1998-67-224;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00977-6&u=/mcom/1998-67-224/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Fowler:1998:SRA,
  author =       "David Fowler and Eleanor Robson",
  title =        "Square Root Approximations in Old {Babylonian}
                 Mathematics: {YBC 7289} in Context",
  journal =      j-HIST-MATH,
  volume =       "25",
  number =       "4",
  pages =        "366--378",
  month =        nov,
  year =         "1998",
  CODEN =        "HIMADS",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Jun 26 06:19:31 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0315086098922091",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
}

@Article{Giordano:1998:UTG,
  author =       "C. Giordano and A. Laforgia and J. Pecari{\'c}",
  title =        "Unified treatment of {Gautschi--Kershaw} type
                 inequalities for the gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "99",
  number =       "1--2",
  pages =        "167--175",
  day =          "16",
  month =        nov,
  year =         "1998",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:13 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704279800154X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Harris:1998:MAL,
  author =       "Frank E. Harris",
  title =        "More About the Leaky Aquifer Function",
  journal =      j-IJQC,
  volume =       "70",
  number =       "4--5",
  pages =        "623--626",
  month =        "????",
  year =         "1998",
  CODEN =        "IJQCB2",
  DOI =          "https://doi.org/10.1002/(SICI)1097-461X(1998)70:4/5<623::AID-QUA8>3.0.CO%3B2-X",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Tue Oct 4 06:59:18 MDT 2011",
  bibsource =    "http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib",
  URL =          "http://www3.interscience.wiley.com/cgi-bin/abstract?ID=75040;
                 http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=75040&PLACEBO=IE.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Quantum Chem.",
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  onlinedate =   "7 Dec 1998",
}

@Article{Homeier:1998:AHC,
  author =       "Herbert H. H. Homeier",
  title =        "An asymptotically hierarchy-consistent, iterative
                 sequence transformation for convergence acceleration of
                 {Fourier} series",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "18",
  number =       "1",
  pages =        "1--30",
  month =        sep,
  year =         "1998",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Sep 29 08:36:54 MDT 2003",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/13/2/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/13/2/fulltext.pdf;
                 http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA972",
  ZMnumber =     "914.65140",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "convergence acceleration",
  tech =         "Technical Report TC-NA-97-2, Institut f{\"u}r
                 {Physikalische} und {Theoretische Chemie,
                 Universit{\"a}t Regensburg, D-93040 Regensburg}, 1997",
}

@Article{Homeier:1998:CAM,
  author =       "H. H. H. Homeier",
  title =        "On Convergence Acceleration of Multipolar and
                 Orthogonal Expansions",
  journal =      j-INTERNET-J-CHEM,
  volume =       "1",
  number =       "Article 28",
  pages =        "????",
  year =         "1998",
  CODEN =        "IJCHFJ",
  ISSN =         "1099-8292",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the {4$^{th}$ Electronic Computational
                 Chemistry Conference}.",
  URL =          "http://www.ijc.com/articles/1998v1/28/",
  fjournal =     "Internet Journal of Chemistry",
  keywords =     "convergence acceleration",
  tech =         "Technical Report TC-QM-97-5, Institut f{\"u}r
                 {Physikalische} und {Theoretische Chemie,
                 Universit{\"a}t Regensburg, D-93040 Regensburg}, 1997",
}

@Article{Jukic:1998:DTN,
  author =       "D. Juki{\'c} and T. Maros{\v{s}}evi{\'c} and R.
                 Scitovski",
  title =        "Discrete total $ l_p $-norm approximation problem for
                 the exponential function",
  journal =      j-APPL-MATH-COMP,
  volume =       "94",
  number =       "2--3",
  pages =        "137--143",
  day =          "15",
  month =        aug,
  year =         "1998",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/S0096-3003(97)10068-6",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Nov 20 21:03:11 MST 2012",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300397100686",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Kiranon:1998:SRV,
  author =       "W. Kiranon and N. Kumprasert",
  title =        "Square-rooting and vector summation circuits using
                 current conveyors",
  journal =      "IEE Proceedings on Circuits, Devices and Systems [see
                 also IEE Proceedings G - Circuits, Devices and
                 Systems]",
  volume =       "145",
  number =       "2",
  pages =        "139",
  month =        apr,
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Recently, Lui [1995] presented a square-rooting
                 circuit using CCII, MOS transistors and a buffered
                 unity-gain inverting amplifier. It is interesting since
                 it finds various applications as described in his
                 paper. However, an error occurred in the \ldots{}",
}

@InBook{Knuth:1998:EP,
  author =       "Donald E. Knuth",
  title =        "Evaluation of polynomials",
  crossref =     "Knuth:1998:SA",
  chapter =      "4",
  pages =        "485--524",
  year =         "1998",
  bibdate =      "Fri Oct 20 11:29:58 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "number of multiplications to evaluate a polynomial",
  remark =       "This is the definitive treatment of the rearrangement
                 of polynomial coefficients to reduce the multiplication
                 count. See \cite{Todd:1955:MWN} and references therein
                 to early papers on the subject.",
}

@Article{Kramer:1998:PWC,
  author =       "W. Kramer",
  title =        "A priori worst case error bounds for floating-point
                 computations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "7",
  pages =        "750--756",
  month =        jul,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.709374",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See \cite{Tang:1992:TDI}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709374",
  abstract =     "A new technique for the a priori calculation of
                 rigorous error bounds for floating-point computations
                 is introduced. The theorems given in the paper combined
                 with interval arithmetic lead to the implementation of
                 reliable software routines, which enable the user to
                 compute the desired error bounds automatically by a
                 suitable computer program. As a prominent example, a
                 table-lookup algorithm for calculating the function $ e
                 x p(x) - 1 $ that has been published by P. T. P. Tang
                 (1992) is analyzed using these new tools. The result
                 shows the high quality of the new approach",
  acknowledgement = ack-nhfb,
  author-dates = "1952--2014 (WK)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kravanja:1998:ZMS,
  author =       "P. Kravanja and O. Ragos and M. N. Vrahatis and F. A.
                 Zafiropoulos",
  title =        "{ZEBEC}: a mathematical software package for computing
                 simple zeros of {Bessel} functions of real order and
                 complex argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "113",
  number =       "2--3",
  pages =        "220--238",
  month =        oct,
  year =         "1998",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(98)00064-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:30 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465598000642",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@InProceedings{Kuhlmann:1998:FLP,
  author =       "M. Kuhlmann and K. K. Parhi",
  booktitle =    "{Proceedings of the 1998 International Conference on
                 Computer Design: VLSI in Computers and Processors. ICCD
                 '98}",
  title =        "Fast low-power shared division and square-root
                 architecture",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "128--135",
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper addresses a fast low-power implementation
                 of a shared division and square-root architecture. Two
                 approaches are considered in this paper; these include
                 the SRT (Sweeney, Robertson and Tocher) approach which
                 does not require prescaling and \ldots{}",
}

@Article{Lefevre:1998:TCR,
  author =       "V. Lef{\`e}vre and J.-M. Muller and A. Tisserand",
  title =        "Toward correctly rounded transcendentals",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "11",
  pages =        "1235--1243",
  month =        nov,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.736435",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "The Table Maker's Dilemma is the problem of always
                 getting correctly rounded results when computing the
                 elementary functions. After a brief presentation of
                 this problem, we present new developments that have
                 helped us to solve this problem for the \ldots{}",
}

@Article{Lopez:1998:SSC,
  author =       "Jos{\'e}L. L{\'o}pez",
  title =        "Several series containing gamma and polygamma
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "90",
  number =       "1",
  pages =        "15--23",
  day =          "6",
  month =        apr,
  year =         "1998",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:07 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042798000077",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Miller:1998:CGI,
  author =       "Allen R. Miller and Ira S. Moskowitz",
  title =        "On certain generalized incomplete gamma functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "91",
  number =       "2",
  pages =        "179--190",
  day =          "4",
  month =        may,
  year =         "1998",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:08 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042798000314",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Morozov:1998:NWR,
  author =       "D. Kh. Morozov and V. V. Voitsekhovich",
  title =        "A new wide-range approximation of modified {Bessel}
                 functions in terms of elementary functions",
  journal =      "Rev. Mexicana F\'\i s.",
  volume =       "44",
  number =       "3",
  pages =        "231--234",
  year =         "1998",
  CODEN =        "RMXFAT",
  ISSN =         "0035-001X",
  MRclass =      "65D20",
  MRnumber =     "MR1629601",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Revista Mexicana de F\'\i sica",
}

@Article{Nguyen:1998:MLS,
  author =       "Phong Nguyen",
  title =        "A {Montgomery}-Like Square Root for the Number Field
                 Sieve",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1423",
  pages =        "151--??",
  year =         "1998",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:52:18 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1423.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1423/14230151.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1423/14230151.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Palumbo:1998:GSI,
  author =       "Biagio Palumbo",
  title =        "A generalization of some inequalities for the gamma
                 function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "88",
  number =       "2",
  pages =        "255--268",
  day =          "2",
  month =        mar,
  year =         "1998",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:06 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042797001878",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Qiu:1998:SIG,
  author =       "S.-L. Qiu and M. K. Vamanamurthy and M. Vuorinen",
  title =        "Some Inequalities for the Growth of Elliptic
                 Integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "29",
  number =       "5",
  pages =        "1224--1237",
  month =        sep,
  year =         "1998",
  CODEN =        "SJMAAH",
  DOI =          "https://doi.org/10.1137/S0036141096310491",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  bibdate =      "Sat Dec 5 14:39:16 MST 1998",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/29/5;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/31049",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@Article{Rivolo:1998:CDR,
  author =       "M. T. Rivolo and A. Simi",
  title =        "Il Calcolo delle Radici Quadrate e Cubiche in {Italia}
                 da {Fibonacci} a {Bombelli}. ({Italian}) [{The}
                 calculation of square and cube roots in {Italy} from
                 {Fibonacci} to {Bombelli}]",
  journal =      j-ARCH-HIST-EXACT-SCI,
  volume =       "52",
  number =       "2",
  pages =        "161--193",
  month =        feb,
  year =         "1998",
  CODEN =        "AHESAN",
  DOI =          "https://doi.org/10.1007/s004070050015",
  ISSN =         "0003-9519 (print), 1432-0657 (electronic)",
  ISSN-L =       "0003-9519",
  MRclass =      "01A35 (01A40)",
  MRnumber =     "1610136 (99d:01015)",
  MRreviewer =   "Massimo Galuzzi",
  bibdate =      "Fri Feb 4 21:50:33 MST 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=52&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=52&issue=2&spage=161",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for History of Exact Sciences",
  journal-URL =  "http://link.springer.com/journal/407",
  language =     "Italian",
  MRtitle =      "The computation of square and cube roots in {Italy}
                 from {Fibonacci} to {Bombelli}",
}

@Article{Russinoff:1998:MCP,
  author =       "David M. Russinoff",
  title =        "A Mechanically Checked Proof of {IEEE} Compliance of
                 the Floating Point Multiplication, Division and Square
                 Root Algorithms of the {AMD-K7} Processor",
  journal =      j-LMS-J-COMPUT-MATH,
  volume =       "1",
  pages =        "148--200",
  year =         "1998",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1112/S1461157000000176",
  ISSN =         "1461-1570",
  ISSN-L =       "1461-1570",
  MRclass =      "68M07 (65Y99 68T15)",
  MRnumber =     "99m:68015",
  MRreviewer =   "J. Michel Muller",
  bibdate =      "Fri Nov 29 08:13:48 2002",
  bibsource =    "http://journals.cambridge.org/action/displayJournal?jid=JCM;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lms-j-comput-math.bib",
  note =         "Appendices A and B available to subscribers
                 electronically
                 (http://www.lms.ac.uk/jcm/1/lms98001/appendix-a/ and
                 http://www.lms.ac.uk/jcm/1/lms98001/appendix-b/)",
  URL =          "http://www.lms.ac.uk/jcm/1/lms1998-001/",
  acknowledgement = ack-nhfb,
  ajournal =     "LMS J. Comput. Math.",
  fjournal =     "LMS Journal of Computation and Mathematics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=JCM",
  onlinedate =   "01 February 2010",
}

@Article{Segura:1998:PCF,
  author =       "J. Segura and A. Gil",
  title =        "Parabolic cylinder functions of integer and
                 half-integer orders for nonnegative arguments",
  journal =      j-COMP-PHYS-COMM,
  volume =       "115",
  number =       "1",
  pages =        "69--86",
  day =          "1",
  month =        dec,
  year =         "1998",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(98)00097-6",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:32 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465598000976",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Sidi:1998:UBC,
  author =       "Avram Sidi and Yair Shapira",
  title =        "Upper bounds for convergence rates of acceleration
                 methods with initial iterations",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "18",
  number =       "2",
  pages =        "113--132",
  month =        sep,
  year =         "1998",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Sep 29 08:36:55 MDT 2003",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/14/1/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/14/1/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "convergence acceleration",
}

@Article{Wei:1998:NFS,
  author =       "Liqiang Wei",
  title =        "New formula for $9$--$j$ symbols and their direct
                 calculation",
  journal =      j-COMPUT-PHYS,
  volume =       "12",
  number =       "6",
  pages =        "632--??",
  month =        nov,
  year =         "1998",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168745",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:46:17 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168745",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}

@InProceedings{Agarwal:1999:SAM,
  author =       "R. C. Agarwal and F. G. Gustavson and M. S.
                 Schmookler",
  title =        "Series approximation methods for divide and square
                 root in the {Power3{\TM}} processor",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "116--123",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-144.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-144.ps",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH; computer arithmetic; IEEE",
  summary =      "The Power3 processor is a 64-bit implementation of the
                 PowerPC TM architecture and is the successor to the
                 Power2 TM processor for workstations and servers which
                 REQUIRE high performance floating point capability. The
                 previous \ldots{}",
}

@Article{Alzer:1999:SPP,
  author =       "Horst Alzer and O. G. Ruehr",
  title =        "A submultiplicative property of the psi function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "101",
  number =       "1--2",
  pages =        "53--60",
  day =          "15",
  month =        jan,
  year =         "1999",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:39:42 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042798001903",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Book{Andrews:1999:SF,
  author =       "George E. Andrews and Richard Askey and Ranjan Roy",
  title =        "Special Functions",
  volume =       "71",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xvi + 664",
  year =         "1999",
  DOI =          "https://doi.org/10.1017/CBO9781107325937",
  ISBN =         "0-521-62321-9 (hardcover), 0-521-78988-5 (paperback),
                 1-107-32593-5 (e-book)",
  ISBN-13 =      "978-0-521-62321-6 (hardcover), 978-0-521-78988-2
                 (paperback), 978-1-107-32593-7 (e-book)",
  LCCN =         "QA351 .A74 1999",
  bibdate =      "Mon Sep 17 18:52:30 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$90.00 (hardcover), US\$34.95 (paperback)",
  series =       "Encyclopedia of mathematics and its applications",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special",
  tableofcontents = "Frontmatter / i--vi \\
                 Contents / vii--xii \\
                 Preface / xiii--xvi \\
                 1: The Gamma and Beta Functions / 1--60 \\
                 2: The Hypergeometric Functions / 61--123 \\
                 3: Hypergeometric Transformations and Identities /
                 124--186 \\
                 4: Bessel Functions and Confluent Hypergeometric
                 Functions / 187--239 \\
                 5: Orthogonal Polynomials / 240--276 \\
                 6: Special Orthogonal Polynomials / 277--354 \\
                 7: Topics in Orthogonal Polynomials / 355--400 \\
                 8: The Selberg Integral and Its Applications / 401--444
                 \\
                 9: Spherical Harmonics / 445--480 \\
                 10: Introduction to $q$-Series / 481--552 \\
                 11: Partitions / 553--576 \\
                 12: Bailey Chains / 577--594 \\
                 A: Infinite Products / 595--598 \\
                 B: Summability and Fractional Integration / 599--610
                 \\
                 C: Asymptotic Expansions / 611--616 \\
                 D: Euler--Maclaurin Summation Formula / 617--628 \\
                 E: Lagrange Inversion Formula / 629--636 \\
                 F: Series Solutions of Differential Equations /
                 637--640 \\
                 Bibliography / 641--654 \\
                 Index / 655--658 \\
                 Subject Index / 659--662 \\
                 Symbol Index / 663--664",
  xxURL =        "http://www.loc.gov/catdir/toc/cam024/98025757.html;
                 http://www.loc.gov/catdir/description/cam029/98025757.html",
}

@Article{Bach:1999:NTS,
  author =       "E. Bach and K. Huber",
  title =        "Note on taking square-roots modulo {$N$}",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "45",
  number =       "2",
  pages =        "807--809",
  month =        mar,
  year =         "1999",
  CODEN =        "IETTAW",
  DOI =          "https://doi.org/10.1109/18.749034",
  ISSN =         "0018-9448 (print), 1557-9654 (electronic)",
  ISSN-L =       "0018-9448",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Information Theory",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
  summary =      "In this article it is shown how Gauss' (1981) famous
                 cyclotomic sum formula can be used for extracting
                 square-roots modulo \ldots{}",
}

@InProceedings{Batten:1999:IBO,
  author =       "D. Batten and S. Jinturkar and J. Glossner and M.
                 Schulte and R. Peri and P. D'arcy",
  editor =       "????",
  booktitle =    "Proceedings of the International Conference on Signal
                 Processing Applications and Technologies, Orlando,
                 Florida, November, 1999",
  title =        "Interactions Between Optimizations and a New Type of
                 {DSP} Intrinsic Function",
  publisher =    "????",
  address =      "????",
  year =         "1999",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sun Mar 04 11:05:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Shortened version in \cite{Batten:1999:IFB}.",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-09.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Batten:1999:IFB,
  author =       "D. Batten and P. D'arcy",
  title =        "Intrinsic Functions Boost Compilers",
  journal =      "Electrical Engineering Times",
  volume =       "1085",
  pages =        "104--104",
  month =        nov,
  year =         "1999",
  bibdate =      "Sun Mar 04 11:06:22 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Beebe:1999:FAE,
  author =       "Nelson H. F. Beebe",
  title =        "Fast Approximate Exponential Functions",
  type =         "Report",
  institution =  inst-CSC,
  address =      inst-CSC:adr,
  day =          "7",
  month =        dec,
  year =         "1999",
  bibdate =      "Sat Feb 02 15:08:59 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This package contains software conforming to 1989
                 ANSI/ISO Standard C (ANSI X3.159-1989, ISO/IEC
                 9899-1990) and 1998 ISO Standard C++ (ISO/IEC
                 14882:1998) for testing an interesting algorithm for
                 fast approximate exp() functions, published in
                 \cite{Schraudolph:1999:FCA}. There is a font error in
                 figure 2 of that paper: all carets should be replaced
                 by underscore.",
  acknowledgement = ack-nhfb,
  remark =       "From the report: ``Schraudolph's formula for the
                 approximate exponential function computes $ a \times x
                 + b - c $ in floating-point arithmetic, then converts
                 it to a 32-bit integer which is stored in the
                 appropriate integer word overlaying the floating-point
                 representation. The entire cost is thus a
                 floating-point multiply and add (one instruction on
                 some RISC architectures), a conversion to an integer,
                 and a storage to memory.''",
}

@InCollection{Brezinski:1999:EEC,
  author =       "C. Brezinski",
  booktitle =    "Error control and adaptivity in scientific computing
                 ({Antalya}, 1998)",
  title =        "Error estimates and convergence acceleration",
  volume =       "536",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "87--94",
  year =         "1999",
  MRclass =      "65B05 (65D15)",
  MRnumber =     "1735125",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "NATO Sci. Ser. C Math. Phys. Sci.",
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
}

@InProceedings{Bui:1999:DSI,
  author =       "H. Bui and S. Tahar",
  booktitle =    "1999 {IEEE} Canadian Conference on Electrical and
                 Computer Engineering, 9--12 May 1999",
  title =        "Design and synthesis of an {IEEE-754} exponential
                 function",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "450--455",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 17:14:11 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We have designed a floating-point exponential function
                 using the table-driven method. The algorithm was first
                 implemented using sequential VHDL and later translated
                 to Concurrent Verilog. The main part of the work
                 consisted of creating modules that \ldots{}",
}

@Article{Cappuccino:1999:HSS,
  author =       "G. Cappuccino and G. Cocorullo and P. Corsonello and
                 S. Perri",
  title =        "High speed self-timed pipelined datapath for square
                 rooting",
  journal =      "IEE Proceedings on Circuits, Devices and Systems [see
                 also IEE Proceedings G --- Circuits, Devices and
                 Systems]",
  volume =       "146",
  number =       "1",
  pages =        "16--22",
  month =        feb,
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The authors describe a new high-performance self-timed
                 circuit for asynchronous square rooting. The new
                 architecture is based on a modified nonrestoring
                 algorithm. An asynchronous pipelined cellular array
                 without auxiliary system for the \ldots{}",
}

@Article{Carlson:1999:TSI,
  author =       "B. C. Carlson",
  title =        "Toward Symbolic Integration of Elliptic Integrals",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "28",
  number =       "6",
  pages =        "739--753",
  month =        dec,
  year =         "1999",
  CODEN =        "JSYCEH",
  DOI =          "https://doi.org/10.1006/jsco.1999.0336",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  bibdate =      "Tue Mar 7 11:48:04 MST 2000",
  bibsource =    "http://www.idealibrary.com/cgi-bin/links/toc/sy;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production;
                 http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production/pdf;
                 http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production/ref",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
}

@InProceedings{Cornea-Hasegan:1999:CPO,
  author =       "M. A. Cornea-Hasegan and R. A. Golliver and P.
                 Markstein",
  title =        "Correctness proofs outline for {Newton--Raphson} based
                 floating-point divide and square root algorithms",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "96--105",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-121.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-121.ps",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH; computer arithmetic; IEEE",
  summary =      "This paper describes a study of a class of algorithms
                 for the floating-point divide and square root
                 operations, based on the Newton--Raphson iterative
                 method. The two main goals were. (1) Proving the IEEE
                 correctness of these iterative floating-point
                 \ldots{}",
}

@Article{Corsonello:1999:HPS,
  author =       "P. Corsonello and S. Perri",
  title =        "High performance square rooting circuit using hybrid
                 radix-$2$ adders",
  journal =      j-ELECT-LETTERS,
  volume =       "35",
  number =       "3",
  pages =        "185--186",
  day =          "4",
  month =        feb,
  year =         "1999",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "A new high performance bit parallel architecture for
                 computing square roots is proposed. The architecture
                 implements a non-restoring algorithm and is structured
                 as a pipelined cellular array. To improve the
                 performance, hybrid radix-$2$ adders are \ldots{}",
}

@TechReport{DiDonato:1999:TFC,
  author =       "Armido R. DiDonato and Russ Gnoffo",
  title =        "Testing a {Fortran 90} Compiler Using the {NSWC
                 Fortran 77 Mathematics Library}",
  type =         "Technical Report",
  number =       "NSWCDD/TR-98/75",
  institution =  "Naval Surface Warfare Center",
  address =      "Dahlgren, VA 22448-5100, USA",
  pages =        "v + 64",
  month =        feb,
  year =         "1999",
  bibdate =      "Tue Jun 13 11:49:57 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  URL =          "https://apps.dtic.mil/sti/pdfs/ADA360604.pdf",
  abstract =     "This report describes the analysis and associated
                 Fortran program (TEST90) that were developed to aid in
                 establishing the validity of a new Fortran 90 mainframe
                 compiler. The FORTRAN 77 Naval Surface Warfare Center
                 (NSWC) Mathematics library (MLJB) is used as a source
                 of routines for checking the Fortran 90 compiler. At
                 the same time, this study can be considered as an aid
                 to determine whether MLIB can operate in a Fortran 90
                 environment. The inputs for the routines were chosen so
                 that many of the different possible paths of the
                 routines were executed. Seventy-four directly callable
                 routines, with 293 supporting routines, were chosen for
                 testing. All but 17, and their supporting routines,
                 were taken from MLIB. The ones not belonging to MLIB,
                 are double-precision versions of routines in MLIB.
                 Thirteen hundred and twenty five numerical cases were
                 submitted for testing. A true value for each test was
                 obtained independently and given correctly to 35 digits
                 by using MAPLE software. If the difference in the test
                 output and the corresponding true value exceeds a
                 prespecified error tolerance, an error message is
                 printed identifying the routine and the input
                 Additional test cases were also prepared to check the
                 bit and string instructions, since these do not appear
                 in MLIB.\par

                 TEST90 has been used to test the latest Fortran 90
                 compilers of the CRAY EL98 and IBM PC machines. No
                 errors were found; however, TEST90 did reveal a complex
                 arithmetic error in an earlier version of the Cray EL98
                 compiler. MLIB routines ran under TEST90 without any
                 problems on both machines.\par

                 The transportability of MLIB allows TEST90 to be used
                 as an aid in testing Fortran 90 compilers on a variety
                 of computers, with a single-precision word length no
                 larger than 64 bits.",
  acknowledgement = ack-nhfb,
}

@Article{Elbert:1999:SFZ,
  author =       "{\'A}rp{\'a}d Elbert and Panayiotis D. Siafarikas",
  title =        "On the Square of the First Zero of the {Bessel}
                 Function {$ J_\nu (z) $}",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "56--77",
  month =        mar,
  year =         "1999",
  CODEN =        "CMBUA3",
  DOI =          "https://doi.org/10.4153/CMB-1999-007-4",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  MRclass =      "33A40",
  bibdate =      "Thu Sep 8 10:22:25 MDT 2011",
  bibsource =    "http://cms.math.ca/cmb/v42/;
                 https://www.math.utah.edu/pub/tex/bib/canmathbull.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Let $ j_{\nu, 1} $ be the smallest (first) positive
                 zero of the Bessel function $ J_{\nu }(z) $, $ \nu > -
                 1 $, which becomes zero when $ \nu $ approaches $ - 1
                 $. Then $ j_{\nu, 1}^2 $ can be continued analytically
                 to $ - 2 < \nu < - 1 $, where it takes on negative
                 values. We show that $ j_{\nu, 1}^2 $ is a convex
                 function of $ \nu $ in the interval $ - 2 < \nu \leq 0
                 $, as an addition to an old result [{\'A}. Elbert and
                 A. Laforgia, SIAM J. Math. Anal. {\bf 15}(1984),
                 206--212], stating this convexity for $ \nu > 0 $. Also
                 the monotonicity properties of the functions $ \frac
                 {j_{\nu, 1}^24 (\nu + 1)} $, $ \frac {j_{\nu, 1}^24(\nu
                 + 1) \sqrt {\nu + 2}} $ are determined. Our approach is
                 based on the series expansion of Bessel function $
                 J_{\nu }(z) $ and it turned out to be effective,
                 especially when $ - 2 < \nu < - 1 $.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "33A40",
  fjournal =     "Canadian mathematical bulletin = Bulletin canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cmb/",
  journalabbrev = "CMB",
  refnum =       "7139",
  xxpages =      "56--67",
}

@TechReport{Ercegovac:1999:IGD,
  author =       "Milo{\v{s}} D. Ercegovac and Laurent Imbert and David
                 W. Matula and Jean-Michel Muller and Guoheng Wei",
  title =        "Improving {Goldschmidt} Division, Square Root, and
                 Square Root Reciprocal",
  type =         "Research Report",
  number =       "99-41",
  institution =  "Laboratoire de l'Informatique du Parall{\'e}lisme",
  address =      "Lyon, France",
  pages =        "ii + 17",
  month =        sep,
  year =         "1999",
  bibdate =      "Mon Dec 11 07:53:15 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://inria.hal.science/inria-00072909/file/RR1999-41.pdf",
  abstract =     "The aim of this paper is to accelerate division,
                 square root and square root reciprocal computations,
                 when Goldschmidt method is used on a pipelined
                 multiplier. This is done by replacing the last
                 iteration by the addition of a correcting term that can
                 be looked up during the early iterations. We describe
                 several variants of the Goldschmidt algorithm assuming
                 4-cycle pipelined multiplier and discuss obtained
                 number of cycles and error achieved. Extensions to
                 other than 4-cycle multipliers are given",
  acknowledgement = ack-nhfb,
  keywords =     "Computer Arithmetic; Convergence division; Division;
                 Goldschmidt iteration; Square root; Square root
                 reciprocal",
}

@Article{Fabijonas:1999:RAE,
  author =       "Bruce R. Fabijonas and F. W. J. Olver",
  title =        "On the Reversion of an Asymptotic Expansion and the
                 Zeros of the {Airy} Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "41",
  number =       "4",
  pages =        "762--773",
  month =        dec,
  year =         "1999",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/S0036144598349538",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "http://epubs.siam.org/toc/siread/41/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/34953",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "Dec-1999",
}

@Article{Fuller:1999:HVH,
  author =       "A. Thomas Fuller",
  title =        "{Horner} versus {Holdred}: an Episode in the History
                 of Root Computation",
  journal =      j-HIST-MATH,
  volume =       "26",
  number =       "1",
  pages =        "29--51",
  day =          "1",
  month =        feb,
  year =         "1999",
  CODEN =        "HIMADS",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Jun 26 06:19:37 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0315086098922145",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
}

@Article{Gautschi:1999:NRC,
  author =       "Walter Gautschi",
  title =        "A Note on the Recursive Calculation of Incomplete
                 Gamma Functions",
  journal =      j-TOMS,
  volume =       "25",
  number =       "1",
  pages =        "101--107",
  month =        mar,
  year =         "1999",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 15 19:01:02 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://doi.acm.org/10.1145/305658.305717;
                 http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Gautschi:1999:NRC;
                 http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p101-gautschi/",
  abstract =     "It is known that the recurrence relation for
                 incomplete gamma functions $ \Gamma (a + n, x), 0 \le a
                 < 1 $, $ n = 0, 1, 2 \ldots $, when $x$ is positive, is
                 unstable---more so the larger $x$. Nevertheless, the
                 recursion can be used in the range $ 0 \le n \le x $
                 practically without error growth, and in larger ranges
                 $ 0 \le n \le N $ with a loss of accuracy that can be
                 controlled by suitably limiting $N$.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; reliability",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Stability (and instability). {\bf
                 G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation.",
}

@TechReport{Gourdon:1999:NCC,
  author =       "Xavier Gourdon and Pascal Sebah",
  title =        "Numbers, constants, and computation",
  institution =  "????",
  address =      "Paris, France",
  year =         "1999",
  bibdate =      "Sat Mar 15 16:28:07 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "World-Wide Web site.",
  URL =          "http://numbers.computation.free.fr/Constants/home.html",
  acknowledgement = ack-nhfb,
  annote =       "Although this site concentrates mainly on computation
                 of particular mathematical constants, it also treats
                 high-precision computation of inverse and square
                 root.",
}

@Article{Harrison:1999:CTF,
  author =       "John Harrison and Ted Kubaska and Shane Story and Ping
                 Tak Peter Tang",
  title =        "The Computation of Transcendental Functions on the
                 {IA-64} Architecture",
  journal =      j-INTEL-TECH-J,
  number =       "Q4",
  pages =        "7",
  day =          "22",
  month =        nov,
  year =         "1999",
  bibdate =      "Fri Jun 01 06:02:08 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://developer.intel.com/technology/itj/q41999/articles/art_5.htm;
                 http://developer.intel.com/technology/itj/q41999/pdf/transendental.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Hayashi:1999:SRR,
  author =       "Takao Hayashi",
  title =        "A set of rules for the root-extraction prescribed by
                 the sixteenth-century {Indian} mathematicians,
                 {N{\=\i}laka{\d{n}}{\d{t}}ha Somastuvan} and
                 {{\'S}a{\.n}kara V{\=a}riyar}",
  journal =      j-HIST-SCI-2,
  volume =       "9",
  number =       "2",
  pages =        "135--153",
  month =        nov,
  year =         "1999",
  CODEN =        "HISCDU",
  ISSN =         "0285-4821",
  ISSN-L =       "0285-4821",
  MRclass =      "01A32",
  MRnumber =     "1762168",
  MRreviewer =   "A. I. Volodarski{\u\i}",
  bibdate =      "Sat Oct 6 17:22:25 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/histscijpn.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Scientiarum. Second Series. International
                 Journal of the History of Science Society of Japan",
  journal-URL =  "http://hssj.info/",
}

@Article{Homeier:1999:CAL,
  author =       "H. H. H. Homeier",
  title =        "Convergence acceleration of logarithmically convergent
                 series avoiding summation",
  journal =      j-APPL-MATH-LETT,
  volume =       "12",
  number =       "3",
  pages =        "29--32",
  year =         "1999",
  CODEN =        "AMLEEL",
  DOI =          "https://doi.org/10.1016/S0893-9659(98)00167-0",
  ISSN =         "0893-9659 (print), 1873-5452 (electronic)",
  ISSN-L =       "0893-9659",
  MRclass =      "65B05",
  MRnumber =     "1749733",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08939659",
  keywords =     "convergence acceleration",
}

@InProceedings{Hyogo:1999:LVF,
  author =       "A. Hyogo and Y. Fukutomi and K. Sekine",
  booktitle =    "Proceedings of the 1999 {IEEE} International Symposium
                 on Circuits and Systems: {ISCAS '99}, 2 June 1999",
  title =        "Low voltage four-quadrant analog multiplier using
                 square-root circuit based on {CMOS} pair",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "274--277",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We proposed a square-root circuit based on CMOS pairs.
                 In this paper, we propose a low voltage four-quadrant
                 analog multiplier using the square-root circuit. Also
                 we confirmed this operation by PSpice \ldots{}",
}

@Article{Iordache:1999:ARS,
  author =       "Cristina Iordache and David W. Matula",
  title =        "Analysis of Reciprocal and Square Root Reciprocal
                 Instructions in the {AMD K6-2} Implementation of
                 {3DNow!}",
  journal =      j-ELECT-NOTES-THEOR-COMP-SCI,
  volume =       "24",
  pages =        "34--62",
  year =         "1999",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/S1571-0661(05)80621-8",
  ISSN =         "1571-0661",
  bibdate =      "Fri Jun 24 20:23:13 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Reciprocal and root reciprocal functions at ``half''
                 and IEEE single precision formats are specified in the
                 AMD 3DNow! instruction set. Implementations in the
                 recently released AMD K6-2 microprocessor are analyzed
                 herein by exhaustive computation and timing loops to
                 ascertain the accuracy and monotonicity properties of
                 the output and throughput\slash latency cycle counts.
                 Periodicities in stepwise function output were observed
                 and employed to construct an underlying bipartite table
                 that can serve as the core of the respective reciprocal
                 function outputs. The recommended RISC instruction
                 macros generated single precision reciprocals and root
                 reciprocals accurate to a unit in the last place.
                 However, the root reciprocal functions failed to
                 satisfy the desirable monotonicity property typically
                 implemented as an industry standard for elementary
                 functions on x86 floating point units. Reasons for the
                 failure are provided and an adjusted table is shown to
                 satisfy the monotonicity standard. Results are
                 summarized in Table 1 and described in the body of this
                 report.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Notes in Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15710661",
}

@InProceedings{Iordache:1999:IPR,
  author =       "Cristina Iordache and David W. Matula",
  title =        "On Infinitely Precise Rounding for Division, Square
                 Root, Reciprocal and Square Root Reciprocal",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "233--240",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-164.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-164.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Iordache.pdf",
  abstract =     "Quotients, reciprocals, square roots and square root
                 reciprocals all have the property that infinitely
                 precise p-bit rounded results for p-bit input operands
                 can be obtained from approximate results of bounded
                 accuracy. We investigate lower bounds on the number of
                 bits of an approximation accurate to a unit in the last
                 place sufficient to guarantee that correct round and
                 sticky bits can be determined. Known lower bounds for
                 quotients and square roots are given and/or sharpened,
                 and a new lower bound for root reciprocals is proved.
                 Specifically for reciprocals, quotients and square
                 roots, tight bounds of order $ 2 p + O(1) $ are
                 presented. For infinitely precise rounding of the root
                 reciprocal a lower bound can be found at $ 3 p + O(1)
                 $, but exhaustive testing for small sizes of the
                 operand suggests that in practice $ (2 + \epsilon)p $
                 for small $ \epsilon $ is usually sufficient.
                 Algorithms can be designed for obtaining the round and
                 sticky bits based on the bit pattern of an
                 approximation computed to the required accuracy. We
                 show that some improvement of the known lower bound for
                 reciprocals and division is achievable at the cost of
                 somewhat more complex hardware for rounding. Tests for
                 the exactness of the quotient and square root are also
                 provided.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic; IEEE",
  summary =      "Quotients, reciprocals, square roots and square root
                 reciprocals all have the property that infinitely
                 precise p-bit rounded results for p-bit input operands
                 can be obtained from approximate results of bounded
                 accuracy. We investigate lower bounds \ldots{}",
}

@Article{Jamieson:1999:NRF,
  author =       "M. J. Jamieson",
  title =        "Notes: On rational function approximations to square
                 roots",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "106",
  number =       "1",
  pages =        "50--52",
  month =        jan,
  year =         "1999",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11Yxx",
  MRnumber =     "1 674 202",
  bibdate =      "Tue Jun 22 10:29:34 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Book{Jeffreys:1999:MMP,
  author =       "Harold Jeffreys and Bertha {Swirles Jeffreys}",
  title =        "Methods of Mathematical Physics",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Third",
  pages =        "viii + 718",
  year =         "1999",
  ISBN =         "0-521-66402-0 (paperback)",
  ISBN-13 =      "978-0-521-66402-8 (paperback)",
  LCCN =         "QA401 .J4 1999",
  bibdate =      "Thu Aug 17 10:48:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprint of \cite{Jeffreys:1956:MMP}.",
  URL =          "https://en.wikipedia.org/wiki/Bertha_Swirles;
                 https://en.wikipedia.org/wiki/Harold_Jeffreys",
  acknowledgement = ack-nhfb,
  author-dates = "Sir Harold Jeffreys (22 April 1891--18 March 1989);
                 Lady Bertha Swirles Jeffreys (22 May 1903--18 December
                 1999)",
  remark =       "First edition 1946, second edition 1950, third edition
                 1956, first paperback edition 1972, reprinted 1978,
                 1980, 1988, 1992, 1999, 2001. Third edition preface is
                 dated April 1953. Second edition preface is dated 15
                 November 1948. First edition preface is dated 1946.",
  subject-dates = "Douglas Rayner Hartree (27 March 1897--12 February
                 1958)",
  tableofcontents = "Preface \\
                 Authors' Notes \\
                 1: The Real Variable \\
                 2: Scalars and Vectors \\
                 3: Tensors \\
                 4: Matrices \\
                 5: Multiple Integrals \\
                 6: Potential Theory \\
                 7: Operational Methods \\
                 8: Physical Applications of the Operational Method \\
                 9: Numerical Methods \\
                 10: Calculus of Variations \\
                 11: Functions of a Complex Variable \\
                 12: Contour Integration and Bromwich's Integral \\
                 13: Conformal Representation \\
                 14: Fourier's Theorem \\
                 15: The Factorial and Related Functions \\
                 16: Solution of Linear Differential Equation \\
                 17: Asymptotic Expansions \\
                 18: The Equations of Potential, Waves, and Heat
                 Conduction \\
                 19: Waves in One Dimension and Waves With Spherical
                 Symmetry \\
                 20: Conduction of Heat in One and Three Dimensions \\
                 21: Bessel Functions \\
                 22: Applications of Bessel Functions \\
                 23: The Confluent Hypergeometric Function \\
                 24: Legendre Functions and Associated Functions \\
                 25: Elliptic Functions \\
                 Notes \\
                 Appendix on Notation \\
                 Index",
}

@Misc{Kahan:1999:SRD,
  author =       "W. Kahan",
  title =        "Square Root Without Division",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "23",
  month =        feb,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:01:49 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/reciprt.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Krukier:1999:CAT,
  author =       "L. A. Krukier",
  title =        "Convergence acceleration of triangular iterative
                 methods based on the skew-symmetric part of the
                 matrix",
  journal =      j-APPL-NUM-MATH,
  volume =       "30",
  number =       "2--3",
  pages =        "281--290",
  day =          "10",
  month =        jun,
  year =         "1999",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Wed Jul 28 14:37:31 MDT 1999",
  bibsource =    "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1999&volume=30&issue=2-3;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1999&volume=30&issue=2-3&aid=981",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}

@Article{Kzaz:1999:CAG,
  author =       "M. Kzaz",
  title =        "Convergence acceleration of the {Gauss--Laguerre}
                 quadrature formula",
  journal =      j-APPL-NUM-MATH,
  volume =       "29",
  number =       "2",
  pages =        "201--220",
  day =          "1",
  month =        feb,
  year =         "1999",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Wed Jul 28 14:37:22 MDT 1999",
  bibsource =    "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1999&volume=29&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.com/cas/tree/store/apnum/sub/1999/29/2/940.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}

@Article{Lang:1999:VHR,
  author =       "T. Lang and P. Montuschi",
  title =        "Very high radix square root with prescaling and
                 rounding and a combined division\slash square root
                 unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "8",
  pages =        "827--841",
  month =        aug,
  year =         "1999",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.795124",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "An algorithm for square root with prescaling and
                 selection by rounding is developed and combined with a
                 similar scheme for division. Since division is usually
                 more frequent than square root, the main concern of the
                 combined implementation is to \ldots{}",
}

@InProceedings{Lee:1999:STS,
  author =       "Young-Sang Lee and Jun-Woo Kang and Lee-Sup Kim and
                 Seung-Ho Hwang",
  booktitle =    "6th International Conference on {VLSI} and {CAD}:
                 {ICVC '99}",
  title =        "Self-timed shared division and square-root
                 implementation using full redundant signed digit
                 numbers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "541--544",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "A radix-$2$ square root implementation for self-timed
                 dividers using redundant signed-digit (RSD) adders is
                 presented. In this method, two self-timed RSD adder
                 stages are used for each result bit selection. A very
                 efficient and simple result bit \ldots{}",
}

@InProceedings{Lozier:1999:DDM,
  author =       "Daniel W. Lozier and B. R. Miller and B. V. Saunders",
  title =        "Design of a Digital Mathematical Library for Science,
                 Technology and Education",
  crossref =     "IEEE:1999:PIF",
  pages =        "118--128",
  year =         "1999",
  bibdate =      "Fri Jul 09 06:33:35 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://dlmf.nist.gov/about/publications/nistir6297.ps.gz",
  acknowledgement = ack-nhfb,
  remark =       "Preprint: NISTIR 6297, Feb. 1999, 13 pages",
}

@Article{Morita:1999:CEI,
  author =       "T. Morita",
  title =        "Calculation of the elliptic integrals of the first and
                 second kinds with complex modulus",
  journal =      j-NUM-MATH,
  volume =       "82",
  number =       "4",
  pages =        "677--688",
  month =        jun,
  year =         "1999",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon Oct 18 10:45:11 MDT 1999",
  bibsource =    "http://link.springer-ny.com/link/service/journals/00211/tocs/t9082004.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer-ny.com/link/service/journals/00211/bibs/9082004/90820677.htm;
                 http://link.springer-ny.com/link/service/journals/00211/papers/9082004/90820677.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Muller:1999:CAT,
  author =       "J. M{\"u}ller",
  title =        "Convergence acceleration of {Taylor} sections by
                 convolution",
  journal =      j-CONST-APPROX,
  volume =       "15",
  number =       "4",
  pages =        "523--536",
  year =         "1999",
  DOI =          "https://doi.org/10.1007/s003659900120",
  ISSN =         "0176-4276 (print), 1432-0940 (electronic)",
  ISSN-L =       "0176-4276",
  MRclass =      "41A58 (30E10)",
  MRnumber =     "1702803 (2000i:41040)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Constructive Approximation",
  journal-URL =  "http://link.springer.com/journal/365",
  keywords =     "convergence acceleration",
}

@Article{Muroi:1999:ESR,
  author =       "Kazuo Muroi",
  title =        "Extraction of square roots in {Babylonian}
                 mathematics",
  journal =      j-HIST-SCI-2,
  volume =       "9",
  number =       "2",
  pages =        "127--133",
  month =        nov,
  year =         "1999",
  CODEN =        "HISCDU",
  ISSN =         "0285-4821",
  ISSN-L =       "0285-4821",
  MRclass =      "01A17",
  MRnumber =     "1762167",
  MRreviewer =   "Bruno Poizat",
  bibdate =      "Sat Oct 6 17:22:25 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/histscijpn.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Scientiarum. Second Series. International
                 Journal of the History of Science Society of Japan",
  journal-URL =  "http://hssj.info/",
}

@InProceedings{Nannarelli:1999:LPR,
  author =       "A. Nannarelli and T. Lang",
  booktitle =    "{(ICCD '99)} International Conference on Computer
                 Design",
  title =        "Low-power radix-$4$ combined division and square
                 root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "236--242",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Because of the similarities in the algorithm it is
                 quite common to implement division and square root in
                 the same unit. The purpose of this work is to implement
                 a low-power combined radix-$4$ division and square root
                 floating-point double precision \ldots{}",
}

@InProceedings{Oberman:1999:FPD,
  author =       "S. F. Oberman",
  title =        "Floating point division and square root algorithms and
                 implementation in the {AMD-K7{\TM}} microprocessor",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "106--115",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-139.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-139.ps",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH; computer arithmetic; IEEE",
  summary =      "This paper presents the AMD-K7 IEEE 754 and $\times$87
                 compliant floating point division and square root
                 algorithms and implementation. The AMD-K7 processor
                 employs an iterative implementation of a series
                 expansion to converge quadratically to the \ldots{}",
}

@InProceedings{Parhami:1999:ALT,
  author =       "B. Parhami",
  booktitle =    "Conference Record of the Thirty-Third Asilomar
                 Conference on Signals, Systems, and Computers, 1999",
  title =        "Analysis of the lookup table size for square-rooting",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1327--1330",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Convergence methods are widely used for division,
                 reciprocation, and square-rooting. With such methods,
                 it is common to use an initial table lookup step for
                 obtaining an approximate result that leads to faster
                 convergence. In the case of division \ldots{}",
}

@Article{Russinoff:1999:MCP,
  author =       "David M. Russinoff",
  title =        "A mechanically checked proof of correctness of the
                 {AMD K5} floating point square root microcode",
  journal =      j-FORM-METHODS-SYST-DES,
  volume =       "14",
  number =       "1",
  pages =        "75--125",
  month =        jan,
  year =         "1999",
  CODEN =        "FMSDE6",
  ISSN =         "0925-9856 (print), 1572-8102 (electronic)",
  ISSN-L =       "0925-9856",
  bibdate =      "Sat Jun 02 07:51:51 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Special issue on arithmetic circuits.",
  URL =          "http://www.wkap.nl/jrnltoc.htm/0925-9856;
                 http://www.wkap.nl/oasis.htm/194808",
  acknowledgement = ack-nhfb,
  fjournal =     "Formal Methods in System Design",
}

@Article{Schraudolph:1999:FCA,
  author =       "N. N. Schraudolph",
  title =        "A Fast, Compact Approximation of the Exponential
                 Function",
  journal =      j-NEURAL-COMP,
  volume =       "11",
  number =       "4",
  pages =        "853--862",
  day =          "1",
  month =        may,
  year =         "1999",
  CODEN =        "NEUCEB",
  DOI =          "https://doi.org/10.1162/089976699300016467",
  ISSN =         "0899-7667 (print), 1530-888x (electronic)",
  ISSN-L =       "0899-7667",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Ingenta database",
  URL =          "https://www.mitpressjournals.org/doi/abs/10.1162/089976699300016467",
  acknowledgement = ack-nhfb,
  fjournal =     "Neural Computation",
  journal-URL =  "http://www.mitpressjournals.org/loi/neco",
  pagecount =    "10",
}

@Article{Schulte:1999:AEF,
  author =       "M. Schulte and J. Stine",
  title =        "Approximating Elementary Functions with Symmetric
                 Bipartite Tables",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "8",
  pages =        "842--847",
  year =         "1999",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.795125",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 24 20:20:58 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-10.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Schulte:1999:ESO,
  author =       "M. J. Schulte and K. E. Wires",
  title =        "Efficient Second Order Approximations for Reciprocals
                 and Square Roots",
  crossref =     "Luk:1999:PSA",
  volume =       "3807",
  pages =        "10--18",
  year =         "1999",
  bibdate =      "Sun Mar 04 11:10:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-05.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schulte:1999:HSI,
  author =       "Michael J. Schulte and Kent E. Wires",
  title =        "High-Speed Inverse Square Roots",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "124--131",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-109.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-109.ps",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH; computer arithmetic; IEEE",
  summary =      "Inverse square roots are used in several digital
                 signal processing, multimedia, and scientific computing
                 applications. This paper presents a high-speed method
                 for computing inverse square roots. This method uses a
                 table lookup, operand modification, \ldots{}",
}

@Article{Segura:1999:EGT,
  author =       "J. Segura and A. Gil",
  title =        "{ELF} and {GNOME}: Two tiny codes to evaluate the real
                 zeros of the {Bessel} functions of the first kind for
                 real orders",
  journal =      j-COMP-PHYS-COMM,
  volume =       "117",
  number =       "3",
  pages =        "250--262",
  day =          "11",
  month =        mar,
  year =         "1999",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(98)00193-3",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:36 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465598001933",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Seidel:1999:HSR,
  author =       "P.-M. Seidel",
  title =        "High-speed redundant reciprocal approximation",
  journal =      j-INTEGRATION-VLSI-J,
  volume =       "28",
  number =       "1",
  pages =        "1--12",
  month =        sep,
  year =         "1999",
  CODEN =        "IVJODL",
  ISSN =         "0167-9260 (print), 1872-7522 (electronic)",
  ISSN-L =       "0167-9260",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Integration, the VLSI journal",
  pagecount =    "12",
}

@Article{Stine:1999:STA,
  author =       "E. Stine and M. J. Schulte",
  title =        "The Symmetric Table Addition Method for Accurate
                 Function Approximation",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "21",
  number =       "2",
  pages =        "167--177",
  month =        jun,
  year =         "1999",
  CODEN =        "JVSPED",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Sun Mar 04 11:02:59 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-11.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@InProceedings{Story:1999:NAI,
  author =       "S. Story and P. T. P. Tang",
  title =        "New Algorithms for Improved Transcendental Functions
                 on {IA-64}",
  crossref =     "Koren:1999:ISC",
  pages =        "4--11",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-118.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-118.ps",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH; computer arithmetic; IEEE",
}

@Book{Suetin:1999:OPT,
  author =       "P. K. (Pavel Kondratevich) Suetin",
  title =        "Orthogonal polynomials in two variables",
  volume =       "3",
  publisher =    "Gordon and Breach Science Publishers",
  address =      "Amsterdam, The Netherlands",
  pages =        "xx + 348",
  year =         "1999",
  ISBN =         "90-5699-167-1",
  ISBN-13 =      "978-90-5699-167-8",
  LCCN =         "QA404.5 .S8813 1999",
  bibdate =      "Sat Oct 30 17:21:54 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  note =         "Translated from the Russian by E. V. Pankratiev.",
  series =       "Analytical methods and special functions",
  acknowledgement = ack-nhfb,
  remark =       "Originally published in Russian in 1988 by Nauka,
                 Moscow.",
  subject =      "Orthogonal polynomials",
}

@Article{Vrahatis:1999:ESP,
  author =       "M. N. Vrahatis and O. Ragos and T. Skiniotis and F. A.
                 Zafiropoulos and T. N. Grapsa",
  title =        "Erratum to: {{\booktitle{RFSFNS: a portable package
                 for the numerical determination of the number and the
                 calculation of roots of Bessel functions}} [Comput.
                 Phys. Commun. {\bf 92} (1995) 252--266]}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "117",
  number =       "3",
  pages =        "290--290",
  day =          "11",
  month =        mar,
  year =         "1999",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(98)00109-X",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:36 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Vrahatis:1995:RPP}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S001046559800109X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Vyridis:1999:ICA,
  author =       "D. G. Vyridis and S. D. Panteliou and I. N. Katz",
  title =        "An inverse convergence approach for arguments of
                 {Jacobian} elliptic functions",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "37",
  number =       "2",
  pages =        "21--26",
  month =        jan,
  year =         "1999",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:56 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122198002508",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Wieder:1999:ANH,
  author =       "Thomas Wieder",
  title =        "{Algorithm 794}: Numerical {Hankel} transform by the
                 {Fortran} program {HANKEL}",
  journal =      j-TOMS,
  volume =       "25",
  number =       "2",
  pages =        "240--250",
  month =        jun,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/317275.317284",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 20 18:21:35 MDT 1999",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "ftp://netlib.bell-labs.com/netlib/toms/794.gz;
                 http://phase.etl.go.jp/netlib/toms/794;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p240-wieder/;
                 http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Wieder:1999:ANH;
                 http://www.hensa.ac.uk/netlib/toms/794.gz;
                 http://www.netlib.no/netlib/toms/794;
                 http://www.netlib.org/toms/794",
  abstract =     "The numerical evaluation of the Hankel transform poses
                 the problems of both infinite integration and Bessel
                 function calculation. Using the corresponding numerical
                 program routines from the literature, a Fortran program
                 has been written to perform the Hankel transform for
                 real functions, given either in analytical form as
                 subroutines or in discrete form as tabulated data.",
  accepted =     "February 1999",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Hankel transform; numerical analysis",
  subject =      "Software --- Programming Languages --- Language
                 Classifications (D.3.2): FORTRAN 77; Theory of
                 Computation --- Analysis of Algorithms and Problem
                 Complexity --- Numerical Algorithms and Problems
                 (F.2.1): Computation of transforms",
}

@TechReport{Zimmermann:1999:KSR,
  author =       "Paul Zimmermann",
  title =        "{Karatsuba} Square Root",
  type =         "Research Report",
  number =       "3805",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "8",
  year =         "1999",
  bibdate =      "Sun Sep 10 08:56:48 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-3805.pdf;
                 ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-3805.ps.gz;
                 http://www.inria.fr/rrrt/rr-3805.html",
  abstract =     "We exhibit an algorithm to compute the square-root
                 with remainder of a $n$-word number in $ 3 / 2 $ word
                 operations, where $ K(n) $ is the number of words
                 operations to multiply two $n$-word numbers using
                 Karatsuba's algorithm. If the remainder is not needed,
                 the cost can be reduced to $ K(n) $ on average. This
                 algorithm can be used for floating-point or polynomial
                 computations too; although not optimal asymptotically,
                 its simplicity gives a wide range of use, from about 50
                 to 1,000,000 digits, as shown by computer
                 experiments.",
  acknowledgement = ack-nhfb,
}

@Article{Alhargan:2000:ACA,
  author =       "Fayez A. Alhargan",
  title =        "Algorithms for the Computation of all {Mathieu}
                 Functions of Integer Orders",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "390--407",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/358407.358420",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The paper presents methods for the computation of all
                 Mathieu functions of integer order, which cover a large
                 range of $n$ and $h$; previous algorithms were limited
                 to small values of $n$. The algorithms are given in
                 sufficient details to enable straightforward
                 implementation. The algorithms can handle a large range
                 of the order $n$ (0-200) and the parameter $h$ (0-4$n$
                 ).",
  accepted =     "19 May 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Alhargan:2000:ASC,
  author =       "Fayez A. Alhargan",
  title =        "{Algorithm 804}: subroutines for the computation of
                 {Mathieu} functions of integer orders",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "408--414",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/358407.358422",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Computer subroutines in C++ for computing Mathieu
                 functions of integer orders are described. The core
                 routines for computing Mathieu characteristic numbers
                 and Mathieu coefficients are described in details, the
                 rest of the subroutines are standard implementation of
                 the series summations for each function. The routines
                 can handle a large range of the order $n$ and the
                 parameter $h$.",
  accepted =     "19 May 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Anderson:2000:RAF,
  author =       "Stuart Anderson",
  title =        "Remark on {Algorithm 723}: {Fresnel} integrals",
  journal =      j-TOMS,
  volume =       "26",
  number =       "4",
  pages =        "617--617",
  month =        dec,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/365723.365737",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  accepted =     "16 October 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ball:2000:ACZ,
  author =       "James S. Ball",
  title =        "Automatic Computation of Zeros of {Bessel} Functions
                 and Other Special Functions",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "21",
  number =       "4",
  pages =        "1458--1464",
  month =        jul,
  year =         "2000",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/S1064827598339074",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Fri Oct 27 13:32:22 MDT 2000",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/21/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/33907",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@InProceedings{Batten:2000:NAD,
  author =       "D. Batten and S. Jinturkar and J. Glossner and M.
                 Schulte and P. D'arcy",
  title =        "A New Approach to {DSP} Intrinsic Functions",
  crossref =     "Sprague:2000:PAH",
  pages =        "2892--2901",
  year =         "2000",
  bibdate =      "Sun Mar 04 11:18:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2000-01.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Becken:2000:ACG,
  author =       "W. Becken and P. Schmelcher",
  title =        "The analytic continuation of the {Gaussian}
                 hypergeometric function {$_2 F_1 (a, b; c; z)$} for
                 arbitrary parameters",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "126",
  number =       "1--2",
  pages =        "449--478",
  day =          "30",
  month =        dec,
  year =         "2000",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00267-3",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "33C05 (33F05)",
  MRnumber =     "MR1806771 (2002e:33003)",
  bibdate =      "Sat Feb 25 12:43:38 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700002673",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InCollection{Borwein:2000:AGM,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  crossref =     "Berggren:2000:PSB",
  pages =        "537--552",
  year =         "2000",
  DOI =          "https://doi.org/10.1007/978-1-4757-3240-5_56",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprint of \cite{Borwein:1984:AGM}.",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_56",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}

@Article{Borwein:2000:CSR,
  author =       "Jonathan M. Borwein and David M. Bradley and Richard
                 E. Crandall",
  title =        "Computational Strategies for the {Riemann} Zeta
                 Function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "121",
  number =       "1--2",
  pages =        "247--296",
  month =        sep,
  year =         "2000",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00336-8",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "11M06 (11Y35 33F05)",
  MRnumber =     "1780051",
  MRreviewer =   "Cem Y. Y{\i}ld{\i}r{\i}m",
  bibdate =      "Mon Oct 24 11:41:28 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://people.reed.edu/~crandall/papers/attach01.pdf",
  abstract =     "We provide a compendium of evaluation methods for the
                 Riemann zeta function, presenting formulae ranging from
                 historical attempts to recently found convergent series
                 to curious oddities old and new. We concentrate
                 primarily on practical computational issues, such
                 issues depending on the domain of the argument, the
                 desired speed of computation, and the incidence of what
                 we call ``value recycling''.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 98:118.",
}

@Book{Bressoud:2000:CCN,
  author =       "David M. Bressoud and S. Wagon",
  title =        "A course in computational number theory",
  publisher =    "Key College Publishers in cooperation with Springer",
  address =      "New York, NY, USA",
  pages =        "xii + 367",
  year =         "2000",
  ISBN =         "1-930190-10-7",
  ISBN-13 =      "978-1-930190-10-8",
  LCCN =         "QA241 .B788 2000",
  bibdate =      "Fri Sep 26 14:29:31 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0818/99016037-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0818/99016037-t.html",
  acknowledgement = ack-nhfb,
  subject =      "Number theory; Algorithms",
}

@Article{Brezinski:2000:CAD,
  author =       "C. Brezinski",
  title =        "Convergence acceleration during the 20th century",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "122",
  number =       "1--2",
  pages =        "1--21",
  month =        oct,
  year =         "2000",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00360-5",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65-03 (01A60)",
  MRnumber =     "1794649",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Numerical analysis 2000, Vol. II: Interpolation and
                 extrapolation",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "convergence acceleration",
}

@Article{Carlson:2000:RTE,
  author =       "B. C. Carlson and James FitzSimons",
  title =        "Reduction theorems for elliptic integrands with the
                 square root of two quadratic factors",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "118",
  number =       "1--2",
  pages =        "71--85",
  day =          "1",
  month =        jun,
  year =         "2000",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:43:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704270000282X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Cawley:2000:FCA,
  author =       "G. C. Cawley",
  title =        "On a Fast, Compact Approximation of the Exponential
                 Function",
  journal =      j-NEURAL-COMP,
  volume =       "12",
  number =       "9",
  pages =        "2009--2012",
  day =          "1",
  month =        sep,
  year =         "2000",
  CODEN =        "NEUCEB",
  ISSN =         "0899-7667 (print), 1530-888x (electronic)",
  ISSN-L =       "0899-7667",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Neural Computation",
  journal-URL =  "http://www.mitpressjournals.org/loi/neco",
  pagecount =    "4",
}

@Article{Cherri:2000:PCC,
  author =       "A. K. Cherri and M. S. Alam",
  title =        "Parallel computation of complex elementary functions
                 using quaternary signed-digit arithmetic",
  journal =      "Optics and Laser Technology",
  volume =       "32",
  number =       "6",
  pages =        "391--399",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "0030-3992",
  bibdate =      "Sat Dec 7 09:21:28 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  pagecount =    "9",
}

@InProceedings{Chu:2000:CPT,
  author =       "Wanming Chu and Yamin Li",
  booktitle =    "{ACAC 2000}: 5th Australasian Computer Architecture
                 Conference",
  title =        "Cost\slash performance tradeoff of $n$-select square
                 root implementations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "9--16",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Hardware square-root units require large numbers of
                 gates even for iterative implementations. In this paper
                 we present four low-cost high-performance
                 fully-pipelined n-select implementations (nS-Root)
                 based on a non-restoring-remainder square root
                 \ldots{}",
}

@Article{Cohen:2000:CAA,
  author =       "Henri Cohen and Fernando {Rodriguez Villegas} and Don
                 Zagier",
  title =        "Convergence Acceleration of Alternating Series",
  journal =      j-EXP-MATH,
  volume =       "9",
  number =       "1",
  pages =        "3--12",
  year =         "2000",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11Y55 (65B05)",
  MRnumber =     "1758796 (2001m:11222)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://projecteuclid.org/euclid.em/1046889587;
                 http://www.math.u-bordeaux.fr/~cohen/sumalt2new.ps",
  ZMnumber =     "0972.11115",
  abstract =     "We discuss some linear acceleration methods for
                 alternating series which are in theory and in practice
                 much better than that of Euler--Van Wijngaarden. One of
                 the algorithms, for instance, allows one to calculate $
                 \sum ( - 1)^k a_k $ with an error of about $ 17.93^{-n}
                 $ from the first $n$ terms for a wide class of
                 sequences $ \{ a_k \} $. Such methods are useful for
                 high precision calculations frequently appearing in
                 number theory.",
  acknowledgement = ack-nhfb,
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  keywords =     "convergence acceleration",
}

@Article{Ercegovac:2000:IGD,
  author =       "Milos D. Ercegovac and Laurent Imbert and David W.
                 Matula and Jean-Michel Muller and Guoheng Wei",
  title =        "Improving {Goldschmidt} Division, Square Root, and
                 Square Root Reciprocal",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "759--763",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863046",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
  summary =      "The aim of this paper is to accelerate division,
                 square root, and square root reciprocal computations
                 when the Goldschmidt method is used on a pipelined
                 multiplier. This is done by replacing the last
                 iteration by the addition of a correcting term
                 \ldots{}",
}

@Article{Ercegovac:2000:RSR,
  author =       "Milos D. Ercegovac and Tom{\'a}s Lang and Jean-Michel
                 Muller and Arnaud Tisserand",
  title =        "Reciprocation, Square Root, Inverse Square Root, and
                 Some Elementary Functions Using Small Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "628--637",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863031",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "68M07 (65B15)",
  MRnumber =     "MR1783602 (2001e:68016)",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  fjournal =     "Institute of Electrical and Electronics Engineers.
                 Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
  summary =      "This paper deals with the computation of reciprocals,
                 square roots, inverse square roots, and some elementary
                 functions using small tables, small multipliers, and,
                 for some functions, a final ``large'' (almost
                 full-length) multiplication. \ldots{}",
}

@Article{Favati:2000:SAC,
  author =       "P. Favati and G. Lotti and O. Menchi and F. Romani",
  title =        "Separable asymptotic cost of evaluating elementary
                 functions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "24",
  number =       "3",
  pages =        "255--274",
  year =         "2000",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65Y20",
  MRnumber =     "MR1780414 (2001d:65174)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  pagecount =    "20",
}

@Article{Galue:2000:MTG,
  author =       "L. Galu{\'e} and H. G. Khajah and Shyam L. Kalla",
  title =        "Multiplication theorems for generalized and
                 double-index {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "118",
  number =       "1--2",
  pages =        "143--150",
  day =          "1",
  month =        jun,
  year =         "2000",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:43:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700002855",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Harris:2000:SBE,
  author =       "Frank E. Harris",
  title =        "Spherical {Bessel} expansions of sine, cosine, and
                 exponential integrals",
  journal =      j-APPL-NUM-MATH,
  volume =       "34",
  number =       "1",
  pages =        "95--98",
  month =        jun,
  year =         "2000",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1016/S0168-9274(99)00031-8",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "33B10; 65D30 (33F05 65D20)",
  MRnumber =     "1755696 (2001a:65027)",
  bibdate =      "Sat Oct 21 13:09:35 MDT 2000",
  bibsource =    "http://www.elsevier.com/locate/issn/01689274;
                 https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.nl/gej-ng/29/17/21/62/27/32/abstract.html;
                 http://www.elsevier.nl/gej-ng/29/17/21/62/27/32/article.pdf;
                 http://www.sciencedirect.com/science/article/pii/S0168927499000318",
  ZMnumber =     "Zbl 0951.33002",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
}

@InProceedings{Hasan:2000:FPI,
  author =       "M. A. Hasan and A. A. Hasan and S. Rahman",
  booktitle =    "Proceedings of the 39th {IEEE} Conference on Decision
                 and Control",
  title =        "Fixed point iterations for computing square roots and
                 the matrix sign function of complex matrices",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "4253--4258",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The purpose of this work has been the development of
                 new set of rational iterations for computing square
                 roots and the matrix sign function of complex matrices.
                 Given any positive integer r{\&}ges;2, we presented a
                 systematic way of deriving rth order \ldots{}",
}

@InProceedings{Hassibi:2000:ESR,
  author =       "B. Hassibi",
  booktitle =    "Proceedings. 2000 {IEEE} International Conference on
                 Acoustics, Speech, and Signal Processing: {ICASSP '00},
                 5--9 June 2000",
  title =        "An efficient square-root algorithm for {BLAST}",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II737--II740",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Bell Labs Layered Space-Time (BLAST) is a scheme for
                 transmitting information over a rich-scattering
                 wireless environment using multiple receive and
                 transmit antennas. The main computational bottleneck in
                 the BLAST algorithm is a ``nulling and \ldots{}",
}

@InProceedings{Hassibi:2000:FSR,
  author =       "B. Hassibi",
  booktitle =    "{Conference Record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers, 2000}",
  title =        "A fast square-root implementation for {BLAST}",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1255--1259",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Bell Labs Layered Space-Time (BLAST) is a scheme for
                 transmitting information over a rich-scattering
                 wireless environment using multiple receive and
                 transmit antennas. The main computational bottleneck in
                 the BLAST algorithm is a ``nulling and \ldots{}",
}

@Article{Holmgren:2000:CAL,
  author =       "Sverker Holmgren and Henrik Brand{\'e}n and Erik
                 Sterner",
  title =        "Convergence Acceleration for the Linearized
                 {Navier--Stokes} Equations using Semicirculant
                 Approximations",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "21",
  number =       "4",
  pages =        "1524--1550",
  month =        jul,
  year =         "2000",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/S1064827597317983",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Fri Oct 27 13:32:22 MDT 2000",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/21/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/31798",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "convergence acceleration",
}

@Misc{Intel:2000:DSR,
  author =       "{Intel}",
  title =        "Divide, Square Root, and Remainder Algorithms for the
                 {Itanium} Architecture",
  howpublished = "Intel Software Development Products",
  month =        jul,
  year =         "2000",
  bibdate =      "Fri Sep 22 17:06:23 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://studylib.net/doc/7921762/divide--square-root-and-remainder-algorithms-for-the-ia-64",
  acknowledgement = ack-nhfb,
}

@Article{Kilbas:2000:CFI,
  author =       "A. A. Kilbas and J. J. Trujillo",
  title =        "Computation of fractional integrals via functions of
                 hypergeometric and {Bessel} type",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "118",
  number =       "1--2",
  pages =        "223--239",
  day =          "1",
  month =        jun,
  year =         "2000",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:43:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700002910",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Lefevre:2000:CRF,
  author =       "V. D. Lefevre and J.-M. Muller",
  booktitle =    "Conference Record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers, 2000",
  title =        "Correctly rounded functions for better arithmetic",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "875--878",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The IEEE 754 standard for floating-point arithmetic
                 requires that the four arithmetic operations and the
                 square root should be correctly rounded. This has
                 improved the accuracy, reliability and portability of
                 numerical software. Unfortunately, such \ldots{}",
}

@Article{Lopez:2000:AES,
  author =       "Jos{\'e} L. L{\'o}pez",
  title =        "Asymptotic Expansions of Symmetric Standard Elliptic
                 Integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "31",
  number =       "4",
  pages =        "754--775",
  year =         "2000",
  CODEN =        "SJMAAH",
  DOI =          "https://doi.org/10.1137/S0036141099351176",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  bibdate =      "Fri Oct 27 08:17:04 MDT 2000",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/31/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/35117",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@InProceedings{Lozier:2000:DPN,
  author =       "Daniel W. Lozier",
  title =        "The {DLMF Project}: a New Initiative in Classical
                 Special Functions",
  crossref =     "Dunkl:2000:PIW",
  pages =        "207--220",
  year =         "2000",
  bibdate =      "Fri Jul 09 06:31:32 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Book{Markstein:2000:IEF,
  author =       "Peter Markstein",
  title =        "{IA-64} and elementary functions: speed and
                 precision",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xix + 298",
  year =         "2000",
  ISBN =         "0-13-018348-2",
  ISBN-13 =      "978-0-13-018348-4",
  LCCN =         "QA76.9.A73 M365 2000",
  bibdate =      "Fri Jan 5 08:00:52 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intel-ia-64.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib;
                 University of California MELVYL catalog.",
  series =       "Hewlett--Packard professional books",
  URL =          "http://www.markstein.org/",
  acknowledgement = ack-nhfb,
  keywords =     "IA-64 (computer architecture)",
  remark =       "Besides recipes for accurate computation of elementary
                 functions, this book also contains algorithms for the
                 correctly-rounded computation of floating-point
                 division and square-root, and of integer division,
                 starting from low-precision reciprocal approximations.
                 There is also a wealth of information on the tradeoffs
                 between integer and floating-point instruction use in a
                 pipelined parallel architecture.",
  tableofcontents = "IA-64 Architecture \\
                 New Architecture Objectives \\
                 VLIW \\
                 Memory Enhancements \\
                 Software Pipelining \\
                 Floating Point Enhancements \\
                 Summary \\
                 IA-64 Instructions And Registers \\
                 Instructions \\
                 Register Sets \\
                 Accessing Memory \\
                 Assembly Language \\
                 Problems \\
                 Increasing Instruction Level Parallelism \\
                 Branching \\
                 Speculation \\
                 Problems \\
                 Floating Point Architecture \\
                 Floating Point Status Register \\
                 Precision \\
                 Fused Multiply-Add \\
                 Division and Square Root Assists \\
                 Floating Comparisons \\
                 Communication between Floating Point and General
                 Purpose Registers \\
                 Fixed Point Multiplication \\
                 SIMD Arithmetic \\
                 Problems \\
                 Programming For IA-64 \\
                 Compiler Options \\
                 Pragmas \\
                 Floating Point Data Types \\
                 In-Line Assembly \\
                 The fenv.h Header \\
                 Extended Examples \\
                 Quad Precision \\
                 Problems \\
                 Computation of Elementary Functions \\
                 Mathematical Preliminaries \\
                 Floating Point \\
                 Approximation and Error Analysis \\
                 The Exclusion Theorem \\
                 Ulps \\
                 Problems \\
                 Approximation Of Functions \\
                 Taylor Series \\
                 Lagrangian Interpolation \\
                 Chebychev Approximation \\
                 Remez Approximation \\
                 Practical Considerations \\
                 Function Evaluation \\
                 Table Construction \\
                 Problems \\
                 Division \\
                 Approximations for the Reciprocal \\
                 Computing the Quotient \\
                 Division Using Only Final Precision Results \\
                 Fast Variants of Division \\
                 Remainder \\
                 Integer Division \\
                 An Implementation of Division \\
                 Problems \\
                 Square Root \\
                 Approximations \\
                 Rounding the Square Root \\
                 Computing the Square Root \\
                 Calculating the Reciprocal Square Root \\
                 An Implementation of Square Root \\
                 Problems \\
                 Exponential Functions \\
                 Definitions and Formulas \\
                 Argument Reduction \\
                 Error Containment \\
                 Computing the Exponential \\
                 The Function expm \\
                 Problems \\
                 Logarithmic Functions \\
                 General Relations \\
                 Argument Reductions \\
                 Error Analysis \\
                 The Function log1p \\
                 Computing the Logarithm \\
                 Problems \\
                 The Power Function \\
                 Definition \\
                 Single Precision \\
                 Double Precision \\
                 Double-Extended Precision \\
                 Quad Precision \\
                 Computing the Power Function \\
                 Problems \\
                 Trigonometric Functions \\
                 Formulas and Identities \\
                 Argument Reduction \\
                 Error Analysis \\
                 Computing the Trigonometric Functions \\
                 Problems \\
                 Inverse Sine And Cosine \\
                 Definitions and Formulas \\
                 Argument Reduction \\
                 Error Analysis \\
                 Computing the arcsin \\
                 Problems \\
                 Inverse Tangent Functions \\
                 Definitions and Formulas \\
                 Argument Reduction \\
                 Error Analysis \\
                 Computing the arctan \\
                 Problems \\
                 Hyperbolic Functions \\
                 Definitions and Formulas \\
                 Argument Reduction \\
                 Error Analysis \\
                 Computing the Hyperbolic Functions \\
                 Problems \\
                 Inverse Hyperbolic Functions \\
                 Definitions and Formulas. arcsinh. arccosh. arctanh \\
                 Problems \\
                 Odds And Ends \\
                 Correctly Rounded Functions \\
                 Monotonicity \\
                 Alternative Algorithms \\
                 Testing \\
                 New Architectural Directions \\
                 Problems \\
                 In-Line Assembly \\
                 Solutions To Problems \\
                 Bibliography \\
                 Subject Index",
}

@Article{Paliouras:2000:FPP,
  author =       "V. Paliouras and K. Karagianni and T. Stouraitis",
  title =        "A floating-point processor for fast and accurate
                 sine\slash cosine evaluation",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "47",
  number =       "5",
  pages =        "441--451",
  month =        may,
  year =         "2000",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.842112",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "A VLSI architecture for fast and accurate
                 floating-point sine/cosine evaluation is presented,
                 combining floating-point and simple fixed-point
                 arithmetic. The algorithm implemented by the
                 architecture is based on second order polynomial
                 interpolation \ldots{}",
}

@Book{Simon:2000:DCF,
  author =       "Marvin Kenneth Simon and Mohamed-Slim Alouini",
  title =        "Digital communication over fading channels: a unified
                 approach to performance analysis",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xix + 544",
  year =         "2000",
  ISBN =         "0-471-31779-9",
  ISBN-13 =      "978-0-471-31779-1",
  LCCN =         "TK5103.7 .S523 2000",
  bibdate =      "Sat Dec 16 17:34:06 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley series in telecommunications and signal
                 processing",
  URL =          "http://www.loc.gov/catdir/bios/wiley043/99056352.html;
                 http://www.loc.gov/catdir/description/wiley035/99056352.html;
                 http://www.loc.gov/catdir/toc/onix06/99056352.html",
  acknowledgement = ack-nhfb,
  author-dates = "1939--",
  subject =      "Digital communications; Reliability; Mathematics;
                 Radio; Transmitters and transmission; Fading",
}

@InProceedings{Takahashi:2000:IMP,
  author =       "D. Takahashi",
  booktitle =    "Proceedings of the 2000 International Workshops on
                 Parallel Processing",
  title =        "Implementation of multiple-precision parallel division
                 and square root on distributed-memory parallel
                 computers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "229--235",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present efficient parallel algorithms for
                 multiple-precision division and square root operation
                 of more than several million decimal digits on
                 distributed-memory parallel computers. It is well known
                 that multiple-precision division and square \ldots{}",
}

@InProceedings{Tchoumatchenko:2000:FBS,
  author =       "V. Tchoumatchenko and T. Vassileva and P. Gurov",
  booktitle =    "{Proceedings of the 22nd EUROMICRO Conference
                 EUROMICRO 96. 'Beyond 2000: Hardware and Software
                 Design Strategies'}",
  title =        "A {FPGA} based square-root coprocessor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "520--525",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present an FPGA implementation of a non-restoring
                 integer square-root algorithm, that uses estimates for
                 result-digit selection and radix-$2$ redundant addition
                 in recurrence. On-the-fly conversion of the
                 result-digit and signed-digit adder/ \ldots{}",
}

@Article{Temme:2000:NAA,
  author =       "Nico M. Temme",
  title =        "Numerical and asymptotic aspects of parabolic cylinder
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "121",
  number =       "1--2",
  pages =        "221--246",
  day =          "1",
  month =        sep,
  year =         "2000",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:43:36 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700003472",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Tommiska:2000:AEI,
  author =       "M. T. Tommiska",
  booktitle =    "Proceedings of the 2000 Third {IEEE} International
                 Caracas Conference on Devices, Circuits and Systems,
                 15--17 March 2000",
  title =        "Area-efficient implementation of a fast square root
                 algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "S18/1--S18/4",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "An area-efficient implementation of a fast-converging
                 square-root algorithm is presented. The design of
                 special arithmetic operations differs in many ways from
                 the traditional tasks that digital designers are used
                 to, and the role of \ldots{}",
}

@Article{Wachspress:2000:EEF,
  author =       "E. L. Wachspress",
  title =        "Evaluating elliptic functions and their inverses",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "39",
  number =       "3--4",
  pages =        "131--136",
  month =        feb,
  year =         "2000",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/S0898-1221(99)00339-9",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:06 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122199003399",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "arithmetic-geometric mean (AGM)",
}

@TechReport{Zimmermann:2000:PGF,
  author =       "Paul Zimmermann",
  title =        "A proof of {GMP} fast division and square root
                 implementations",
  type =         "Technical report",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "14",
  month =        sep,
  year =         "2000",
  bibdate =      "Sun Sep 10 08:48:46 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz",
  abstract =     "This short note gives a detailed correctness proof of
                 fast (i.e., subquadratic) versions of the GNU MP {\tt
                 mpn\_bz\_divrem\_n} and {\tt mpn\_sqrtrem} functions,
                 together with complete GMP code. The {\tt
                 mpn\_bz\_divrem\_n} function divides (with remainder) a
                 number of $ 2 n $ limbs by a divisor of $n$ limbs in $
                 2 K(n) $, where $ K(n) $ is the time spent in a $ (n
                 \times n) $ multiplication, using the
                 Moenck--Borodin--Jebelean--Burnikel--Ziegler algorithm.
                 The {\tt mpn\_sqrtrem} computes the square root and the
                 remainder of a number of $ 2 n $ limbs (square root and
                 remainder have about $n$ limbs each) in time $ 3 K(n) /
                 2 $; it uses Karatsuba Square Root.",
  acknowledgement = ack-nhfb,
}

@Book{Arfken:2001:MMP,
  author =       "George B. (George Brown) Arfken and Hans-Jurgen
                 Weber",
  title =        "Mathematical methods for physicists",
  publisher =    "Harcourt/Academic Press",
  address =      "San Diego, CA, USA",
  edition =      "Fifth",
  pages =        "xiv + 1112",
  year =         "2001",
  ISBN =         "0-12-059825-6, 0-12-059826-4",
  ISBN-13 =      "978-0-12-059825-0, 978-0-12-059826-7",
  LCCN =         "QA37.3 .A74 2001",
  MRclass =      "00A06, 15-01, 26-01, 30-01, 34-01, 35-01, 65-01",
  bibdate =      "Wed Mar 15 06:50:49 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://catalog.hathitrust.org/api/volumes/oclc/45705658.html",
  acknowledgement = ack-nhfb,
  author-dates = "1922--",
  subject =      "Mathematics; Mathematical physics; Matem{\'a}ticas;
                 F{\'i}sica matem{\'a}tica; Mathematical physics;
                 Mathematics; Wiskundige methoden; Natuurkunde;
                 Matem{\'a}tica; F{\'i}sica; Math{\'e}matiques; Physique
                 math{\'e}matique",
  tableofcontents = "1: Vector Analysis / 1 \\
                 1.2: Rotation of the Coordinate Axes / 8 \\
                 1.3: Scalar or Dot Product / 13 \\
                 1.4: Vector or Cross Product / 19 \\
                 1.5: Triple Scalar Product, Triple Vector Product / 27
                 \\
                 1.6: Gradient, [down triangle, open] / 35 \\
                 1.7: Divergence, [down triangle, open] / 40 \\
                 1.8: Curl, [down triangle, open] x / 44 \\
                 1.9: Successive Applications of [down triangle, open] /
                 51 \\
                 1.10: Vector Integration / 55 \\
                 1.11: Gauss's Theorem / 61 \\
                 1.12: Stokes's Theorem / 65 \\
                 1.13: Potential Theory / 69 \\
                 1.14: Gauss's Law, Poisson's Equation / 80 \\
                 1.15: Dirac Delta Function / 84 \\
                 1.16: Helmholtz's Theorem / 96 \\
                 2: Curved Coordinates, Tensors / 103 \\
                 2.1: Orthogonal Coordinates / 103 \\
                 2.2: Differential Vector Operators / 108 \\
                 2.3: Special Coordinate Systems: Introduction / 113 \\
                 2.4: Circular Cylindrical Coordinates / 114 \\
                 2.5: Spherical Polar Coordinates / 121 \\
                 2.6: Tensor Analysis / 131 \\
                 2.7: Contraction, Direct Product / 137 \\
                 2.8: Quotient Rule / 139 \\
                 2.9: Pseudotensors, Dual Tensors / 141 \\
                 2.10: Non-Cartesian Tensors / 150 \\
                 2.11: Tensor Derivative Operators / 160 \\
                 3: Determinants and Matrices / 165 \\
                 3.1: Determinants / 165 \\
                 3.2: Matrices / 174 \\
                 3.3: Orthogonal Matrices / 192 \\
                 3.4: Hermitian Matrices, Unitary Matrices / 206 \\
                 3.5: Diagonalization of Matrices / 213 \\
                 3.6: Normal Matrices / 227 \\
                 4: Group Theory / 237 \\
                 4.1: Introduction to Group Theory / 237 \\
                 4.2: Generators of Continuous Groups / 242 \\
                 4.3: Orbital Angular Momentum / 258 \\
                 4.4: Angular Momentum Coupling / 263 \\
                 4.5: Homogeneous Lorentz Group / 275 \\
                 4.6: Lorentz Covariance of Maxwell's Equations / 278
                 \\
                 4.7: Discrete Groups / 286 \\
                 5: Infinite Series / 303 \\
                 5.2: Convergence Tests / 306 \\
                 5.3: Alternating Series / 322 \\
                 5.4: Algebra of Series / 325 \\
                 5.5: Series of Functions / 329 \\
                 5.6: Taylor's Expansion / 334 \\
                 5.7: Power Series / 346 \\
                 5.8: Elliptic Integrals / 354 \\
                 5.9: Bernoulli Numbers, Euler--Maclaurin Formula / 360
                 \\
                 5.10: Asymptotic Series / 373 \\
                 5.11: Infinite Products / 381 \\
                 6: Functions of a Complex Variable I / 389 \\
                 6.1: Complex Algebra / 390 \\
                 6.2: Cauchy--Riemann Conditions / 399 \\
                 6.3: Cauchy's Integral Theorem / 404 \\
                 6.4: Cauchy's Integral Formula / 411 \\
                 6.5: Laurent Expansion / 416 \\
                 6.6: Mapping / 425 \\
                 6.7: Conformal Mapping / 434 \\
                 7: Functions of a Complex Variable II / 439 \\
                 7.1: Singularities / 439 \\
                 7.2: Calculus of Residues / 444 \\
                 7.3: Dispersion Relations / 469 \\
                 7.4: Method of Steepest Descents / 477 \\
                 8: Differential Equations / 487 \\
                 8.1: Partial Differential Equations / 487 \\
                 8.2: First-Order Differential Equations / 496 \\
                 8.3: Separation of Variables / 506 \\
                 8.4: Singular Points / 516 \\
                 8.5: Series Solutions--Frobenius's Method / 518 \\
                 8.6: A Second Solution / 533 \\
                 8.7: Nonhomogeneous Equation--Green's Function / 548
                 \\
                 8.8: Numerical Solutions / 567 \\
                 9: Sturm--Liouville Theory / 575 \\
                 9.1: Self-Adjoint ODEs / 575 \\
                 9.2: Hermitian Operators / 588 \\
                 9.3: Gram--Schmidt Orthogonalization / 596 \\
                 9.4: Completeness of Eigenfunctions / 604 \\
                 9.5: Green's Function--Eigenfunction Expansion / 616
                 \\
                 10: Gamma-Factorial Function / 631 \\
                 10.1: Definitions, Simple Properties / 631 \\
                 10.2: Digamma and Polygamma Functions / 643 \\
                 10.3: Stirling's Series / 649 \\
                 10.4: Beta Function / 654 \\
                 10.5: Incomplete Gamma Function / 660 \\
                 11: Bessel Functions / 669 \\
                 11.1: Bessel Functions of the First Kind J[subscript
                 v](x) / 669 \\
                 11.2: Orthogonality / 688 \\
                 11.3: Neumann Functions, Bessel Functions of the Second
                 Kind / 694 \\
                 11.4: Hankel Functions / 702 \\
                 11.5: Modified Bessel Functions I[subscript v](x) and
                 K[subscript v](x) / 709 \\
                 11.6: Asymptotic Expansions / 716 \\
                 11.7: Spherical Bessel Functions / 722 \\
                 12: Legendre Functions / 739 \\
                 12.1: Generating Function / 739 \\
                 12.2: Recurrence Relations / 748 \\
                 12.3: Orthogonality / 755 \\
                 12.4: Alternate Definitions / 767 \\
                 12.5: Associated Legendre Functions / 771 \\
                 12.6G: Spherical Harmonics / 786 \\
                 12.7: Orbital Angular Momentum Operators / 792 \\
                 12.8: Addition Theorem for Spherical Harmonics / 796
                 \\
                 12.9: Integrals of Three Ys / 802 \\
                 12.10: Legendre Functions of the Second Kind / 806 \\
                 12.11: Vector Spherical Harmonics / 813 \\
                 13: Special Functions / 817 \\
                 13.1: Hermite Functions / 817 \\
                 13.2: Laguerre Functions / 828 \\
                 13.3: Chebyshev Polynomials / 839 \\
                 13.4: Hypergeometric Functions / 850 \\
                 13.5: Confluent Hypergeometric Functions / 855 \\
                 14: Fourier Series / 863 \\
                 14.1: General Properties / 863 \\
                 14.2: Advantages, Uses of Fouries Series / 870 \\
                 14.3: Applications of Fourier Series / 874 \\
                 14.4: Properties of Fourier Series / 886 \\
                 14.5: Gibbs Phenomenon / 893 \\
                 14.6: Discrete Fourier Transform / 898 \\
                 15: Integral Transforms / 905 \\
                 15.1: Integral Transforms / 905 \\
                 15.2: Development of the Fourier Integral / 909 \\
                 15.3: Fourier Transforms--Inversion Theorem / 911 \\
                 15.4: Fourier Transform of Derivatives / 920 \\
                 15.5: Convolution Theorem / 924 \\
                 15.6: Momentum Representation / 928 \\
                 15.7: Transfer Functions / 935 \\
                 15.8: Laplace Transforms / 938 \\
                 15.9: Laplace Transform of Derivatives / 946 \\
                 15.10: Other Properties / 953 \\
                 15.11: Convolution or Faltungs Theorem / 965 \\
                 15.12: Inverse Laplace Transform / 969 \\
                 16: Integral Equations / 983 \\
                 16.2: Integral Transforms, Generating Functions / 991
                 \\
                 16.3: Neumann Series, Separable Kernels / 997 \\
                 16.4: Hilbert--Schmidt Theory / 1009 \\
                 17: Calculus of Variations / 1017 \\
                 17.1: A Dependent and an Independent Variable / 1018
                 \\
                 17.2: Applications of the Euler Equation / 1023 \\
                 17.3: Several Dependent Variables / 1031 \\
                 17.4: Several Independent Variables / 1036 \\
                 17.5: Several Dependent and Independent Variables /
                 1038 \\
                 17.6: Lagrangian Multipliers / 1039 \\
                 17.7: Variation With Constraints / 1045 \\
                 17.8: Rayleigh--Ritz Variational Technique / 1052 \\
                 18: Nonlinear Methods and Chaos / 1059 \\
                 18.2: Logistic Map / 1060 \\
                 18.3: Sensitivity to Initial Conditions / 1064 \\
                 18.4: Nonlinear Differential Equations / 1068 \\
                 Appendix 1: Real Zeros of a Function / 1085 \\
                 Appendix 2: Gaussian Quadrature / 1089",
}

@Book{Askey:2001:SFG,
  editor =       "R. A. Askey and Tom H. Koornwinder and Walter J.
                 Schempp",
  title =        "Special Functions: Group Theoretical Aspects and
                 Applications",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxxiv + 311",
  year =         "2001",
  ISBN =         "90-277-1822-9",
  ISBN-13 =      "978-90-277-1822-8",
  LCCN =         "QA1 M428 v. 18 c.2",
  bibdate =      "Sat Oct 30 17:58:21 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Mathematics and Its Applications",
  acknowledgement = ack-nhfb,
}

@Article{Bashagha:2001:NRS,
  author =       "A. E. Bashagha",
  title =        "Novel radix-$2$ $k$ square root module",
  journal =      "Circuits, Devices and Systems, IEE Proceedings [see
                 also IEE Proceedings G-Circuits, Devices and Systems]",
  volume =       "148",
  number =       "4",
  pages =        "190--196",
  month =        aug,
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The conventional two's complement radix-$2$ $k$ square
                 root algorithm requires a set of $2^k$ full precision
                 comparisons to generate all the $2^k$ possible values
                 of the partial remainder. The correct remainder is the
                 minimum \ldots{}",
}

@Article{Berg:2001:CMF,
  author =       "Christian Berg and Henrik L. Pedersen",
  title =        "A completely monotone function related to the Gamma
                 function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "133",
  number =       "1--2",
  pages =        "219--230",
  day =          "1",
  month =        aug,
  year =         "2001",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700006440",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Berry:2001:WSF,
  author =       "Michael Berry",
  title =        "Why are special functions special?",
  journal =      j-PHYS-TODAY,
  volume =       "54",
  number =       "4",
  pages =        "11--12",
  month =        apr,
  year =         "2001",
  CODEN =        "PHTOAD",
  DOI =          "https://doi.org/10.1063/1.1372098",
  ISSN =         "0031-9228 (print), 1945-0699 (electronic)",
  ISSN-L =       "0031-9228",
  bibdate =      "Sat Feb 19 13:23:33 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.physicstoday.org/resource/1/phtoad/v54/i4/p11_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Today",
  journal-URL =  "http://www.physicstoday.org/",
}

@Article{Boisvert:2001:MM,
  author =       "Ronald F. Boisvert and M. J. Donahue and Daniel W.
                 Lozier and R. McMichael and B. W. Rust",
  title =        "Mathematics and Measurement",
  journal =      "NIST Journal of Research",
  volume =       "106",
  number =       "1",
  pages =        "293--313",
  month =        jan # "\slash " # feb,
  year =         "2001",
  bibdate =      "Fri Jul 09 06:26:11 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Book{Boyd:2001:CFS,
  author =       "John Philip Boyd",
  title =        "{Chebyshev} and {Fourier} spectral methods",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Second (revised).",
  pages =        "1375",
  year =         "2001",
  ISBN =         "0-486-41183-4 (paperback), 0-486-14192-6 (e-book)",
  ISBN-13 =      "978-0-486-41183-5 (paperback), 978-0-486-14192-3
                 (e-book)",
  LCCN =         "QA404.5 .B69 2001",
  bibdate =      "Sat Feb 17 14:05:46 MST 2024",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Dover Books on Mathematics",
  URL =          "http://www.freading.com/ebooks/details/r:download/ZnJlYWQ6OTc4MDQ4NjE0MTkyMzpl",
  abstract =     "Completely revised text focuses on use of spectral
                 methods to solve boundary value, eigenvalue, and
                 time-dependent problems, but also covers Hermite,
                 Laguerre, rational Chebyshev, sinc, and spherical
                 harmonic functions, as well as cardinal functions,
                 linear eigenvalue problems, matrix-solving methods,
                 coordinate transformations, spherical and cylindrical
                 geometry, and more. Includes 7 appendices and over 160
                 text figures.",
  acknowledgement = ack-nhfb,
  author-dates = "1951--",
  subject =      "Chebyshev polynomials; Fourier analysis; Spectral
                 theory (Mathematics); Polyn{\'y}omes de Tchebychev;
                 Analyse de Fourier; Spectre (Math{\'y}ematiques);
                 MATHEMATICS; General.; Chebyshev polynomials; Fourier
                 analysis; Spectral theory (Mathematics)",
  tableofcontents = "1. Introduction \\
                 2. Chebyshev and Fourier Series \\
                 3. Galerkin and Weighted Residual Methods \\
                 4. Interpolation, Collocation and All That \\
                 5. Cardinal Functions \\
                 6. Pseudospectral Methods for BVPs \\
                 7. Linear Eigenvalue Problems \\
                 8. Symmetry and Parity \\
                 9. Explicit Time-Integration Methods \\
                 10. Partial Summation, the FFT and MMT \\
                 11. Aliasing, Spectral Blocking, and Blow-Up \\
                 12. Implicit Schemes and the Slow Manifold \\
                 13. Splitting and its Cousins \\
                 14. Semi-Lagrangian Advection \\
                 15. Matrix-Solving Methods \\
                 16. Coordinate Transformations \\
                 17. Methods for Unbounded Intervals \\
                 18. Spherical and Cylindrical Geometry \\
                 19. Special Tricks \\
                 20. Symbolic Calculations \\
                 21. The Tau Method \\
                 22. Domain Decomposition Methods \\
                 23. Books and Reviews",
}

@InProceedings{Burgess:2001:DIR,
  author =       "N. Burgess and C. Hinds",
  booktitle =    "Conference Record of the Thirty-Fifth Asilomar
                 Conference on Signals, Systems and Computers, 2001",
  title =        "Design issues in radix-$4$ {SRT} square root {\&}
                 divide unit",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1646--1650",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper introduces a number of design issues not
                 covered in the open literature that arose during the
                 design of a radix-$4$ SRT divide/square root unit for a
                 vector processing chip. These include compression of
                 the partial remainder's m.s.b.'s, \ldots{}",
}

@Book{Bustoz:2001:SFC,
  editor =       "Joaquin Bustoz and Mourad Ismail and S. K. (Sergei
                 Konstantinovich) Suslov",
  title =        "Special functions 2000: current perspective and future
                 directions",
  volume =       "30",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "xi + 520",
  year =         "2001",
  ISBN =         "0-7923-7119-4, 0-7923-7120-8",
  ISBN-13 =      "978-0-7923-7119-9, 978-0-7923-7120-5",
  LCCN =         "QA351 .S694 2001",
  bibdate =      "Sat Oct 30 17:31:39 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  series =       "NATO science series. Series II, Mathematics, physics,
                 and chemistry",
  acknowledgement = ack-nhfb,
  subject =      "functions, special; congresses",
  tableofcontents = "Preface \\
                 Foreword \\
                 Bailey's transform, lemma, chains and tree / George E.
                 Andrews 1 \\
                 Riemann--Hilbert problems for multiple orthogonal
                 polynomials / Walter Van Assche, Jeffrey S. Geronimo,
                 Arno B. J. Kuijlaars 23 \\
                 Flowers which we cannot yet see growing in Ramanujan's
                 garden of hypergeometric series, elliptic functions and
                 $q$'s / Bruce C. Berndt 61 \\
                 Orthogonal rational functions and continued fractions
                 [et al.] 87 \\
                 Orthogonal polynomials and reflection groups / Charles
                 F. Dunkl 111 \\
                 The bispectral problem: an overview / F. Alberto
                 Grunbaum 129 \\
                 The Bochner--Krall problem: some new perspectives / Luc
                 Haine 141 \\
                 Lectures on $q$-orthogonal polynomials / Mourad E. H.
                 Ismail 179 \\
                 The Askey--Wilson function transform scheme / Erik
                 Koelink, Jasper V. Stokman 221 \\
                 Arithmetic of the partition function / Ken Ono 243 \\
                 The associated classical orthogonal polynomials / Mizan
                 Rahman 255 \\
                 Special functions defined by analytic difference
                 equations / S. N. M. Ruijsenaars 281 \\
                 The factorization method, self-similar potentials and
                 quantum algebras / V. P. Spiridonov 335 \\
                 Generalized eigenvalue problem and a new family of
                 rational functions biorthogonal on elliptic grids / V.
                 P. Spiridonov, A. S. Zhedanov 365 \\
                 Orthogonal polynomials and combinatorics / Dennis
                 Stanton 389 \\
                 Basic exponential functions on a $q$-quadratic grid /
                 Sergei K. Suslov 411 \\
                 Projection operator method for quantum groups / V. N.
                 Tolstoy 457 \\
                 Uniform asymptotic expansions / R. Wong 489 \\
                 Exponential asymptotics / R. Wong 505 \\
                 Index 519",
}

@InCollection{Corless:2001:RAE,
  author =       "Robert M. Corless and James H. Davenport and David J.
                 Jeffrey and Gurjeet Litt and Stephen M. Watt",
  booktitle =    "Artificial intelligence and symbolic computation
                 (Madrid, 2000)",
  title =        "Reasoning about the elementary functions of complex
                 analysis",
  volume =       "1930",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "115--126",
  year =         "2001",
  MRclass =      "68W30 (30C35)",
  MRnumber =     "MR1882755 (2002m:68126)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Lecture Notes in Comput. Sci.",
  acknowledgement = ack-nhfb,
}

@Book{Dunkl:2001:OPS,
  author =       "Charles F. Dunkl and Yuan Xu",
  title =        "Orthogonal Polynomials of Several Variables",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xv + 390",
  year =         "2001",
  DOI =          "https://doi.org/10.1017/CBO9780511565717",
  ISBN =         "0-511-56571-2 (e-book), 0-521-80043-9 (hardcover),
                 1-107-09582-4",
  ISBN-13 =      "978-0-511-56571-7 (e-book), 978-0-521-80043-3
                 (hardcover), 978-1-107-09582-3",
  LCCN =         "QA404.5 .D86 2001",
  bibdate =      "Sat Nov 11 07:30:57 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This is the first modern book on orthogonal
                 polynomials of several variables, which are valuable
                 tools used in multivariate analysis, including
                 approximations and numerical integration. The book
                 presents the theory in elegant form and with modern
                 concepts and notation. It introduces the general theory
                 and emphasizes the classical types of orthogonal
                 polynomials whose weight functions are supported on
                 standard domains such as the cube, the simplex, the
                 sphere and the ball. It also focuses on those of
                 Gaussian type, for which fairly explicit formulae
                 exist. The authors' approach blends classical analysis
                 and symmetry-group-theoretic methods.",
  acknowledgement = ack-nhfb,
  remark =       "See also second edition \cite{Dunkl:2014:OPS}",
  tableofcontents = "1. Background \\
                 2. Examples of Orthogonal Polynomials in Several
                 Variables \\
                 3. General Properties of Orthogonal Polynomials in
                 Several Variables \\
                 4. Root Systems and Coxeter groups \\
                 5. Spherical Harmonics Associated with Reflection
                 Groups \\
                 6. Classical and Generalized Classical Orthogonal
                 Polynomials \\
                 7. Summability of Orthogonal Expansions \\
                 8. Orthogonal Polynomials Associated with Symmetric
                 Groups \\
                 9. Orthogonal Polynomials Associated with Octahedral
                 Groups and Applications",
}

@Article{Eklund:2001:CEF,
  author =       "Neil Eklund",
  title =        "{CORDIC}: Elementary Function Computation Using
                 Recursive Sequences",
  journal =      j-COLLEGE-MATH-J,
  volume =       "32",
  number =       "5",
  pages =        "330--333",
  month =        nov,
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/07468342.2001.11921899",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:53:12 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/collegemathj.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/07468342.2001.11921899",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  onlinedate =   "30 Jan 2018",
}

@Article{Elbert:2001:CZB,
  author =       "{\'A}rp{\'a}d Elbert and Andrea Laforgia",
  title =        "A conjecture on the zeros of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "133",
  number =       "1--2",
  pages =        "683--683",
  day =          "1",
  month =        aug,
  year =         "2001",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700007172",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Elbert:2001:SRR,
  author =       "{\'A}. Elbert",
  title =        "Some recent results on the zeros of {Bessel} functions
                 and orthogonal polynomials",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "133",
  number =       "1--2",
  pages =        "65--83",
  day =          "1",
  month =        aug,
  year =         "2001",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704270000635X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Book{Garvan:2001:SCN,
  editor =       "Frank (Frank G.) Garvan and Mourad Ismail",
  title =        "Symbolic computation, number theory, special
                 functions, physics, and combinatorics",
  volume =       "4",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "x + 283",
  year =         "2001",
  ISBN =         "1-4020-0101-0",
  ISBN-13 =      "978-1-4020-0101-7",
  LCCN =         "QA295 .S86 2001",
  bibdate =      "Sat Oct 30 17:31:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  series =       "Developments in mathematics",
  acknowledgement = ack-nhfb,
  subject =      "q-series; Congresses; Algebra; Data processing; Number
                 theory; Functions, Special; Mathematical physics;
                 Combinatorial analysis",
}

@Article{Giordano:2001:IMP,
  author =       "C. Giordano and A. Laforgia",
  title =        "Inequalities and monotonicity properties for the gamma
                 function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "133",
  number =       "1--2",
  pages =        "387--396",
  day =          "1",
  month =        aug,
  year =         "2001",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700006592",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Unpublished{Godfrey:2001:NCC,
  author =       "P. Godfrey",
  title =        "A Note on the Computation of the Convergent {Lanczos}
                 Complex Gamma Approximation",
  year =         "2001",
  bibdate =      "Mon Nov 24 21:04:40 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Unpublished Web file.",
  URL =          "http://my.fit.edu/~gabdo/gamma.txt",
  acknowledgement = ack-nhfb,
}

@Article{Harris:2001:KFL,
  author =       "Frank E. Harris",
  title =        "On {Kryachko}'s formula for the leaky aquifer
                 function",
  journal =      j-IJQC,
  volume =       "81",
  number =       "5",
  pages =        "332--334",
  month =        "????",
  year =         "2001",
  CODEN =        "IJQCB2",
  DOI =          "https://doi.org/10.1002/1097-461X(2001)81:5<332::AID-QUA1002>3.0.CO%3B2-W",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Wed Apr 4 11:48:33 MDT 2001",
  bibsource =    "http://www.interscience.wiley.com/jpages/0020-7608;
                 http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc2000.bib",
  URL =          "http://www3.interscience.wiley.com/cgi-bin/abstract/76507286/START;
                 http://www3.interscience.wiley.com/cgi-bin/fulltext/76507286/FILE?TPL=ftx_start;
                 http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=76507286&PLACEBO=IE.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Quantum Chem.",
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
}

@Article{Karatsuba:2001:ARE,
  author =       "Ekatherina A. Karatsuba",
  title =        "On the asymptotic representation of the {Euler} gamma
                 function by {Ramanujan}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "135",
  number =       "2",
  pages =        "225--240",
  day =          "15",
  month =        oct,
  year =         "2001",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:20 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700005860",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Lang:2001:CRR,
  author =       "Tom{\'a}s Lang and Elisardo Antelo",
  booktitle =    "Proceedings of the 15th {IEEE} Symposium on Computer
                 Arithmetic, 11--13 June 2001",
  title =        "Correctly Rounded Reciprocal Square-Root by Digit
                 Recurrence and Radix-$4$ Implementation",
  crossref =     "Burgess:2001:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "83--93",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "We present a reciprocal square-root algorithm by digit
                 recurrence and selection by a staircase function, and
                 the radix-$4$ implementation. As similar algorithms for
                 division and square-root, the results are obtained
                 correctly rounded in a \ldots{}",
}

@Article{Lether:2001:VPA,
  author =       "F. G. Lether",
  title =        "Variable Precision Algorithm for the Numerical
                 Computation of the {Fermi--Dirac} Function {$ F_j(x) $}
                 of Order $ j = - 3 / 2 $",
  journal =      j-J-SCI-COMPUT,
  volume =       "16",
  number =       "1",
  pages =        "69--79",
  month =        mar,
  year =         "2001",
  CODEN =        "JSCOEB",
  DOI =          "https://doi.org/10.1023/A:1011150530703",
  ISSN =         "0885-7474 (print), 1573-7691 (electronic)",
  ISSN-L =       "0885-7474",
  bibdate =      "Sat Dec 22 13:05:47 MST 2012",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0885-7474&volume=16&issue=1;
                 https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jscicomput.bib",
  URL =          "http://link.springer.com/content/pdf/10.1023/A%3A1011150530703;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0885-7474&volume=16&issue=1&spage=69-79",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Scientific Computing",
  journal-URL =  "http://link.springer.com/journal/10915",
}

@TechReport{Li:2001:LLF,
  author =       "Ren-Cang Li and Peter Markstein and Jon P. Okada and
                 James W. Thomas",
  title =        "The {\tt libm} library and floating-point arithmetic
                 for {HP-UX} on {Itanium}",
  type =         "Technical report",
  institution =  pub-HP,
  address =      pub-HP:adr,
  pages =        "??",
  month =        apr,
  year =         "2001",
  bibdate =      "Fri Jun 24 20:12:09 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://h21007.www2.hp.com/dspp/ddl/ddl_Download_File_TRX/1,1249,942,00.pdf;
                 http://h21007.www2.hp.com/dspp/tech/tech_TechDocumentDetailPage_IDX/1,1701,981,00.html",
  acknowledgement = ack-nhfb,
}

@Article{Loenko:2001:CEF,
  author =       "M. Yu. Loenko",
  title =        "Computation of elementary functions with guaranteed
                 accuracy",
  journal =      j-PROGRAMMIROVANIE,
  volume =       "2",
  pages =        "68--80",
  year =         "2001",
  CODEN =        "PROGD3",
  ISSN =         "0132-3474, 0361-7688",
  MRclass =      "65D15 (65G20)",
  MRnumber =     "MR1867584",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi\u\i skaya Akademiya Nauk. Programmirovanie",
}

@Article{Meyer:2001:JEF,
  author =       "Kenneth R. Meyer",
  title =        "{Jacobi} Elliptic Functions from a Dynamical Systems
                 Point of View",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "108",
  number =       "8",
  pages =        "729--737",
  month =        oct,
  year =         "2001",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jan 30 12:00:14 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00029890.html;
                 http://www.jstor.org/stable/i346008;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2695616",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Muller:2001:CCH,
  author =       "Keith E. Muller",
  title =        "Computing the confluent hypergeometric function, {$
                 M(a, b, x) $}",
  journal =      j-NUM-MATH,
  volume =       "90",
  number =       "1",
  pages =        "179--196",
  month =        nov,
  year =         "2001",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s002110100285",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Feb 3 10:07:57 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/journals/00211/tocs/t1090001.htm;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0029-599X;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath2000.bib",
  URL =          "http://link.springer-ny.com/link/service/journals/00211/bibs/1090001/10900179.htm;
                 http://link.springer-ny.com/link/service/journals/00211/papers/1090001/10900179.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Nagel:2001:EHF,
  author =       "Bengt Nagel",
  title =        "An expansion of the hypergeometric function in
                 {Bessel} functions",
  journal =      j-J-MATH-PHYS,
  volume =       "42",
  number =       "12",
  pages =        "5910--5914",
  month =        dec,
  year =         "2001",
  CODEN =        "JMAPAQ",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Thu Mar 28 19:47:21 MST 2002",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
}

@Article{Plagianakos:2001:LCP,
  author =       "V. P. Plagianakos and N. K. Nousis and M. N.
                 Vrahatis",
  title =        "Locating and computing in parallel all the simple
                 roots of special functions using {PVM}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "133",
  number =       "1--2",
  pages =        "545--554",
  day =          "1",
  month =        aug,
  year =         "2001",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00675-0",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700006750",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Plofker:2001:EIT,
  author =       "Kim Plofker",
  title =        "The {``Error''} in the {Indian} ``{Taylor} Series
                 Approximation'' to the Sine",
  journal =      j-HIST-MATH,
  volume =       "28",
  number =       "4",
  pages =        "283--295",
  month =        nov,
  year =         "2001",
  CODEN =        "HIMADS",
  DOI =          "https://doi.org/10.1006/hmat.2001.2331",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Jun 26 06:20:02 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0315086001923316",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
}

@Article{Rabi:2001:OCA,
  author =       "J. A. Rabi and M. J. S. de Lemos",
  title =        "Optimization of convergence acceleration in multigrid
                 numerical solutions of conductive-convective problems",
  journal =      j-APPL-MATH-COMP,
  volume =       "124",
  number =       "2",
  pages =        "215--226",
  day =          "25",
  month =        oct,
  year =         "2001",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sun Nov 18 09:58:00 MST 2001",
  bibsource =    "http://www.elsevier.com/locate/issn/00963003;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.com/gej-ng/10/9/12/113/31/31/abstract.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "convergence acceleration",
}

@Article{Rahavachary:2001:LSS,
  author =       "Saty Rahavachary",
  title =        "Letters: Setting the {\tt sqrt()} record straight",
  journal =      j-DDJ,
  volume =       "26",
  number =       "4",
  pages =        "12--12",
  month =        apr,
  year =         "2001",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Mar 13 15:22:36 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ddj.com/",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Article{Rappoport:2001:CVP,
  author =       "J. M. Rappoport",
  title =        "Canonical vector polynomials for the computation of
                 complex order {Bessel} functions with the tau method",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "41",
  number =       "3--4",
  pages =        "399--406",
  month =        feb,
  year =         "2001",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:14 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122100002820",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Rump:2001:RPS,
  author =       "Siegfried M. Rump",
  title =        "Rigorous and Portable Standard Functions",
  journal =      j-BIT-NUM-MATH,
  volume =       "41",
  number =       "3",
  pages =        "540--562",
  month =        jun,
  year =         "2001",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1023/A:1021971313412",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 15:06:04 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3;
                 http://www.mai.liu.se/BIT/contents/bit41.html;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=540",
  abstract =     "Today's floating point implementations of elementary
                 transcendental functions are usually very accurate.
                 However, with few exceptions, the actual accuracy is
                 not known. In the present paper we describe a rigorous,
                 accurate, fast and portable implementation of the
                 elementary standard functions based on some existing
                 approximate standard functions. The scheme is outlined
                 for IEEE 754, but not difficult to adapt to other
                 floating point formats. A Matlab implementation is
                 available on the net. Accuracy of the proposed
                 algorithms can be rigorously estimated. As an example
                 we prove that the relative accuracy of the exponential
                 function is better than 2.07 eps in a slightly reduced
                 argument range (eps denoting the relative rounding
                 error unit). Otherwise, extensive computational tests
                 suggest for all elementary functions and all suitable
                 arguments an accuracy better than about 3 eps.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "elementary functions; floating-point arithmetic",
}

@Article{Smith:2001:AFS,
  author =       "David M. Smith",
  title =        "{Algorithm 814}: {Fortran 90} software for
                 floating-point multiple precision arithmetic, gamma and
                 related functions",
  journal =      j-TOMS,
  volume =       "27",
  number =       "4",
  pages =        "377--387",
  month =        dec,
  year =         "2001",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 13 08:49:29 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Book{Srivastava:2001:SAZ,
  author =       "H. M. Srivastava and Choi Junesang",
  title =        "Series Associated with the Zeta and Related
                 Functions",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "ix + 388",
  year =         "2001",
  DOI =          "https://doi.org/10.1007/978-94-015-9672-5",
  ISBN =         "0-7923-7054-6",
  ISBN-13 =      "978-0-7923-7054-3",
  LCCN =         "QA351 .S74 2001",
  bibdate =      "Wed Jun 10 16:22:26 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0822/2001035764-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0822/2001035764-t.html",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Zeta; Series",
  tableofcontents = "Acknowledgements / ix \\
                 1. Introduction and Preliminaries \\
                 1.1. Gamma and Beta functions / 1 \\
                 1.2. Polygamma functions / 13 \\
                 1.3. The multiple Gamma functions / 24 \\
                 1.4. The Gaussian hypergeometric function and its
                 generalization / 44 \\
                 1.5. Stirling numbers of the first and second kind / 56
                 \\
                 1.6. Bernoulli and Euler polynomials and numbers / 59
                 \\
                 Problems / 67 \\
                 2. The Zeta and Related Functions \\
                 2.1. Multiple Hurwitz Zeta functions / 77 \\
                 2.2. The Hurwitz (or generalized) Zeta function / 88
                 \\
                 2.3. The Riemann Zeta function / 96 \\
                 2.4. Polylogarithm functions / 106 \\
                 2.5. Hurwitz--Lerch Zeta functions / 121 \\
                 Problems / 128 \\
                 3. Series Involving Zeta Functions \\
                 3.1. Historical introduction / 142 \\
                 3.2. Use of the Binomial theorem / 143 \\
                 3.3. Use of generating functions / 152 \\
                 3.4. Use of multiple Gamma functions / 159 \\
                 3.5. Use of hypergeometric identities / 250 \\
                 3.6. Other methods and their applications / 260 \\
                 Problems / 269 \\
                 4. Evaluations and Series Representations \\
                 4.1. Evaluation of $\zeta(2n)$ / 275 \\
                 4.2. Rapidly convergent series for $\zeta(2n + 1)$ /
                 280 \\
                 4.3. Further series representations / 289 \\
                 4.4. Computational results / 295 \\
                 Problems / 304 \\
                 5. Determinants of the Laplacians \\
                 5.1. The $n$-dimensional problem / 315 \\
                 5.2. Computations using the simple and multiple Gamma
                 functions / 318 \\
                 5.3. Computations using series of Zeta functions / 325
                 \\
                 5.4. Remarks and observations / 328 \\
                 Problems / 329 \\
                 6. Miscellaneous Results \\
                 6.1. Bernoulli and Euler polynomials at rational
                 arguments / 335 \\
                 6.2. Closed-form summation of trigonometric series /
                 341 \\
                 6.3. Integrals associated with the use of the
                 Euler--Maclaurin summation formula / 344 \\
                 Problems / 350 \\
                 Bibliography / 353 \\
                 Author Index / 379 \\
                 Subject Index / 383",
}

@InProceedings{Takagi:2001:HAC,
  author =       "N. Takagi",
  booktitle =    "Proceedings of the 15th {IEEE} Symposium on Computer
                 Arithmetic, 11--13 June 2001",
  title =        "A Hardware Algorithm for Computing Reciprocal Square
                 Root",
  crossref =     "Burgess:2001:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "94--100",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "A hardware algorithm for computing the reciprocal
                 square root which appears frequently in multimedia and
                 graphics applications is proposed. The reciprocal
                 square root is computed by iteration of
                 carry-propagation-free additions, shifts, and
                 \ldots{}",
}

@Article{Thorsley:2001:AEH,
  author =       "Michael D. Thorsley and Marita C. Chidichimo",
  title =        "An asymptotic expansion for the hypergeometric
                 function {$_2 F_1 (a, b; c; x)$}",
  journal =      j-J-MATH-PHYS,
  volume =       "42",
  number =       "4",
  pages =        "1921--1930",
  month =        apr,
  year =         "2001",
  CODEN =        "JMAPAQ",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Wed Apr 18 05:33:53 MDT 2001",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
}

@Article{Verdonk:2001:PRIa,
  author =       "Brigitte Verdonk and Annie Cuyt and Dennis
                 Verschaeren",
  title =        "A precision- and range-independent tool for testing
                 floating-point arithmetic {I}: {Basic} operations,
                 square root, and remainder",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "92--118",
  month =        mar,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/382043.382404",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/382043.382404;
                 http://www.win.ua.ac.be/~cant/ieeecc754.html",
  abstract =     "This paper introduces a precision- and
                 range-independent tool for testing the compliance of
                 hardware or software implementations of
                 (multiprecision) floating-point arithmetic with the
                 principles of the IEEE standards 754 and 854. The tool
                 consists of a driver program, offering many options to
                 test only specific aspects of the IEEE standards, and a
                 large set of test vectors, encoded in a
                 precision-independent syntax to allow the testing of
                 basic and extended hardware formats as well as
                 multiprecision floating-point implementations. The
                 suite of test vectors stems on one hand from the
                 integration and fully precision- and range-independent
                 generalization of existing hardware test sets, and on
                 the other hand from the systematic testing of exact
                 rounding for all combinations of round and sticky bits
                 that can occur. The former constitutes only 50\% of the
                 resulting test set. In the latter we especially focus
                 on hard-to-round cases. In addition, the test suite
                 implicitly tests properties of floating-point
                 operations, following the idea of Paranoia, and it
                 reports which of the three IEEE-compliant underflow
                 mechanisms is used by the floating-point implementation
                 under consideration. We also check whether that
                 underflow mechanism is used consistently. The tool is
                 backward compatible with the UCBTEST package and with
                 Coonen's test syntax.",
  accepted =     "23 February 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "arithmetic; floating-point; floating-point testing;
                 IEEE floating-point standard; multiprecision;
                 validation; Verification",
  subject =      "Primary Classification: G. Mathematics of Computing
                 G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer
                 arithmetic\\
                 Additional Classification: D. Software D.3 PROGRAMMING
                 LANGUAGES D.3.0 General Subjects: Standards",
}

@Article{Weniger:2001:IID,
  author =       "Ernst Joachim Weniger",
  title =        "Irregular input data in convergence acceleration and
                 summation processes: {General} considerations and some
                 special {Gaussian} hypergeometric series as model
                 problems",
  journal =      j-COMP-PHYS-COMM,
  volume =       "133",
  number =       "2--3",
  pages =        "202--228",
  day =          "15",
  month =        jan,
  year =         "2001",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(00)00175-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Dec 01 09:12:48 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  keywords =     "convergence acceleration",
  remark =       "This paper concentrates on $_2 F_1 (a, b; c; z)$.",
}

@InProceedings{Zheng:2001:ARE,
  author =       "Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui",
  booktitle =    "Proceedings of the 4th International Conference on
                 {ASIC}",
  title =        "The application of redundant encoding in iterative
                 implementation of division and square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "603--606",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The purpose of this paper is to discuss the speed
                 improvement in division and square root computation
                 with small area penalty. The digit recurrence SRT
                 algorithm and functional iteration Newton--Raphson
                 algorithm are generally used in modern \ldots{}",
}

@Misc{Ziv:2001:APM,
  author =       "Abraham Ziv and Moshe Olshansky and Ealan Henis and
                 Anna Reitman",
  title =        "Accurate Portable Mathematical Library ({IBM
                 APMathLib})",
  howpublished = "World-Wide Web document",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  day =          "20",
  month =        dec,
  year =         "2001",
  bibdate =      "Wed Nov 24 08:06:54 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "ftp://www-126.ibm.com/pub/mathlib/mathlib12.20.2001.tar.gz;
                 http://oss.software.ibm.com/mathlib/",
  acknowledgement = ack-nhfb,
}

@Article{Al-Jarrah:2002:GSB,
  author =       "A. Al-Jarrah and K. M. Dempsey and M. L. Glasser",
  title =        "Generalized series of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "143",
  number =       "1",
  pages =        "1--8",
  day =          "1",
  month =        jun,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:28 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042701005052",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Bertot:2002:PGS,
  author =       "Yves Bertot and Nicolas Magaud and Paul Zimmermann",
  title =        "A Proof of {GMP} Square Root",
  journal =      j-J-AUTOM-REASON,
  volume =       "29",
  number =       "3--4",
  pages =        "225--252",
  month =        sep,
  year =         "2002",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1023/A:1021987403425",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  bibdate =      "Sat Feb 08 08:59:09 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "https://link.springer.com/article/10.1023/A:1021987403425",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
  keywords =     "GNU Multiple Precision library",
}

@InCollection{Boisvert:2002:HMF,
  author =       "Ronald F. Boisvert and Daniel W. Lozier",
  title =        "Handbook of Mathematical Functions",
  crossref =     "Lide:2002:CEM",
  pages =        "135--139",
  year =         "2002",
  bibdate =      "Fri Jul 09 06:28:13 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Also printed as NIST Special Publication 958, Jan.
                 2001.",
  URL =          "https://nvlpubs.nist.gov/nistpubs/sp958-lide/135-139.pdf;
                 https://nvlpubs.nist.gov/nistpubs/sp958-lide/html/135-139.html",
  acknowledgement = ack-nhfb,
  remark =       "This article describes the history of the creation of
                 the famous 1964 book by Milton Abramowitz and Irene
                 Stegun named in the title.",
}

@Article{Bradford:2002:RAE,
  author =       "Russell Bradford and Robert M. Corless and James H.
                 Davenport and David J. Jeffrey and Stephen M. Watt",
  title =        "Reasoning about the elementary functions of complex
                 analysis",
  journal =      j-ANN-MATH-ARTIF-INTELL,
  volume =       "36",
  number =       "3",
  pages =        "303--318",
  year =         "2002",
  CODEN =        "AMAIEC",
  ISSN =         "1012-2443 (print), 1573-7470 (electronic)",
  ISSN-L =       "1012-2443",
  MRclass =      "30-01 (03B35 68W30)",
  MRnumber =     "MR1950025 (2003m:30001)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Artificial intelligence and symbolic computation
                 (Madrid, 2000)",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematics and Artificial Intelligence",
  journal-URL =  "http://link.springer.com/journal/10472",
}

@InProceedings{Bradford:2002:TBS,
  author =       "Russell Bradford and James H. Davenport",
  booktitle =    "Proceedings of the 2002 International Symposium on
                 Symbolic and Algebraic Computation",
  title =        "Towards better simplification of elementary
                 functions",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "16--22 (electronic)",
  year =         "2002",
  MRclass =      "68W30 (33B10)",
  MRnumber =     "MR2035228",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bryc:2002:UAR,
  author =       "W. Bryc",
  title =        "A uniform approximation to the right normal tail
                 integral",
  journal =      j-APPL-MATH-COMP,
  volume =       "127",
  number =       "2--3",
  pages =        "365--374",
  day =          "15",
  month =        apr,
  year =         "2002",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/S0096-3003(01)00015-7",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Wed Feb 27 08:48:29 MST 2002",
  bibsource =    "http://www.elsevier.com/locate/issn/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.com/gej-ng/10/9/12/123/27/44/abstract.html;
                 http://www.sciencedirect.com/science/article/pii/S0096300301000157",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Ceberio:2002:HRI,
  author =       "M. Ceberio and L. Granvilliers",
  title =        "{Horner}'s Rule for Interval Evaluation Revisited",
  journal =      j-COMPUTING,
  volume =       "69",
  number =       "1",
  pages =        "51--81",
  month =        mar,
  year =         "2002",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/s00607-002-1448-y",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Nov 5 07:12:39 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/journals/00607/tocs/t2069001.htm;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.de/link/service/journals/00607/bibs/2069001/20690051.htm;
                 http://link.springer.de/link/service/journals/00607/papers/2069001/20690051.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "interval arithmetic; number of multiplications to
                 evaluate a polynomial",
}

@InProceedings{Chiani:2002:IEB,
  author =       "M. Chiani and D. Dardari",
  booktitle =    "Global Telecommunications Conference, 2002. {GLOBECOM
                 '02}. {IEEE}",
  title =        "Improved exponential bounds and approximation for the
                 {$Q$}-function with application to average error
                 probability computation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  year =         "2002",
  DOI =          "https://doi.org/10.1109/glocom.2002.1188428",
  bibdate =      "Sat Dec 16 16:54:47 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/1188428/",
  acknowledgement = ack-nhfb,
}

@Article{Fabijonas:2002:LMC,
  author =       "Bruce R. Fabijonas",
  title =        "{Laplace}'s method on a computer algebra system with
                 an application to the real valued modified {Bessel}
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "146",
  number =       "2",
  pages =        "323--342",
  day =          "15",
  month =        sep,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:30 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042702003643",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Gautschi:2002:GQA,
  author =       "W. Gautschi",
  title =        "{Gauss} quadrature approximations to hypergeometric
                 and confluent hypergeometric functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "139",
  number =       "1",
  pages =        "173--187",
  day =          "1",
  month =        feb,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "33F05 (33C05 33C15 65D20)",
  MRnumber =     "MR1876879 (2002m:33029)",
  bibdate =      "Thu Dec 01 09:11:13 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  remark =       "The paper treats ordinary and confluent hypergeometric
                 functions $_2 F_1$ and $_1 F_1$, using their integral
                 representations to obtain Gaussian quadrature rules.",
}

@Article{Gil:2002:AAB,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 819}: {AIZ}, {BIZ}: two {Fortran 77}
                 routines for the computation of complex {Airy}
                 functions",
  journal =      j-TOMS,
  volume =       "28",
  number =       "3",
  pages =        "325--336",
  month =        sep,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/569147.569150",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Two Fortran 77 routines for the evaluation of Airy
                 functions of complex arguments $ A i(z) $, $ B i(z) $
                 and their derivatives are presented. The routines are
                 based on the use of Gaussian quadrature, Maclaurin
                 series and asymptotic expansions. Comparison with a
                 previous code by D. E. Amos (ACM TOMS 12 (1986)) is
                 provided.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gil:2002:AGH,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 822}: {GIZ}, {HIZ}: two {Fortran} 77
                 routines for the computation of complex {Scorer}
                 functions",
  journal =      j-TOMS,
  volume =       "28",
  number =       "4",
  pages =        "436--447",
  month =        dec,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/592843.592847",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 08:17:55 MST 2003",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Two Fortran 77 routines for the evaluation of Scorer
                 functions of complex arguments $ G i(z) $, $ H i(z) $
                 and their derivatives are presented. The routines are
                 based on the use of quadrature, Maclaurin series and
                 asymptotic expansions. For real $z$ comparison with a
                 previous code by A. J. Macleod (J. Comput. Appl. Math.
                 53 (1994)) is provided.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@TechReport{Gil:2002:CSF,
  author =       "A. Gil and J. Segura and N. M. Temme",
  title =        "Computing special functions by using quadrature
                 rules",
  type =         "Report",
  number =       "MAS-R0230",
  institution =  pub-CWI,
  address =      pub-CWI:adr,
  pages =        "11",
  year =         "2002",
  LCCN =         "QA9.A1 R426 MAS-R0230",
  bibdate =      "Sat Oct 30 19:13:12 2010",
  bibsource =    "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Published in \cite{Gil:2003:CSF}.",
  acknowledgement = ack-nhfb,
}

@Article{Gil:2002:EMB,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Evaluation of the Modified {Bessel} Function of the
                 Third Kind of Imaginary Orders",
  journal =      j-J-COMPUT-PHYS,
  volume =       "175",
  number =       "2",
  pages =        "398--411",
  day =          "20",
  month =        jan,
  year =         "2002",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1006/jcph.2001.6894",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 22:12:13 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0021999101968949",
  abstract =     "The evaluation of the modified Bessel function of the
                 third kind of purely imaginary order $ \mathrm
                 {K}_{ia}(x) $ is discussed; we also present analogous
                 results for the derivative. The methods are based on
                 the use of Maclaurin series, nonoscillatory integral
                 representations, asymptotic expansions, and a continued
                 fraction method, depending on the ranges of x and a. We
                 discuss the range of applicability of the different
                 approaches considered and conclude that power series,
                 the continued fraction method, and the nonoscillatory
                 integral representation can be used to accurately
                 compute the function $ \mathrm {K}_{ia}(x) $ in the
                 range $ 0 \leq a \leq 200 $, $ 0 \leq x \leq 100 $;
                 using a similar scheme the derivative $ \mathrm
                 {K}'_{ia(x)} $ can also be computed within these
                 ranges.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}

@Article{Gray:2002:ARE,
  author =       "Norman Gray",
  title =        "Automatic reduction of elliptic integrals using
                 {Carlson}'s relations",
  journal =      j-MATH-COMPUT,
  volume =       "71",
  number =       "237",
  pages =        "311--318",
  month =        jan,
  year =         "2002",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Thu Jan 31 06:16:28 MST 2002",
  bibsource =    "http://www.ams.org/mcom/2002-71-237;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/journal-getitem?pii=S0025-5718-01-01333-3;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.dvi;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.pdf;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.ps;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.tex",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Hassenpflug:2002:EAS,
  author =       "W. C. Hassenpflug",
  title =        "Error analysis in the series evaluation of the
                 exponential type integral {$ e^z E_1 (z) $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "43",
  number =       "1--2",
  pages =        "207--266",
  month =        jan,
  year =         "2002",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:20 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122101002838",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Kilbas:2002:ARH,
  author =       "Anatoly A. Kilbas and Luis Rodr{\'\i}guez and Juan J.
                 Trujillo",
  title =        "Asymptotic representations for hypergeometric-{Bessel}
                 type function and fractional integrals",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "149",
  number =       "2",
  pages =        "469--487",
  day =          "15",
  month =        dec,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:32 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042702005629",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Book{Korenev:2002:BFT,
  author =       "B. G. (Boris Grigorevich) Korenev",
  title =        "{Bessel} functions and their applications",
  publisher =    pub-TAYLOR-FRANCIS,
  address =      pub-TAYLOR-FRANCIS:adr,
  pages =        "ix + 276",
  year =         "2002",
  ISBN =         "0-415-28130-X (hardcover)",
  ISBN-13 =      "978-0-415-28130-0 (hardcover)",
  LCCN =         "QA408 .K67 2002",
  bibdate =      "Sat Oct 30 17:01:51 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  series =       "Analytical methods and special functions",
  acknowledgement = ack-nhfb,
  subject =      "Bessel functions",
  xxaddress =    pub-CRC:adr,
  xxpublisher =  pub-CRC,
}

@Book{Li:2002:SWF,
  author =       "Le-Wei Li and Xiao-Kang Kang and Mook-Seng Leong",
  title =        "Spheroidal Wave Functions in Electromagnetic Theory",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiii + 295",
  year =         "2002",
  ISBN =         "0-471-03170-4 (hardcover)",
  ISBN-13 =      "978-0-471-03170-3 (hardcover)",
  LCCN =         "QC670 .L49 2002",
  bibdate =      "Sat Apr 1 14:32:29 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley series in microwave and optical engineering",
  URL =          "http://www.loc.gov/catdir/bios/wiley043/2001045399.html;
                 http://www.loc.gov/catdir/description/wiley036/2001045399.html;
                 http://www.loc.gov/catdir/toc/onix07/2001045399.html",
  acknowledgement = ack-nhfb,
  subject =      "Electromagnetic theory; Spheroidal functions",
  tableofcontents = "Preface \\
                 Acknowledgments \\
                 Introduction \\
                 Spheroidal Coordinates and Wave Functions \\
                 Dyadic Green's Functions in Spheroidal Systems \\
                 EM Scattering by a Conducting Spheroid \\
                 EM Scattering by a Coated Dielectric Spheroid \\
                 Spheroidal Antennas \\
                 SAR Distributions in a Spheroidal Head Model \\
                 Analysis of Rainfall Attenuation Using Oblate Raindrops
                 \\
                 EM Eigenfrequencies in a Spheroidal Cavity \\
                 Appendix A: Expressions of Spheroidal Vector Wave
                 Functions \\
                 Appendix B: Intermediates $I_{t,\ell}^{mn}(c)$ in
                 Closed Form \\
                 Appendix C: ${\cal U}^{q(i),t}$ and ${\cal V}^{(i),t}$
                 Used in the Matrix Equation System \\
                 References \\
                 Index",
}

@Article{McCluskey:2002:MLF,
  author =       "Glen McCluskey",
  title =        "Math Library Functions in {C9X}",
  journal =      j-LOGIN,
  volume =       "27",
  number =       "2",
  pages =        "8--13",
  month =        apr,
  year =         "2002",
  CODEN =        "LOGNEM",
  ISSN =         "1044-6397",
  bibdate =      "Tue Apr 11 10:52:14 MDT 2006",
  bibsource =    "http://www.usenix.org/publications/login/2002-04/index.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.usenix.org/publications/login/2002-04/pdfs/mccluskey.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     ";login: the USENIX Association newsletter",
  remark =       "This is a short tutorial on some of the new math
                 library functions in C99.",
}

@Article{Paris:2002:EBU,
  author =       "R. B. Paris",
  title =        "Error bounds for the uniform asymptotic expansion of
                 the incomplete gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "147",
  number =       "1",
  pages =        "215--231",
  day =          "1",
  month =        oct,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:30 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704270200434X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Paris:2002:UAE,
  author =       "R. B. Paris",
  title =        "A uniform asymptotic expansion for the incomplete
                 gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "148",
  number =       "2",
  pages =        "323--339",
  month =        nov,
  year =         "2002",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/s0377-0427(02)00553-8",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 18 09:18:08 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See related work \cite{Paris:2016:UAE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Pineiro:2002:HRL,
  author =       "J.-A. Pineiro and M. D. Ercegovac and J. D. Bruguera",
  booktitle =    "{The IEEE International Conference on
                 Application-Specific Systems, Architectures and
                 Processors, 2002. Proceedings. 17--19 July 2002}",
  title =        "High-radix logarithm with selection by rounding",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "101--110",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "A high-radix digit-recurrence algorithm or the
                 computation of the logarithm is presented in this
                 paper. Selection by rounding is used in iterations
                 j/spl ges/2, and selection by table in the first
                 iteration is combined with a restricted digit-set
                 \ldots{}",
}

@Article{Pineiro:2002:HSD,
  author =       "J. A. Pi{\~n}eiro and J. D. Bruguera",
  title =        "High-Speed Double Precision Computation of Reciprocal,
                 Division, Square Root, and Inverse Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "51",
  number =       "12",
  pages =        "1377--1388",
  month =        dec,
  year =         "2002",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2002.1146704",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A new method for the high-speed computation of
                 double-precision floating-point reciprocal, division,
                 square root, and inverse square root operations is
                 presented in this paper. This method employs a
                 second-degree minimax polynomial approximation to
                 \ldots{}",
}

@Book{Samko:2002:HIT,
  author =       "S. G. (Stefan Grigorevich) Samko",
  title =        "Hypersingular integrals and their applications",
  volume =       "5",
  publisher =    pub-TAYLOR-FRANCIS,
  address =      pub-TAYLOR-FRANCIS:adr,
  pages =        "xvii + 359",
  year =         "2002",
  ISBN =         "0-415-27268-8",
  ISBN-13 =      "978-0-415-27268-1",
  LCCN =         "QA403.5 .S26 2002",
  bibdate =      "Sat Oct 30 17:22:10 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  series =       "Analytical methods and special functions",
  acknowledgement = ack-nhfb,
  subject =      "singular integrals",
}

@InProceedings{Sawada:2002:FVD,
  author =       "J. Sawada",
  title =        "Formal verification of divide and square root
                 algorithms using series calculation",
  crossref =     "Borrione:2002:TIW",
  pages =        "31--49",
  year =         "2002",
  bibdate =      "Fri Jun 24 15:14:00 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sawada:2002:MVS,
  author =       "Jun Sawada and Ruben Gamboa",
  title =        "Mechanical Verification of a Square Root Algorithm
                 Using {Taylor}'s Theorem",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2517",
  pages =        "274--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Nov 30 20:58:00 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2517.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.de/link/service/series/0558/bibs/2517/25170274.htm;
                 http://link.springer.de/link/service/series/0558/papers/2517/25170274.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Misc{Sebah:2002:IGF,
  author =       "Pascal Sebah and Xavier Gourdon",
  title =        "Introduction to the Gamma Function",
  howpublished = "World-Wide Web document",
  day =          "4",
  month =        feb,
  year =         "2002",
  bibdate =      "Sat May 01 16:07:51 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://numbers.computation.free.fr/Constants/constants.html;
                 http://numbers.computation.free.fr/Constants/Miscellaneous/gammaFunction.ps",
  acknowledgement = ack-nhfb,
}

@Article{Shore:2002:RMM,
  author =       "Haim Shore",
  title =        "Response Modeling Methodology ({RMM})-Exploring the
                 Properties of the Implied Error Distribution",
  journal =      j-COMMUN-STAT-THEORY-METH,
  volume =       "31",
  number =       "12",
  pages =        "2225--2249",
  year =         "2002",
  CODEN =        "CSTMDC",
  DOI =          "https://doi.org/10.1081/STA-120017223",
  ISSN =         "0361-0926 (print), 1532-415X (electronic)",
  ISSN-L =       "0361-0926",
  bibdate =      "Wed Jan 27 05:41:30 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/communstattheorymeth2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Theory and Methods",
  journal-URL =  "http://www.tandfonline.com/loi/lsta20",
}

@Article{Tornaria:2002:SRM,
  author =       "Gonzalo Tornar{\'\i}a",
  title =        "Square Roots Modulo $p$",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2286",
  pages =        "430--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:12 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2286.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2286/22860430.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2286/22860430.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Book{Vladimirov:2002:MTG,
  author =       "V. S. (Vasilii Sergeevich) Vladimirov",
  title =        "Methods of the theory of generalized functions",
  volume =       "6",
  publisher =    pub-TAYLOR-FRANCIS,
  address =      pub-TAYLOR-FRANCIS:adr,
  pages =        "xiv + 311",
  year =         "2002",
  ISBN =         "0-415-27356-0",
  ISBN-13 =      "978-0-415-27356-5",
  LCCN =         "QC20.7.T45 V53 2002",
  bibdate =      "Sat Oct 30 17:22:15 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  series =       "Analytical methods and special functions",
  acknowledgement = ack-nhfb,
  subject =      "Theory of distributions (Functional analysis);
                 Integral transforms; Mathematical physics",
}

@Article{Aarts:2003:ASF,
  author =       "Ronald M. Aarts and Augustus J. E. M. Janssen",
  title =        "Approximation of the {Struve} function {$ H_1 $}
                 occurring in impedance calculations",
  journal =      j-J-ACOUST-SOC-AM,
  volume =       "113",
  number =       "5",
  pages =        "2635--2637",
  month =        may,
  year =         "2003",
  CODEN =        "JASMAN",
  DOI =          "https://doi.org/10.1121/1.1564019",
  ISSN =         "0001-4966",
  ISSN-L =       "0001-4966",
  bibdate =      "Tue Mar 28 07:23:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Acoustical Society of America",
  journal-URL =  "http://scitation.aip.org/content/asa/journal/jasa",
}

@Article{Abad:2003:AEQ,
  author =       "J. Abad and J. Sesma",
  title =        "Asymptotic expansion of the quasiconfluent
                 hypergeometric function",
  journal =      j-J-MATH-PHYS,
  volume =       "44",
  number =       "4",
  pages =        "1723--1729",
  month =        apr,
  year =         "2003",
  CODEN =        "JMAPAQ",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Tue Dec 16 11:36:01 MST 2003",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
}

@Article{Agou:2003:SPR,
  author =       "Simon Joseph Agou and Marc Del{\'e}glise and
                 Jean-Louis Nicolas",
  title =        "Short Polynomial Representations for Square Roots
                 Modulo $p$",
  journal =      j-DESIGNS-CODES-CRYPTOGR,
  volume =       "28",
  number =       "1",
  pages =        "33--44",
  month =        jan,
  year =         "2003",
  CODEN =        "DCCREC",
  ISSN =         "0925-1022 (print), 1573-7586 (electronic)",
  ISSN-L =       "0925-1022",
  bibdate =      "Thu Dec 11 06:27:20 MST 2003",
  bibsource =    "http://www.wkap.nl/jrnltoc.htm/0925-1022;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Designs, codes, and cryptography",
  journal-URL =  "http://link.springer.com/journal/10623",
}

@Article{Alzer:2003:GHM,
  author =       "Horst Alzer",
  title =        "On {Gautschi}'s harmonic mean inequality for the gamma
                 function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "157",
  number =       "1",
  pages =        "243--249",
  day =          "1",
  month =        aug,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:37 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042703004564",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Beaumont:2003:BSE,
  author =       "James Beaumont and Russell Bradford and James H.
                 Davenport",
  booktitle =    "Proceedings of the 2003 International Symposium on
                 Symbolic and Algebraic Computation",
  title =        "Better simplification of elementary functions through
                 power series",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "30--36 (electronic)",
  year =         "2003",
  MRclass =      "33F10 (68W30)",
  MRnumber =     "MR2035192 (2005e:33018)",
  MRreviewer =   "Ekatherina A. Karatsuba",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "A new algorithm testing the correctness of
                 simplifications of elementary functions in the presence
                 of branch cuts is proposed.",
}

@Article{Buhring:2003:PSH,
  author =       "Wolfgang B{\"u}hring",
  title =        "Partial sums of hypergeometric functions of unit
                 argument",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "132",
  number =       "2",
  pages =        "407--415",
  month =        "????",
  year =         "2003",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "33C20",
  MRnumber =     "MR2022363 (2005f:33011)",
  bibdate =      "Thu Dec 01 09:53:54 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}

@Article{Chiani:2003:NEB,
  author =       "M. Chiani and D. Dardari and M. K. Simon",
  title =        "New exponential bounds and approximations for the
                 computation of error probability in fading channels",
  journal =      j-IEEE-TRANS-WIREL-COMMUN,
  volume =       "24",
  number =       "5",
  pages =        "840--845",
  month =        may,
  year =         "2003",
  CODEN =        "ITWCAX",
  DOI =          "https://doi.org/10.1109/twc.2003.814350",
  ISSN =         "1536-1276 (print), 1558-2248 (electronic)",
  ISSN-L =       "1536-1276",
  bibdate =      "Sat Dec 16 15:47:42 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/1210748/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Wireless Communications",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7693",
}

@TechReport{Cornea:2003:DSR,
  author =       "M. Cornea and J. Harrison and C. Iordache and B. Norin
                 and S. Story",
  title =        "Division, Square Root and Remainder Algorithms for the
                 {Intel Itanium} Architecture",
  type =         "Report",
  institution =  pub-INTEL,
  address =      pub-INTEL:adr,
  month =        nov,
  year =         "2003",
  bibdate =      "Fri Jun 24 12:05:58 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Coussement:2003:AMO,
  author =       "Els Coussement and Walter {Van Assche}",
  title =        "Asymptotics of multiple orthogonal polynomials
                 associated with the modified {Bessel} functions of the
                 first kind",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "153",
  number =       "1--2",
  pages =        "141--149",
  day =          "1",
  month =        apr,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:34 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042702005964",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Dominici:2003:NDS,
  author =       "Diego Dominici",
  title =        "Nested derivatives: a simple method for computing
                 series expansions of inverse functions",
  journal =      j-INT-J-MATH-MATH-SCI,
  volume =       "58",
  pages =        "3699--3715",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "0161-1712 (print), 1687-0425 (electronic)",
  ISSN-L =       "0161-1712",
  MRclass =      "41A58 (33F10)",
  MRnumber =     "MR2031140 (2005f:41079)",
  MRreviewer =   "Tord H. Ganelius",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www2.newpaltz.edu/~dominicd/NESTED14.pdf",
  abstract =     "We give an algorithm to compute the series expansion
                 for the inverse of a given function. The algorithm is
                 extremely easy to implement and gives the first $N$
                 terms of the series. We show several examples of its
                 application in calculating the inverses of some special
                 functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematics and Mathematical
                 Sciences",
  journal-URL =  "https://www.hindawi.com/journals/ijmms/",
  keywords =     "error function, erf(x); incomplete beta function,
                 B(nu,mu,x); incomplete gamma function, gamma(nu,x);
                 logarithm integral, li(x); Maple; sine integral,
                 Si(x)",
}

@InProceedings{Ercegovac:2003:DRA,
  author =       "M. D. Ercegovac and J.-M. Muller",
  booktitle =    "Conference Record of the Thirty-Seventh Asilomar
                 Conference on Signals, Systems and Computers, 2003",
  title =        "Digit-recurrence algorithms for division and square
                 root with limited precision primitives",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1440--1444",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We propose a digit-recurrence algorithm for square
                 root using limited-precision multipliers, adders, and
                 table-lookups. The algorithm, except in the
                 initialization, uses the digit-recurrence algorithm for
                 division with limited-precision primitives \ldots{}",
}

@Article{Fabijonas:2003:ACM,
  author =       "B. R. Fabijonas and Daniel W. Lozier and J. M.
                 Rappoport",
  title =        "Algorithms and Codes for the {Macdonald} Function:
                 Recent Progress and Comparisons",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "161",
  number =       "1",
  pages =        "179--192",
  month =        "????",
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "33F05 (33C10 65D20)",
  MRnumber =     "MR2018582",
  bibdate =      "Fri Jul 09 06:21:51 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir6596.ps",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Galue:2003:FRG,
  author =       "L. Galu{\'e} and A. Al-Zamel and Shyam L. Kalla",
  title =        "Further results on generalized hypergeometric
                 functions",
  journal =      j-APPL-MATH-COMP,
  volume =       "136",
  number =       "1",
  pages =        "17--25",
  day =          "25",
  month =        mar,
  year =         "2003",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Jan 9 08:40:52 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Gautschi:2003:EEI,
  author =       "W. Gautschi and F. E. Harris and N. M. Temme",
  title =        "Expansions of the exponential integral in incomplete
                 gamma functions",
  journal =      j-APPL-MATH-LETT,
  volume =       "16",
  number =       "7",
  pages =        "1095--1099",
  month =        oct,
  year =         "2003",
  CODEN =        "AMLEEL",
  DOI =          "https://doi.org/10.1016/S0893-9659(03)90100-5",
  ISSN =         "0893-9659 (print), 1873-5452 (electronic)",
  ISSN-L =       "0893-9659",
  MRclass =      "33B20",
  bibdate =      "Wed Dec 4 10:29:43 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "1058.33002",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08939659",
}

@Article{Gil:2003:CMB,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Computation of the modified {Bessel} function of the
                 third kind of imaginary orders: uniform {Airy}-type
                 asymptotic expansion",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "153",
  number =       "1--2",
  pages =        "225--234",
  day =          "1",
  month =        apr,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:34 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042702006088",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Gil:2003:CSF,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Computing Special Functions by Using Quadrature
                 Rules",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "33",
  number =       "1--4",
  pages =        "265--275",
  month =        aug,
  year =         "2003",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Sep 29 08:37:11 MDT 2003",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Harrison:2003:FVS,
  author =       "John Harrison",
  title =        "Formal verification of square root algorithms",
  journal =      j-FORM-METHODS-SYST-DES,
  volume =       "22",
  number =       "2",
  pages =        "143--153",
  month =        mar,
  year =         "2003",
  CODEN =        "FMSDE6",
  DOI =          "https://doi.org/10.1023/A:1022973506233",
  ISSN =         "0925-9856 (print), 1572-8102 (electronic)",
  ISSN-L =       "0925-9856",
  bibdate =      "Sat Feb 08 08:47:21 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intel-ia-64.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1023/A:1022973506233",
  abstract =     "We discuss the formal verification of some low-level
                 mathematical software for the Intel Itanium
                 architecture. A number of important algorithms have
                 been proven correct using the HOL Light theorem prover.
                 After briefly surveying some of our formal verification
                 work, we discuss in more detail the verification of a
                 square root algorithm, which helps to illustrate why
                 some features of HOL Light, in particular
                 programmability, make it especially suitable for these
                 applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "Formal Methods in System Design",
  journal-URL =  "https://dl.acm.org/loi/fmsd",
}

@Misc{Intel:2003:DSR,
  author =       "{Intel}",
  title =        "Divide, Square Root, and Remainder Algorithms for the
                 {Itanium} Architecture",
  howpublished = "Intel Software Development Products",
  day =          "18",
  month =        dec,
  year =         "2003",
  bibdate =      "Tue Nov 18 16:23:36 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.intel.com/cd/software/products/asmo-na/eng/219863.htm",
  acknowledgement = ack-nhfb,
}

@Misc{Intel:2003:NID,
  author =       "{Intel}",
  title =        "Non-{IEEE} Division, Square Root, Reciprocal, and
                 Reciprocal Square Root Algorithms for the {Intel
                 Itanium} Architecture",
  howpublished = "Intel Software Development Products",
  day =          "18",
  month =        dec,
  year =         "2003",
  bibdate =      "Tue Nov 18 16:23:36 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.intel.com/cd/software/products/asmo-na/eng/219864.htm",
  acknowledgement = ack-nhfb,
}

@Article{Kzaz:2003:CAG,
  author =       "M. Kzaz and M. Pr{\'e}vost",
  title =        "Convergence Acceleration of {Gauss--Chebyshev}
                 Quadrature Formulae",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "34",
  number =       "2--4",
  pages =        "379--391",
  month =        dec,
  year =         "2003",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Tue Jan 13 17:32:50 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/48/6/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/48/6/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "convergence acceleration",
}

@Article{Lang:2003:RRS,
  author =       "Tom{\'a}s Lang and Elisardo Antelo",
  title =        "Radix-$4$ Reciprocal Square-root and Its Combination
                 with Division and Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "9",
  pages =        "1100--1114",
  month =        sep,
  year =         "2003",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2003.1228508",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "In this work, we present a reciprocal square root
                 algorithm by digit recurrence and selection by a
                 staircase function and the radix-$4$ implementation. As
                 in similar algorithms for division and square root, the
                 results are obtained correctly rounded in a
                 straightforward manner (in contrast to existing methods
                 to compute the reciprocal square root). Although,
                 apparently, a single selection function can only be
                 used for $ j \geq 2 $ (the selection constants are
                 different for $ j = 0 $, $ j = 1 $, and $ j \geq 2 $ ),
                 we show that it is possible to use a single selection
                 function for all iterations. We perform a rough
                 comparison with existing methods and we conclude that
                 our implementation is a low hardware complexity
                 solution with moderate latency, especially for exactly
                 rounded results. We also extend the unit to support
                 division and square root with the same selection
                 function and with slight modifications in the
                 initialization of the reciprocal square root unit.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Lefevre:2003:WCC,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller",
  title =        "Worst Cases for Correct Rounding for the Elementary
                 Functions in Double Precision",
  type =         "Technical report",
  institution =  "INRIA, Projet Spaces, LORIA, Campus Scientifique",
  address =      "B.P. 239, 54506 Vandoeuvre-l{\`e}s-Nancy Cedex,
                 France",
  day =          "14",
  month =        aug,
  year =         "2003",
  bibdate =      "Thu Jul 08 08:27:53 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://perso.ens-lyon.fr/jean-michel.muller/TMDworstcases.pdf",
  abstract =     "We give the results of our search for the worst cases
                 for correct rounding of the major elementary functions
                 in double precision floating-point arithmetic. These
                 results allow the design of reasonably fast routines
                 that will compute these functions with correct
                 rounding, at least in some interval, for any of the
                 four rounding modes specified by the IEEE-754 standard.
                 They will also allow one to easily test libraries that
                 are claimed to provide correctly rounded functions.",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic; elementary functions;
                 floating-point arithmetic; Table Maker's Dilemma",
}

@Article{Lozier:2003:NDL,
  author =       "Daniel W. Lozier",
  title =        "{NIST Digital Library of Mathematical Functions}",
  journal =      j-ANN-MATH-ARTIF-INTELL,
  volume =       "38",
  number =       "1--3",
  pages =        "105--119",
  month =        may,
  year =         "2003",
  CODEN =        "AMAIEC",
  ISSN =         "1012-2443 (print), 1573-7470 (electronic)",
  ISSN-L =       "1012-2443",
  bibdate =      "Fri Jul 09 06:23:08 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/Linz01.ps",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematics and Artificial Intelligence",
  journal-URL =  "http://link.springer.com/journal/10472",
}

@InProceedings{Markstein:2003:FQP,
  author =       "Peter Markstein",
  title =        "A fast quad precision elementary function library for
                 {Itanium}",
  crossref =     "Anonymous:2003:CRN",
  pages =        "5--12",
  year =         "2003",
  bibdate =      "Fri Jun 24 20:14:39 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This talk will describe Itanium's floating point
                 architecture and how it has been used to produce a high
                 performance, highly accurate quad precision elementary
                 function library.\par

                 Itanium's floating-point features will first be
                 described, from the point of view of a computer
                 architect. Many conflicting requirements vie for
                 consideration during the design of a new computer
                 architecture. These include instruction word size,
                 number of registers, the set of operations, arithmetic
                 precisions supported, and memory access. Some of the
                 trade-offs during the design phase will be
                 discussed.\par

                 One of the objectives of the original Itanium design
                 was to accelerate quad precision arithmetic. The talk
                 will describe how the Itanium elementary function
                 library was constructed, with attention to performance
                 and accuracy. Because a pair of double-extended
                 floating point words are used for internal operations
                 involving quad precision numbers, intermediate results,
                 holding 128 bits, provide 15 guard bits during
                 intermediate calculations, resulting in a very low
                 percentage of misrounded results.",
  acknowledgement = ack-nhfb,
}

@Book{Mason:2003:CP,
  author =       "J. C. Mason and D. C. Handscomb",
  title =        "{Chebyshev} Polynomials",
  publisher =    pub-CHAPMAN-HALL-CRC,
  address =      pub-CHAPMAN-HALL-CRC:adr,
  pages =        "xiii + 341",
  year =         "2003",
  ISBN =         "0-8493-0355-9",
  ISBN-13 =      "978-0-8493-0355-5",
  LCCN =         "QA404.5 .M37 2003",
  bibdate =      "Fri Apr 17 09:45:35 MDT 2009",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Chebyshev polynomials",
  xxauthor =     "J. C. Mason and D. C. (David Christopher) Handscomb",
  xxURL =        "http://www.loc.gov/catdir/enhancements/fy0646/2002073578-d.html",
}

@InProceedings{Meunier:2003:EAG,
  author =       "Ludovic Meunier and Bruno Salvy",
  editor =       "Hoon Hong",
  booktitle =    "Proceedings of the 2003 International Symposium on
                 Symbolic and Algebraic Computation: {Philadelphia, PA,
                 USA, August 3--6, 2003}",
  title =        "{ESF}: an automatically generated encyclopedia of
                 special functions",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  month =        aug,
  year =         "2003",
  DOI =          "https://doi.org/10.1145/860854.860898",
  ISBN =         "1-58113-641-2 (paperback)",
  ISBN-13 =      "978-1-58113-641-8 (paperback)",
  LCCN =         "QA76.5 S98 2003; QA76.95.I59 2003",
  bibdate =      "Sat Nov 11 06:21:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "We present our on-going work on the automatic
                 generation of an encyclopedia of special functions on
                 the web, called The Encyclopedia of Special Functions
                 (ESF) (\url{http://algo.inria.fr/esf}). All
                 mathematical formulae in the ESF are computed, typeset
                 and displayed without any human intervention. This is
                 achieved by exploiting a collection of computer algebra
                 algorithms in a systematic way, on top of a specially
                 designed data structure for a class of special
                 functions.",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1145/860854",
  book-URL =     "https://dl.acm.org/doi/proceedings/10.1145/860854",
}

@Article{Ovtchinnikov:2003:CEGb,
  author =       "E. Ovtchinnikov",
  title =        "Convergence Estimates for the Generalized {Davidson}
                 Method for Symmetric Eigenvalue Problems {II}: The
                 Subspace Acceleration",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "41",
  number =       "1",
  pages =        "272--286",
  month =        feb,
  year =         "2003",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/S0036142902411768",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  bibdate =      "Fri Aug 15 05:57:09 MDT 2003",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SINUM/41/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/41176",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  keywords =     "convergence acceleration",
}

@Article{Paris:2003:AEG,
  author =       "R. B. Paris",
  title =        "The asymptotic expansion of a generalised incomplete
                 gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "151",
  number =       "2",
  pages =        "297--306",
  day =          "15",
  month =        feb,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:33 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042702008099",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Paszkowski:2003:CAS,
  author =       "Stefan Paszkowski",
  title =        "Convergence Acceleration of Some Continued Fractions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "32",
  number =       "2--4",
  pages =        "193--247",
  month =        apr,
  year =         "2003",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Sep 29 08:37:11 MDT 2003",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/45/5/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/45/5/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "convergence acceleration",
}

@Article{Pedersen:2003:DGF,
  author =       "Henrik L. Pedersen",
  title =        "The double gamma function and related {Pick}
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "153",
  number =       "1--2",
  pages =        "361--369",
  day =          "1",
  month =        apr,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:34 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042702006040",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Petropoulou:2003:CZB,
  author =       "Eugenia N. Petropoulou and Panayiotis D. Siafarikas
                 and Ioannis D. Stabolas",
  title =        "On the common zeros of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "153",
  number =       "1--2",
  pages =        "387--393",
  day =          "1",
  month =        apr,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:34 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042702006416",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Pineiro:2003:LHR,
  author =       "J.-A. Pineiro and J. D. Bruguera and M. D. Ercegovac",
  booktitle =    "{ISCAS '03. Proceedings of the 2003 International
                 Symposium on Circuits and Systems. 25--28 May 2003}",
  title =        "On-line high-radix exponential with selection by
                 rounding",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "IV-121--IV-124",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "An on-line high-radix algorithm for computing the
                 exponential function (e/sup x/) with arbitrary
                 precision n is presented. Selection by rounding and a
                 redundant digit-set for the digits e/sub j/ are used,
                 with selection by table in the first \ldots{}",
}

@Book{Sidi:2003:PEM,
  author =       "Avram Sidi",
  title =        "Practical Extrapolation Methods: Theory and
                 Applications",
  volume =       "10",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xxii + 519",
  year =         "2003",
  ISBN =         "0-521-66159-5",
  ISBN-13 =      "978-0-521-66159-1",
  LCCN =         "QA281 .S555 2003",
  bibdate =      "Mon Jul 5 16:49:09 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Cambridge monographs on applied and computational
                 mathematics",
  acknowledgement = ack-nhfb,
  subject =      "extrapolation",
  xxURL =        "http://www.loc.gov/catdir/samples/cam033/2002024669.html;
                 http://www.loc.gov/catdir/description/cam022/2002024669.html;
                 http://www.loc.gov/catdir/toc/cam024/2002024669.html",
}

@Misc{Tkachev:2003:EFI,
  author =       "Vladimir G. Tkachev",
  title =        "Elliptic functions: Introduction course",
  howpublished = "Web lecture notes.",
  day =          "25",
  month =        nov,
  year =         "2003",
  bibdate =      "Wed Mar 15 08:43:21 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://users.mai.liu.se/vlatk48/teaching/lect2-agm.pdf",
  acknowledgement = ack-nhfb,
  tableofcontents = "Chapter 1. Elliptic integrals and Jacobi's theta
                 functions / 5 \\
                 1.1. Elliptic integrals and the AGM: real case / 5 \\
                 1.1.3. The arithmetic-geometric mean iteration / 7 \\
                 1.2. Lemniscates and elastic curves / 11 \\
                 1.3. Euler's addition theorem / 18 \\
                 1.4. Theta functions: preliminaries 5 / 24 \\
                 Chapter 2. General theory of doubly periodic functions
                 / 31 \\
                 2.1. Preliminaries / 31 \\
                 2.2. Periods of analytic functions / 33 \\
                 2.3. Existence of doubly periodic functions / 36 \\
                 2.4. Liouville's theorems / 38 \\
                 2.5. The Weierstrass function $\wp(z)$ / 43 \\
                 2.6. Modular forms / 51 \\
                 Bibliography / 61",
}

@InProceedings{Wang:2003:TDF,
  author =       "Xiaojun Wang and B. E. Nelson",
  booktitle =    "{FCCM 2003}: 11th Annual {IEEE} Symposium on
                 Field-Programmable Custom Computing Machines, 9--11
                 April 2003",
  title =        "Tradeoffs of designing floating-point division and
                 square root on {Virtex FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "195--203",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Low latency, high throughput and small area are three
                 major design considerations of an FPGA (field
                 programmable gate array) design. In this paper, we
                 present a high radix SRT division algorithm and a
                 binary restoring square root algorithm. We \ldots{}",
}

@Article{Yousif:2003:CBF,
  author =       "Hashim A. Yousif and Richard Melka",
  title =        "Computing {Bessel} functions of the second kind in
                 extreme parameter regimes",
  journal =      j-COMP-PHYS-COMM,
  volume =       "151",
  number =       "1",
  pages =        "25--34",
  day =          "1",
  month =        mar,
  year =         "2003",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(02)00697-5",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 23:41:27 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465502006975",
  abstract =     "A useful method of computing the integral order Bessel
                 functions of the second kind $ Y_n(x + i y) $ when
                 either, the absolute value of the real part, or the
                 imaginary part of the argument $ z = x + i y $ is
                 small, is described. This method is based on computing
                 the Bessel functions for extreme parameter regimes when
                 $ x \sim 0 $ (or $ y \sim 0 $ ) and is useful because a
                 number existing algorithms and methods fail to give
                 correct results for small $x$ or small $y$. The
                 approximating equations are derived by expanding the
                 Bessel function in Taylor series, are tested and
                 discussed. The present work is a continuation of the
                 previous one conducted in regard to the Bessel function
                 of the first kind. The results of our formalism are
                 compared to the available existing numerical methods
                 used in Mathematica, IMSL, MATLAB, and the Amos
                 library. Our numerical method is easy to implement,
                 efficient, and produces reliable results. In addition,
                 this method reduces the computation of the Bessel
                 functions of the second complex argument to that of
                 real argument which simplify the computation
                 considerably.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Book{Zwillinger:2003:CSM,
  editor =       "Daniel Zwillinger",
  title =        "{CRC} Standard Mathematical Tables and Formulae",
  publisher =    pub-CHAPMAN-HALL-CRC,
  address =      pub-CHAPMAN-HALL-CRC:adr,
  edition =      "31st",
  pages =        "xiv + 910",
  year =         "2003",
  ISBN =         "1-58488-291-3, 1-4200-3534-7 (electronic)",
  ISBN-13 =      "978-1-58488-291-6, 978-1-4200-3534-6 (electronic)",
  LCCN =         "QA47 .M315 2003",
  bibdate =      "Thu Nov 25 11:07:20 MST 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  acknowledgement = ack-nhfb,
  subject =      "mathematics; tables",
}

@Book{Bell:2004:SFS,
  author =       "W. W. (William Wallace) Bell",
  title =        "Special functions for scientists and engineers",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xiv + 247",
  year =         "2004",
  ISBN =         "0-486-43521-0",
  ISBN-13 =      "978-0-486-43521-3",
  LCCN =         "QA351 .B4 2004",
  bibdate =      "Sat Oct 30 16:30:44 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Dover books on mathematics",
  acknowledgement = ack-nhfb,
  remark =       "Reprinting of \cite{Bell:1968:SFS}.",
  subject =      "Functions, Special",
}

@Article{Berrut:2004:APS,
  author =       "Jean-Paul Berrut and Hans D. Mittelmann",
  title =        "Adaptive Point Shifts in Rational Approximation with
                 Optimized Denominator",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "164--165",
  number =       "??",
  pages =        "81--92",
  day =          "1",
  month =        mar,
  year =         "2004",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(03)00485-0",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Tue Mar 24 21:10:48 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the 10th International Congress on
                 Computational and Applied Mathematics University of
                 Leuven, Belgium, 22--26 July 2002. Edited by M. J.
                 Goovaerts, S. Vandewalle, and L. Wuytack.",
  abstract =     "Classical rational interpolation is known to suffer
                 from several drawbacks, such as unattainable points and
                 randomly located poles for a small number of nodes, as
                 well as an erratic behavior of the error as this number
                 grows larger. In a former article, we have suggested to
                 obtain rational interpolants by a procedure that
                 attaches optimally placed poles to the interpolating
                 polynomial, using the barycentric representation of the
                 interpolants. In order to improve upon the condition of
                 the derivatives in the solution of differential
                 equations, we have then experimented with a conformal
                 point shift suggested by Kosloff and Tal-Ezer. As it
                 turned out, such shifts can achieve a spectacular
                 improvement in the quality of the approximation itself
                 for functions with a large gradient in the center of
                 the interval. This leads us to the present work which
                 combines the pole attachment method with shifts
                 optimally adjusted to the interpolated function. Such
                 shifts are also constructed for functions with several
                 shocks away from the extremities of the interval.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "interpolation; optimal interpolation; point shifts;
                 rational approximation",
}

@InCollection{Borwein:2004:AGMa,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  crossref =     "Berggren:2004:PSB",
  pages =        "537--552",
  year =         "2004",
  DOI =          "https://doi.org/10.1007/978-1-4757-4217-6_56",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprint of \cite{Borwein:1984:AGM}.",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_56",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}

@Article{Brisebarre:2004:ACR,
  author =       "N. Brisebarre and J.-M. Muller and Saurabh Kumar
                 Raina",
  title =        "Accelerating correctly rounded floating-point division
                 when the divisor is known in advance",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "8",
  pages =        "1069--1072",
  month =        aug,
  year =         "2004",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2004.37",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "We present techniques for accelerating the
                 floating-point computation of $ x / y $ when $y$ is
                 known before $x$. The proposed algorithms are oriented
                 toward architectures with available fused-mac
                 operations. The goal is to get exactly the same result
                 as with \ldots{}",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "We present techniques for accelerating the
                 floating-point computation of x/y when y is known
                 before x. The proposed algorithms are oriented toward
                 architectures with available fused-mac operations. The
                 goal is to get exactly the same result as with
                 \ldots{}",
}

@Article{Chaudhry:2004:EHC,
  author =       "M. Aslam Chaudhry and Asghar Qadir and H. M.
                 Srivastava and R. B. Paris",
  title =        "Extended hypergeometric and confluent hypergeometric
                 functions",
  journal =      j-APPL-MATH-COMP,
  volume =       "159",
  number =       "2",
  pages =        "589--602",
  day =          "6",
  month =        dec,
  year =         "2004",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon Jul 4 09:15:38 MDT 2005",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Croot:2004:ACC,
  author =       "Ernie Croot and Ren-Cang Li and H. J. Hui June Zhu",
  title =        "The {\em abc\/} conjecture and correctly rounded
                 reciprocal square roots",
  journal =      j-THEOR-COMP-SCI,
  volume =       "315",
  number =       "2--3",
  pages =        "405--417",
  day =          "6",
  month =        may,
  year =         "2004",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Thu Nov 4 10:19:15 MST 2004",
  bibsource =    "http://www.sciencedirect.com/science/journal/03043975;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tcs2000.bib",
  abstract =     "The reciprocal square root calculation $ \alpha = 1 /
                 \sqrt {x} $ is very common in scientific computations.
                 Having a correctly rounded implementation of it is of
                 great importance in producing numerically predictable
                 code among today's heterogeneous computing environment.
                 Existing results suggest that to get the correctly
                 rounded $ \alpha $ in a floating point number system
                 with $p$ significant bits, we may have to compute up to
                 $ 3 p + 1 $ leading bits of $ \alpha $. However,
                 numerical evidence indicates the actual number may be
                 as small as $ 2 p $ plus a few more bits. This paper
                 attempts to bridge the gap by showing that this is
                 indeed true, assuming the {\em abc\/} conjecture which
                 is widely purported to hold. (But our results do not
                 tell exactly how many more bits beyond the $ 2 p $
                 bits, due to the fact that the constants involved in
                 the conjecture are ineffective.) Along the way, rough
                 bounds which are comparable to the existing ones are
                 also proven. The technique used here is a combination
                 of the classical Liouville's estimation and
                 contemporary number theory.",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@InProceedings{deDinechin:2004:PCR,
  author =       "Florent de Dinechin and Catherine Loirat and
                 Jean-Michel Muller",
  title =        "A proven correctly rounded logarithm in
                 double-precision",
  crossref =     "Frougny:2004:RCR",
  pages =        "71--85",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_07_dinechin.pdf",
  abstract =     "This article is a case study in the implementation of
                 a proven, portable, and efficient correctly rounded
                 elementary function in double-precision. We describe
                 the methodology used in the implementation of the
                 natural logarithm in the crlibm library. The discipline
                 required to prove a tight bound on the overall
                 evaluation error allows to design a very efficient
                 implementation with moderate effort.",
  acknowledgement = ack-nhfb,
  keywords =     "arithmetic; correct rounding; elementary functions;
                 floating-point; libm; logarithm",
}

@Article{Defour:2004:PSM,
  author =       "David Defour and Guillaume Hanrot and Vincent
                 Lef{\`e}vre and Jean-Michel Muller and Nathalie Revol
                 and Paul Zimmermann",
  title =        "Proposal for a Standardization of Mathematical
                 Function Implementation in Floating-Point Arithmetic",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "37",
  number =       "1--4",
  pages =        "367--375",
  month =        dec,
  year =         "2004",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Dec 6 07:00:28 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/30/abstract.htm;
                 http://perso.ens-lyon.fr/jean-michel.muller/NumAlg04.pdf;
                 http://www.loria.fr/~zimmerma/papers/PropStandFunctions.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  remark =       "Special Issue: SCAN'2002 International Conference
                 (Guest Editors: Ren {\'e} Alt and Jean-Luc Lamotte)",
}

@InProceedings{Doss:2004:FBI,
  author =       "C. C. Doss and R. L. {Riley, Jr.}",
  booktitle =    "{FCCM 2004}. 12th Annual {IEEE} Symposium on
                 Field-Programmable Custom Computing Machines, 20--23
                 April 2004",
  title =        "{FPGA}-based implementation of a robust {IEEE-754}
                 exponential unit",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "229--238",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 17:14:11 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "This work explores the feasibility of implementing a
                 floating-point exponentiation unit on reconfigurable
                 computing systems. A table-driven exponentiation unit
                 was implemented using synthesizable VHDL. The project
                 included creating pipelined \ldots{}",
}

@TechReport{Ercegovac:2004:CSRa,
  author =       "Milo{\v{s}} Ercegovac and Jean-Michel Muller",
  title =        "Complex Square Root with Operand Prescaling",
  type =         "Research Report",
  number =       "RR2004-42",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "2 + 12",
  month =        sep,
  year =         "2004",
  bibdate =      "Mon Dec 06 11:07:40 2004",
  bibsource =    "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-42.pdf",
  abstract =     "We propose a radix-$r$ digit-recurrence algorithm for
                 complex square-root. The operand is prescaled to allow
                 the selection of square-root digits by rounding of the
                 residual. This leads to a simple hardware
                 implementation. Moreover, the use of digit recurrence
                 approach allows correct rounding of the result. The
                 algorithm, compatible with the complex division, and
                 its design are described at a high-level. We also give
                 rough comparisons of its latency and cost with respect
                 to implementation based on standard floating-point
                 instructions as used in software routines for complex
                 square root.",
  acknowledgement = ack-nhfb,
  keywords =     "complex square-root; Computer arithmetic;
                 digit-recurrence algorithm; operand prescaling.",
}

@InProceedings{Ercegovac:2004:CSRb,
  author =       "Milo{\v{s}} Ercegovac and Jean-Michel Muller",
  booktitle =    "{Proceedings of the 15th IEEE International Conference
                 on Application-Specific Systems, Architectures and
                 Processors, 2004}",
  title =        "Complex square root with operand prescaling",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "52--62",
  year =         "2004",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ASAP.2004.1342458",
  ISBN =         "0-7695-2226-2",
  ISBN-13 =      "978-0-7695-2226-5",
  ISSN =         "1063-6862",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "We propose a radix-r digit-recurrence algorithm for
                 complex square-root. The operand is prescaled to allow
                 the selection of square-root digits by rounding of the
                 residual. This leads to a simple hardware
                 implementation. Moreover, the use of digit \ldots{}",
}

@Article{Fabijonas:2004:AAF,
  author =       "B. R. Fabijonas",
  title =        "{Algorithm 838}: {Airy} Functions",
  journal =      j-TOMS,
  volume =       "30",
  number =       "4",
  pages =        "491--501",
  month =        dec,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1039813.1039819",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a Fortran 90 module, which computes the
                 solutions and their derivatives of Airy's differential
                 equation, both on the real line and in the complex
                 plane. The module also computes the zeros and
                 associated values of the solutions and their
                 derivatives, and the modulus and phase functions on the
                 negative real axis. The computational methods are
                 numerical integration of the differential equation and
                 summation of asymptotic expansions for large argument.
                 These methods were chosen because they are simple,
                 adaptable to any precision, and amenable to rigorous
                 error analysis. The module can be used to validate
                 other codes or as a component in programs that require
                 Airy functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fabijonas:2004:CCA,
  author =       "B. R. Fabijonas and D. W. Lozier and F. W. J. Olver",
  title =        "Computation of complex {Airy} functions and their
                 zeros using asymptotics and the differential equation",
  journal =      j-TOMS,
  volume =       "30",
  number =       "4",
  pages =        "471--490",
  month =        dec,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1039813.1039818",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe a method by which one can compute the
                 solutions of Airy's differential equation, and their
                 derivatives, both on the real line and in the complex
                 plane. The computational methods are numerical
                 integration of the differential equation and summation
                 of asymptotic expansions for large argument. We give
                 details involved in obtaining all of the parameter
                 values, and we control the truncation errors
                 rigorously. Using the same computational methods, we
                 describe an algorithm that computes the zeros and
                 associated values of the Airy functions and their
                 derivatives, and the modulus and phase functions on the
                 negative real axis.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Gebali:2004:EAF,
  author =       "Fayez Gebali and Mohamed Watheq El-Kharashi",
  title =        "{ERL}: an algorithm for fast evaluation of
                 exponential, reciprocal, and logarithmic functions",
  crossref =     "Wahdan:2004:IHE",
  pages =        "269--272",
  year =         "2004",
  bibdate =      "Sat Jul 16 18:04:58 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "A fast algorithm (ERL) is proposed for evaluating
                 Exponential, Reciprocal, and Logarithmic functions. The
                 algorithm requires two to three iterations to complete
                 using simple operations such as multiply, accumulate,
                 and table lookup. The algorithm is independent of the
                 number format used by the machine. Thus it can be
                 implemented using the IEEE 754 floating-point standard
                 or any other special format used by special-purpose
                 processors. The dynamic range of the algorithm is
                 limited only by the dynamic range of the machine on
                 which it is implemented Numerical simulations are
                 performed which verifies the speed and accuracy of the
                 algorithm.",
  acknowledgement = ack-nhfb,
}

@Article{Gil:2004:AMB,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 831}: {Modified} {Bessel} functions of
                 imaginary order and positive argument",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "159--164",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/992200.992204",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 10 07:24:58 MDT 2004",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Fortran 77 programs for the computation of modified
                 Bessel functions of purely imaginary order are
                 presented. The codes compute the functions $ K_{ia}(x)
                 $, $ L_{ia}(x) $ and their derivatives for real $a$ and
                 positive $x$; these functions are independent solutions
                 of the differential equation $ x^2 w'' + x w' + (a^2 -
                 x^2)w = 0 $. The code also computes exponentially
                 scaled functions. The range of computation is $ (x, a)
                 \in (0, 1500] \times [ - 1500, 1500] $ when scaled
                 functions are considered and it is larger than $ (0,
                 500] \times [ - 400, 400] $ for standard IEEE double
                 precision arithmetic. The relative accuracy is better
                 than $ 10^{-13} $ in the range $ (0, 200] \times [ -
                 200, 200] $ and close to $ 10^{-12} $ in $ (0, 1500]
                 \times [ - 1500, 1500] $.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gil:2004:CRZ,
  author =       "Amparo Gil and Wolfram Koepf and Javier Segura",
  title =        "Computing the Real Zeros of Hypergeometric Functions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "36",
  number =       "2",
  pages =        "113--134",
  month =        jun,
  year =         "2004",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Dec 6 07:00:32 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/54/A/2/abstract.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Gil:2004:CSM,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Computing solutions of the modified {Bessel}
                 differential equation for imaginary orders and positive
                 arguments",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "145--158",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/992200.992203",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 10 07:24:58 MDT 2004",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe a variety of methods to compute the
                 functions $ K_{ia}(x) $, $ L_{ia}(x) $ and their
                 derivatives for real $a$ and positive $x$. These
                 functions are numerically satisfactory independent
                 solutions of the differential equation $ x^2 w'' + x w'
                 + (a^2 - x^2)w = 0 $. In the accompanying paper [Gil et
                 al. 2004], we describe the implementation of these
                 methods in Fortran 77 codes.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Guseinov:2004:EIG,
  author =       "I. I. Guseinov and B. A. Mamedov",
  title =        "Evaluation of Incomplete Gamma Functions Using
                 Downward Recursion and Analytical Relations",
  journal =      j-J-MATH-CHEM,
  volume =       "36",
  number =       "4",
  pages =        "341--346",
  month =        aug,
  year =         "2004",
  CODEN =        "JMCHEG",
  DOI =          "https://doi.org/10.1023/B:JOMC.0000044521.18885.d3",
  ISSN =         "0259-9791 (print), 1572-8897 (electronic)",
  ISSN-L =       "0259-9791",
  bibdate =      "Thu Apr 9 18:14:03 MDT 2015",
  bibsource =    "http://link.springer.com/journal/10910/36/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathchem.bib",
  URL =          "http://link.springer.com/article/10.1023/B:JOMC.0000044521.18885.d3",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Chemistry",
  journal-URL =  "http://link.springer.com/journal/10910",
  journalabr =   "J. Math. Chem.",
}

@Misc{Kahan:2004:LTC,
  author =       "W. Kahan",
  title =        "A Logarithm Too Clever by Half",
  howpublished = "World-Wide Web document",
  pages =        "9",
  day =          "9",
  month =        aug,
  year =         "2004",
  bibdate =      "Mon Apr 25 17:39:08 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/LOG10HAF.TXT",
  acknowledgement = ack-nhfb,
  remark =       "Careful analysis of the problem of computing {\tt
                 log10(x)} accurately from {\tt log(x)}.",
}

@Article{Kalmykov:2004:SEH,
  author =       "M. Y. Kalmykov",
  title =        "Series and $ \epsilon $-expansion of the
                 hypergeometric functions",
  journal =      j-NUCL-PHYS-B-PROC-SUPPL,
  volume =       "135",
  number =       "??",
  pages =        "280--284",
  month =        "????",
  year =         "2004",
  CODEN =        "NPBSE7",
  ISSN =         "0920-5632 (print), 1873-3832 (electronic)",
  ISSN-L =       "0920-5632",
  bibdate =      "Thu Dec 01 09:14:29 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Nuclear Physics B, Proceedings Supplements",
  journal-URL =  "http://www.sciencedirect.com/science/journal/09205632",
}

@Book{Kilbas:2004:TTA,
  author =       "A. A. (Anatolii Aleksandrovich) Kilbas and Megumi
                 Saigo",
  title =        "{$H$}-transforms: theory and applications",
  volume =       "9",
  publisher =    pub-CHAPMAN-HALL-CRC,
  address =      pub-CHAPMAN-HALL-CRC:adr,
  pages =        "xii + 389",
  year =         "2004",
  ISBN =         "0-203-48737-0, 0-415-29916-0, 1-58488-116-X",
  ISBN-13 =      "978-0-203-48737-2, 978-1-58488-116-2,
                 978-0-415-29916-9",
  LCCN =         "????",
  bibdate =      "Sat Oct 30 17:20:21 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  series =       "Analytical methods and special functions",
  acknowledgement = ack-nhfb,
  subject =      "$H$-functions; integral transforms",
}

@Article{Kyurkchiev:2004:FCN,
  author =       "N. Kyurkchiev and A. Iliev",
  title =        "Failure of convergence of the {Newton--Weierstrass}
                 iterative method for simultaneous root finding of
                 generalized polynomials",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "47",
  number =       "2--3",
  pages =        "441--446",
  month =        jan # "\slash " # feb,
  year =         "2004",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122104900363",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Book{Lau:2004:NLJ,
  author =       "H. T. (Hang Tong) Lau",
  title =        "A numerical library in {Java} for scientists and
                 engineers",
  publisher =    pub-CHAPMAN-HALL-CRC,
  address =      pub-CHAPMAN-HALL-CRC:adr,
  pages =        "xxiii + 1063",
  year =         "2004",
  ISBN =         "1-58488-430-4",
  ISBN-13 =      "978-1-58488-430-9",
  LCCN =         "QA76.73.J38 L363 2004",
  bibdate =      "Fri Sep 26 14:28:47 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0646/2003055149-d.html",
  acknowledgement = ack-nhfb,
  subject =      "Java (Computer program language)",
}

@InProceedings{Markstein:2004:SDS,
  author =       "Peter Markstein",
  title =        "Software Division and Square Root Using
                 {Goldschmidt}'s Algorithms",
  crossref =     "Frougny:2004:RCR",
  pages =        "146--157",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_12_markstein.pdf",
  abstract =     "Goldschmidt's Algorithms for division and square root
                 are often characterized as being useful for hardware
                 implementation, and lacking self-correction. A
                 reexamination of these algorithms show that there are
                 good software counterparts that retain the speed
                 advantage of Goldschmidt's Algorithm over the
                 Newton--Raphson iteration. A final step is needed,
                 however, to get the last bit rounded correctly.",
  acknowledgement = ack-nhfb,
  keywords =     "division; floating-point; Goldschmidt; square root",
}

@Article{Marsaglia:2004:END,
  author =       "George Marsaglia",
  title =        "Evaluating the Normal Distribution",
  journal =      j-J-STAT-SOFT,
  volume =       "11",
  number =       "4",
  pages =        "1--7",
  month =        "????",
  year =         "2004",
  CODEN =        "JSSOBK",
  ISSN =         "1548-7660",
  bibdate =      "Sat Dec 04 09:18:40 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstatsoft.org/counter.php?id=100&url=v11/i04/cphi.pdf&ct=1",
  accepted =     "2004-07-18",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Software",
  journal-URL =  "http://www.jstatsoft.org/",
  remark =       "This article exhibits accurate, compact, and fast
                 algorithms for computation of the normal distribution
                 function and the complementary normal distribution,
                 which have a simple relation to the error function and
                 the complementary error function. They appear to be
                 improvements on almost all previously-published
                 algorithms for these functions. However, closer study
                 shows that the complementary normal distribution
                 function has an unchecked out-of-bounds array access
                 for $ |x| \geq 17 $, and its Taylor series sum has poor
                 convergence because the tabulated intervals are twice
                 too wide. The Taylor series sum for the normal
                 distribution function is expanded around $ x = 0 $, and
                 thus has poor convergence for large $ |x| $. Neither
                 function takes into account the accuracy loss when the
                 computed result is the larger of the two (their sum is
                 one, and their range is $ [ - \infty, + \infty] $ ),
                 although the text discusses the problem. The article
                 also discusses the historical origin of the term
                 ``error function'', tracing it to J. W. Glaisher in
                 1871.",
  submitted =    "2004-06-05",
}

@Article{Mathar:2004:NRI,
  author =       "Richard J. Mathar",
  title =        "Numerical Representations of the Incomplete Gamma
                 Function of Complex-Valued Argument",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "36",
  number =       "3",
  pages =        "247--264",
  month =        jul,
  year =         "2004",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Dec 6 07:00:32 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/57/A/4/abstract.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Misc{Miller:2004:AMF,
  author =       "Alan Miller",
  title =        "{Alan Miller}'s {Fortran} Software",
  howpublished = "Web site",
  day =          "4",
  month =        feb,
  year =         "2004",
  bibdate =      "Tue Jun 13 12:03:37 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib",
  note =         "From the Web site: All code written by Alan Miller is
                 released into the public domain.",
  URL =          "https://jblevins.org/mirror/amiller/",
  acknowledgement = ack-nhfb,
  remark =       "The Web site contains a section ``Code converted from
                 the Naval Surface Warfare Center Math. Library'' with
                 links to individual Fortran 90 source files.",
}

@Article{Moore:2004:PSW,
  author =       "Ian C. Moore and Michael Cada",
  title =        "Prolate spheroidal wave functions, an introduction to
                 the {Slepian} series and its properties",
  journal =      j-APPL-COMPUT-HARMON-ANAL,
  volume =       "16",
  number =       "3",
  pages =        "208--230",
  month =        may,
  year =         "2004",
  DOI =          "https://doi.org/10.1016/j.acha.2004.03.004",
  ISSN =         "1063-5203 (print), 1096-603x (electronic)",
  ISSN-L =       "1063-5203",
  bibdate =      "Sun Oct 31 09:58:00 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "For decades mathematicians, physicists, and engineers
                 have relied on various orthogonal expansions such as
                 Fourier, Legendre, and Chebyschev to solve a variety of
                 problems. In this paper we exploit the orthogonal
                 properties of prolate spheroidal wave functions (PSWF)
                 in the form of a new orthogonal expansion which we have
                 named the Slepian series. We empirically show that the
                 Slepian series is potentially optimal over more
                 conventional orthogonal expansions for discontinuous
                 functions such as the square wave among others. With
                 regards to interpolation, we explore the connections
                 the Slepian series has to the Shannon sampling theorem.
                 By utilizing Euler's equation, a relationship between
                 the even and odd ordered PSWFs is investigated. We also
                 establish several other key advantages the Slepian
                 series has such as the presence of a free tunable
                 bandwidth parameter.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied and Computational Harmonic Analysis.
                 Time-Frequency and Time-Scale Analysis, Wavelets,
                 Numerical Algorithms, and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/10635203",
  keywords =     "Interpolation; Orthogonal expansion; Prolate
                 spheroidal wave function",
}

@Article{Muller:2004:CSR,
  author =       "Siguna M{\"u}ller",
  title =        "On the Computation of Square Roots in Finite Fields",
  journal =      j-DESIGNS-CODES-CRYPTOGR,
  volume =       "31",
  number =       "3",
  pages =        "301--312",
  month =        mar,
  year =         "2004",
  CODEN =        "DCCREC",
  ISSN =         "0925-1022 (print), 1573-7586 (electronic)",
  ISSN-L =       "0925-1022",
  bibdate =      "Tue Aug 3 16:38:18 MDT 2004",
  bibsource =    "http://www.wkap.nl/jrnltoc.htm/0925-1022;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ipsapp008.kluweronline.com/IPS/content/ext/x/J/4630/I/61/A/8/abstract.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Designs, codes, and cryptography",
  journal-URL =  "http://link.springer.com/journal/10623",
}

@Article{Nagel:2004:CEG,
  author =       "Bengt Nagel",
  title =        "Confluence expansions of the generalized
                 hypergeometric function",
  journal =      j-J-MATH-PHYS,
  volume =       "45",
  number =       "1",
  pages =        "495--508",
  month =        jan,
  year =         "2004",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.1629777",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Tue Oct 25 18:16:52 MDT 2011",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v45/i1/p495_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  onlinedate =   "19 December 2003",
  pagecount =    "14",
}

@InProceedings{Ortiz:2004:SPI,
  author =       "I. Ortiz and M. Jimenez",
  booktitle =    "{MWSCAS '04. The 2004 47th Midwest Symposium on
                 Circuits and Systems. 25--28 July 2004}",
  title =        "Scalable pipeline insertion in floating-point division
                 and square root units",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-225--II-228",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Division and square root are important operations in a
                 number of data processing algorithms. They are
                 inherently time consuming operations and can require a
                 significant amount of resources when implemented in
                 hardware. This work reports the development of
                 scalable, floating-point (FP) division and square root
                 operators with adjustable precision, range, and
                 pipeline granularity. An algorithm for pipeline
                 insertion was used for both operators, enabling speeds
                 up to 204MFLOPS when implemented on a Xilinx Virtex II
                 FPGA.",
  acknowledgement = ack-nhfb,
  summary =      "Division and square root are important operations in a
                 number of data processing algorithms. They are
                 inherently time consuming operations and can require a
                 significant amount of resources when implemented in
                 hardware. This work reports the \ldots{}",
}

@Article{Petkovic:2004:GCS,
  author =       "M. S. Petkovi{\'c} and L. Ranci{\'c}",
  title =        "On the guaranteed convergence of the square-root
                 iteration method",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "170",
  number =       "1",
  pages =        "169--179",
  day =          "1",
  month =        sep,
  year =         "2004",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:00:00 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042704000184",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Pineiro:2004:AAL,
  author =       "J. A. Pi{\~n}eiro and M. D. Ercegovac and J. D.
                 Bruguera",
  title =        "Algorithm and Architecture for Logarithm, Exponential
                 and Powering Computation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "9",
  pages =        "1085--1096",
  year =         "2004",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2004.53",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 24 10:05:48 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ac.usc.es/arquivos/articulos/2004/gac2004-j05.ps",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@PhdThesis{Pugh:2004:ALG,
  author =       "Glendon Ralpha Pugh",
  title =        "An Analysis of the {Lanczos} Gamma Approximation",
  type =         "Ph.D. thesis",
  school =       "Department of Mathematics, University of British
                 Columbia",
  address =      "Vancouver, BC, Canada",
  pages =        "viii + 154",
  month =        "????",
  year =         "2004",
  ISBN =         "0-612-99536-4",
  ISBN-13 =      "978-0-612-99536-9",
  LCCN =         "AW5 .B7 2005-995364",
  bibdate =      "Mon Nov 24 20:55:30 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Book{Raade:2004:MHS,
  author =       "Lennart R{\aa}de and Bertil Westergren",
  title =        "Mathematics Handbook for Science and Engineering",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Fifth",
  pages =        "562",
  year =         "2004",
  ISBN =         "3-540-21141-1 (hardcover)",
  ISBN-13 =      "978-3-540-21141-9 (hardcover)",
  LCCN =         "QA41 .R34 2004",
  bibdate =      "Sat May 15 09:15:39 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0818/2006286513-d.html;
                 http://www.loc.gov/catdir/toc/fy0704/2006286513.html",
  acknowledgement = ack-nhfb,
  libnote =      "Not in my library.",
  subject =      "mathematics; formulae; tables; handbooks, manuals,
                 etc.",
  tableofcontents = "1. Fundamentals \\
                 Discrete Mathematics / 9 \\
                 1.1 Logic / 9 \\
                 1.2 Set Theory / 14 \\
                 1.3 Binary Relations and Functions / 17 \\
                 1.4 Algebraic Structures / 21 \\
                 1.5 Graph Theory / 33 \\
                 1.6 Codes / 37 \\
                 2: Algebra / 43 \\
                 2.1 Basic Algebra of Real Numbers / 43 \\
                 2.2 Number Theory / 49 \\
                 2.3 Complex Numbers / 61 \\
                 2.4 Algebraic Equations / 63 \\
                 3: Geometry and Trigonometry / 66 \\
                 3.1 Plane Figures / 66 \\
                 3.2 Solids / 71 \\
                 3.3 Spherical Trigonometry / 75 \\
                 3.4 Geometrical Vectors / 77 \\
                 3.5 Plane Analytic Geometry / 79 \\
                 3.6 Analytic Geometry in Space / 83 \\
                 3.7 Fractals / 87 \\
                 4: Linear Algebra / 90 \\
                 4.1 Matrices / 90 \\
                 4.2 Determinants / 93 \\
                 4.3 Systems of Linear Equations / 95 \\
                 4.4 Linear Coordinate Transformations / 97 \\
                 4.5 Eigenvalues. Diagonalization / 98 \\
                 4.6 Quadratic Forms / 103 \\
                 4.7 Linear Spaces / 106 \\
                 4.8 Linear Mappings / 108 \\
                 4.9 Tensors / 114 \\
                 4.10 Complex matrices / 114 \\
                 5: The Elementary Functions / 118 \\
                 5.1 A Survey of the Elementary Functions / 118 \\
                 5.2 Polynomials and Rational Functions / 119 \\
                 5.3 Logarithmic, Exponential, Power and Hyperbolic
                 Functions / 121 \\
                 5.4 Trigonometric and Inverse Trigonometric Functions /
                 125 \\
                 6: Differential Calculus (one variable) / 132 \\
                 6.1 Some Basic Concepts / 132 \\
                 6.2 Limits and Continuity / 133 \\
                 6.3 Derivatives / 136 \\
                 6.4 Monotonicity. Extremes of Functions / 139 \\
                 7: Integral Calculus / 141 \\
                 7.1 Indefinite Integrals / 141 \\
                 7.2 Definite Integrals / 146 \\
                 7.3 Applications of Differential and Integral Calculus
                 / 148 \\
                 7.4 Table of Indefinite Integral / 153 \\
                 7.5 Tables of Definite Integrals / 178 \\
                 8: Sequences and Series / 183 \\
                 8.1 Sequences of Numbers / 183 \\
                 8.2 Sequences of Functions / 184 \\
                 8.3 Series of Constant Terms / 185 \\
                 8.4 Series of Functions / 187 \\
                 8.5 Taylor Series / 189 \\
                 8.6 Special Sums and Series / 192 \\
                 9: Ordinary Differential Equations (ODE) / 200 \\
                 9.1 Differential Equations of the First Order / 200 \\
                 9.2 Differential Equations of the Second Order / 202
                 \\
                 9.3 Linear Differential Equations / 205 \\
                 9.4 Autonomous systems / 2313 \\
                 9.5 General Concepts and Results / 216 \\
                 9.6 Linear Difference Equations / 218 \\
                 10: Multidimensional Calculus / 221 \\
                 10.1 The Space Rn / 221 \\
                 10.2 Surfaces. Tangent Planes / 222 \\
                 10.3 Limits and Continuity / 223 \\
                 10.4 Partial Derivatives / 224 \\
                 10.5 Extremes of Functions / 227 \\
                 10.6 Functions $f: R^n \to R^m (R^n \to R^n)$ / 229 \\
                 10.7 Double Integrals / 231 \\
                 10.8 Triple Integrals / 234 \\
                 10.9 Partial Differential Equations / 239 \\
                 11: Vector Analysis / 246 \\
                 11.1 Curves / 246 \\
                 11.2 Vector Fields / 248 \\
                 11.3 Line Integrals / 253 \\
                 11.4 Surface Integrals / 256 \\
                 12: Orthogonal Series and Special Functions / 259 \\
                 12.1 Orthogonal Systems / 259 \\
                 12.2 Orthogonal Polynomials / 263 \\
                 12.3 Bernoulli and Euler Polynomials / 269 \\
                 12.4 Bessel Functions / 270 \\
                 12.5 Functions Defined by Transcendental Integrals /
                 287 \\
                 12.6 Step and Impulse Functions / 297 \\
                 12.7 Functional Analysis / 298 \\
                 12.8 Lebesgue Integrals / 303 \\
                 12.9 Generalized functions (Distributions) / 308 \\
                 13: Transforms / 310 \\
                 13.1 Trigonometric Fourier Series / 310 \\
                 13.2 Fourier Transforms / 315 \\
                 13.3 Discrete Fourier Transforms / 325 \\
                 13.4 The $z$-transform / 327 \\
                 13.5 Laplace Transforms / 330 \\
                 13.6 Dynamical Systems (Filters) / 338 \\
                 13.7 Hankel and Hilbert transforms / 341 \\
                 13.8 Wavelets / 344 \\
                 14: Complex Analysis / 349 \\
                 14.1 Functions of a Complex Variable / 349 \\
                 14.2 Complex Integration / 352 \\
                 14.3 Power Series Expansions / 354 \\
                 14.4 Zeros and Singularities / 355 \\
                 14.5 Conformal Mappings / 356 \\
                 15: Optimization / 365 \\
                 15.1 Calculus of Variations / 365 \\
                 15.2 Linear Optimization / 371 \\
                 15.3 Integer and Combinatorial Optimization / 379 \\
                 15.4 Nonlinear Optimization / 383 \\
                 15.5 Dynamic Optimization / 389 \\
                 16: Numerical Analysis / 391 \\
                 16.1 Approximations and Errors / 391 \\
                 16.2 Numerical Solution of Equations / 392 \\
                 16.3 Perturbation analysis / 397 \\
                 16.4 Interpolation / 398 \\
                 16.5 Numerical Integration and Differentiation / 404
                 \\
                 16.6 Numerical Solutions of Differential Equations /
                 412 \\
                 16.7 Numerical summation / 421 \\
                 17: Probability Theory / 424 \\
                 17.1 Basic Probability Theory / 424 \\
                 17.2 Probability Distributions / 434 \\
                 17.3 Stochastic Processes / 439 \\
                 17.4 Algorithms for Calculation of Probability
                 Distributions / 443 \\
                 17.5 Simulation / 445 \\
                 17.6 Queueing Systems / 449 \\
                 17.7 Reliability / 452 \\
                 17.8 Tables / 459 \\
                 18: Statistics / 479 \\
                 18.1 Descriptive Statistics / 479 \\
                 18.2 Point Estimation / 488 \\
                 18.3 Confidence Intervals / 491 \\
                 18.4 Tables for Confidence Intervals / 495 \\
                 18.5 Tests of Significance / 501 \\
                 18.6 Linear Models / 507 \\
                 18.7 Distribution-free Methods / 512 \\
                 18.8 Statistical Quality Control / 518 \\
                 18.9 Factorial Experiments / 522 \\
                 18.10 Analysis of life time (failure time) data / 525
                 \\
                 18.11 Statistical glossary / 526 \\
                 19: Miscellaneous / 530",
}

@Article{Skorokhodov:2004:STP,
  author =       "S. L. Skorokhodov",
  title =        "Symbolic transformations in the problem of analytic
                 continuation of the hypergeometric function {$_p F_{p -
                 1}(z)$} in the neighborhood of the point $ z = 1 $ in
                 the logarithmic case",
  journal =      j-PROG-COMP-SOFT,
  volume =       "30",
  number =       "3",
  pages =        "150--156",
  month =        "????",
  year =         "2004",
  CODEN =        "PCSODA",
  ISSN =         "0361-7688 (print), 1608-3261 (electronic)",
  ISSN-L =       "0361-7688",
  MRclass =      "3C20 (33B15 33C05 33F05 33F10)",
  MRnumber =     "MR2082811 (2005f:33013)",
  bibdate =      "Thu Dec 01 09:18:16 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Programming and Computer Software; translation of
                 Programmirovaniye (Moscow, USSR) Plenum",
  journal-URL =  "http://link.springer.com/journal/11086",
}

@Article{Thompson:2004:EBB,
  author =       "I. J. Thompson",
  title =        "Erratum to {{\booktitle{Modified Bessel functions $ I
                 \_ n u(z) $ and $ K_\nu (z) $ of real order and complex
                 argument}} [Comput. Phys. Commun. {\bf 47} (1987)
                 245--257]}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "159",
  number =       "3",
  pages =        "243--244",
  day =          "1",
  month =        jun,
  year =         "2004",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2004.02.007",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Apr 24 10:35:27 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Thompson:1987:MBF}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465504001067",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Book{Vallee:2004:AFA,
  author =       "Olivier Vall{\'e}e and Manuel Soares",
  title =        "{Airy} Functions and Applications to Physics",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "x + 194",
  year =         "2004",
  ISBN =         "1-86094-478-7 (hardcover)",
  ISBN-13 =      "978-1-86094-478-9 (hardcover)",
  LCCN =         "QA351 .V35 2004",
  bibdate =      "Tue Dec 5 10:16:05 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The use of special functions, and in particular Airy
                 functions, is rather common in physics. The reason may
                 be found in the need, and even in the necessity, to
                 express a physical phenomenon in terms of an effective
                 and comprehensive analytical form for the whole
                 scientific community. However, for the past twenty
                 years, many physical problems have been resolved by
                 computers. This trend is now becoming the norm as the
                 importance of computers continues to grow. As a last
                 resort, the special functions employed in physics will
                 have to be calculated numerically, even if the analytic
                 formulation of physics is of primary
                 importance.\par

                 Airy functions have periodically been the subject of
                 many review articles, but no noteworthy compilation on
                 this subject has been published since the 1950s. In
                 this work, we provide an exhaustive compilation of the
                 current knowledge on the analytical properties of Airy
                 functions, developing with care the calculus implying
                 the Airy functions.",
  acknowledgement = ack-nhfb,
  remark =       "See also second edition \cite{Vallee:2010:AFA}.",
  shorttableofcontents = "1: A historical introduction: Sir George
                 Biddell Airy / 1 \\
                 2: Definitions and properties / 5 \\
                 3: Primitives and integrals of Airy functions / 37 \\
                 4: Transformations of Airy functions / 71 \\
                 5: The uniform approximation / 91 \\
                 6: Generalisation of Airy functions / 101 \\
                 7: Applications to classical physics / 115 \\
                 8: Applications to quantum physics / 137 \\
                 Appendix A: Numerical computation of the Airy functions
                 / 177 \\
                 Bibliography / 183 \\
                 Index / 193",
  tableofcontents = "Preface / v \\
                 1. A Historical Introduction: Sir George Biddell Airy /
                 1 \\
                 2. Definitions and Properties / 5 \\
                 2.1 The Homogeneous Airy Functions / 5 \\
                 2.1.1 The Airy's equation / 5 \\
                 2.1.2 Elementary properties / 8 \\
                 2.1.2.1 Wronskians of homogeneous Airy functions / 8
                 \\
                 2.1.2.2 Particular values of Airy functions / 8 \\
                 2.1.2.3 Relations between Airy functions / 9 \\
                 2.1.3 Integral representations / 9 \\
                 2.1.4 Ascending and asymptotic series / 11 \\
                 2.1.4.1 Expansion of $\Ai$ near the origin / 11 \\
                 2.1.4.2 Ascending series of $\Ai$ and $\Bi$ / 12 \\
                 2.1.4.3 Asymptotic series of $\Ai$ and $\Bi$ / 13 \\
                 2.2 Properties of Airy Functions / 15 \\
                 2.2.1 Zeros of Airy functions / 15 \\
                 2.2.2 The spectral zeta function / 18 \\
                 2.2.3 Inequalities / 20 \\
                 2.2.4 Connection with Bessel functions / 20 \\
                 2.2.5 Modulus and phase of Airy functions / 21 \\
                 2.2.5.1 Definitions / 21 \\
                 2.2.5.2 Differential equations / 22 \\
                 2.2.5.3 Asymptotic expansions / 23 \\
                 2.2.5.4 Functions of positive arguments / 24 \\
                 2.3 The Inhomogeneous Airy Functions / 25 \\
                 2.3.1 Definitions / 25 \\
                 2.3.2 Properties of inhomogeneous Airy functions / 27
                 \\
                 2.3.2.1 Values at the origin / 27 \\
                 2.3.2.2 Other integral representations / 27 \\
                 2.3.3 Ascending and asymptotic series / 28 \\
                 2.3.3.1 Ascending series / 28 \\
                 2.3.3.2 Asymptotic series / 29 \\
                 2.3.4 Zeros of the Scorer functions / 29 \\
                 2.4 Squares and Products of Airy Functions / 30 \\
                 2.4.1 Differential equation and integral representation
                 / 30 \\
                 2.4.2 A remarkable identity / 32 \\
                 2.4.3 The product $\Ai(x) \Ai(-x)$: Airy wavelets / 32
                 \\
                 3. Primitives and Integrals of Airy Functions / 37 \\
                 3.1 Primitives Containing One Airy Function / 37 \\
                 3.1.1 In terms of Airy functions / 37 \\
                 3.1.2 Ascending series / 38 \\
                 3.1.3 Asymptotic series / 38 \\
                 3.1.4 Primitive of Scorer functions / 39 \\
                 3.1.5 Repeated primitives / 40 \\
                 3.2 Product of Airy Functions / 40 \\
                 3.2.1 The method of Albright / 41 \\
                 3.2.2 Some primitives / 43 \\
                 3.3 Other Primitives / 48 \\
                 3.4 Miscellaneous / 49 \\
                 3.5 Elementary Integrals / 50 \\
                 3.5.1 Particular integrals / 50 \\
                 3.5.2 Integrals containing a single Airy function / 51
                 \\
                 3.5.2.1 Integrals involving algebraic functions / 51
                 \\
                 3.5.2.2 Integrals involving transcendental functions /
                 54 \\
                 3.5.3 Integrals of products of two Airy functions / 56
                 \\
                 3.6 Other Integrals / 60 \\
                 3.6.1 Integrals involving the Volterra $\mu$-function /
                 60 \\
                 3.6.2 Canonisation of cubic form / 64 \\
                 3.6.3 Integrals with three Airy functions / 65 \\
                 3.6.4 Integrals with four Airy functions / 67 \\
                 3.6.5 Double integrals / 68 \\
                 4. Transformations of Airy Functions / 71 \\
                 4.1 Causal Properties of Airy Functions / 71 \\
                 4.1.1 Causal relations / 71 \\
                 4.1.2 Green function of the Airy equation / 73 \\
                 4.2 The Airy Transform / 74 \\
                 4.2.1 Definitions and elementary properties / 74 \\
                 4.2.2 Some examples / 77 \\
                 4.2.3 Airy polynomials / 82 \\
                 4.2.4 Summary of Airy transform / 84 \\
                 4.2.5 Airy averaging / 85 \\
                 4.3 Other Kinds of Transformations / 85 \\
                 4.3.1 Laplace transform of Airy functions / 85 \\
                 4.3.2 Mellin transform of Airy function / 86 \\
                 4.3.3 Fourier transform of Airy functions / 87 \\
                 4.4 Expansion into Fourier-Airy Series / 88 \\
                 5. The Uniform Approximation / 91 \\
                 5.1 Oscillating Integrals / 91 \\
                 5.1.1 The method of stationary phase / 91 \\
                 5.1.2 The uniform approximation of oscillating
                 integrals / 93 \\
                 5.1.3 The Airy uniform approximation / 94 \\
                 5.2 Differential Equation of the Second Order / 95 \\
                 5.2.1 The JWKB method / 95 \\
                 5.2.2 The generalisation of Langer / 97 \\
                 5.3 Inhomogeneous Differential Equations / 98 \\
                 6. Generalisation of Airy Functions / 101 \\
                 6.1 Generalisation of the Airy Integral / 101 \\
                 6.2 Third Order Differential Equations / 105 \\
                 6.2.1 The linear third order differential equation /
                 105 \\
                 6.2.2 Asymptotic solutions / 106 \\
                 6.2.3 The comparison equation / 107 \\
                 6.3 Differential Equation of the Fourth Order / 111 \\
                 7. Applications to Classical Physics / 115 \\
                 7.1 Optics and Electromagnetism / 115 \\
                 7.2 Fluid Mechanics / 119 \\
                 7.2.1 The Tricomi equation / 119 \\
                 7.2.2 The Orr--Sommerfeld equation / 121 \\
                 7.3 Elasticity / 124 \\
                 7.4 The Heat Equation / 127 \\
                 7.5 Nonlinear Physics / 129 \\
                 7.5.1 Korteweg--de Vries equation / 129 \\
                 7.5.1.1 The linearised Korteweg--de Vries equation /
                 129 \\
                 7.5.1.2 Similarity solutions / 131 \\
                 7.5.2 The second Painlev{\'e} equation / 132 \\
                 7.5.2.1 The Painlev{\'e} equations / 132 \\
                 7.5.2.2 An integral equation / 134 \\
                 7.5.2.3 Rational solutions 135 \\
                 8. Applications to Quantum Physics / 137 \\
                 8.1 The Schr{\"o}dinger Equation / 137 \\
                 8.1.1 Particle in a uniform field / 137 \\
                 8.1.2 The $|x|$ potential / 140 \\
                 8.1.3 Uniform approximation of the Schr{\"o}dinger
                 equation / 144 \\
                 8.1.3.1 The JWKB approximation / 145 \\
                 8.1.3.2 The Airy uniform approximation / 146 \\
                 8.1.3.3 Exact vs approximate wave functions / 148 \\
                 8.2 Evaluation of the Franck--Condon Factors / 152 \\
                 8.2.1 The Franck--Condon principle / 153 \\
                 8.2.2 The JWKB approximation / 154 \\
                 8.2.3 The uniform approximation / 157 \\
                 8.3 The Semiclassical Wigner Distribution / 162 \\
                 8.3.1 The Weyl--Wigner formalism / 163 \\
                 8.3.2 The one-dimensional Wigner distribution / 164 \\
                 8.3.3 The two-dimensional Wigner distribution / 166 \\
                 8.3.4 Configuration of the Wigner distribution / 169
                 \\
                 8.4 Airy Transform of the Schr{\"o}dinger Equation /
                 173 \\
                 Appendix A: Numerical Computation of the Airy Functions
                 / 177 \\
                 A.1 The Homogeneous Functions / 177 \\
                 A.2 The Inhomogeneous Functions / 180 \\
                 Bibliography / 183 \\
                 Index / 193",
}

@Article{VanDeun:2004:IAO,
  author =       "J. {Van Deun} and A. Bultheel",
  title =        "An Interpolation Algorithm for Orthogonal Rational
                 Functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "164--165",
  number =       "??",
  pages =        "749--762",
  month =        mar,
  year =         "2004",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(03)00493-X",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Tue Mar 24 21:14:11 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the 10th International Congress on
                 Computational and Applied Mathematics University of
                 Leuven, Belgium, 22--26 July 2002. Edited by M. J.
                 Goovaerts, S. Vandewalle, and L. Wuytack.",
  abstract =     "Let $ A = \{ \alpha_1, \alpha_2, \ldots {} \} $ be a
                 sequence of numbers on the extended real line $
                 \mathcal {R} = \mathcal {R} \union \{ \infty \} $ and $
                 \mu $ a positive bounded Borel measure with support in
                 (a subset of) $ \mathcal {R} $. We introduce rational
                 functions n with poles $ \{ \alpha_1, \ldots {},
                 \alpha_n \} $ that are orthogonal with respect to $ \mu
                 $ (if all poles are at infinity, we recover the
                 polynomial situation). It is well known that under
                 certain conditions on the location of the poles, the
                 system $ \{ \phi_n \} $ is regular such that the
                 orthogonal functions satisfy a three-term recurrence
                 relation similar to the one for orthogonal polynomials.
                 To compute the recurrence coefficients one can use
                 explicit formulas involving inner products. We present
                 a theoretical alternative to these explicit formulas
                 that uses certain interpolation properties of the
                 Riesz--Herglotz--Nevanlinna transform $ \Omega_\mu $ of
                 the measure $ \mu $. Error bounds are derived and some
                 examples serve as illustration.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "interpolation; orthogonal polynomials; orthogonal
                 rational functions; three-term recurrence",
}

@Article{Wang:2004:CHP,
  author =       "Ren-Hong Wang and Cheng-de Zheng",
  title =        "Cubic {Hermite--Pad{\'e}} approximation to the
                 exponential function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "163",
  number =       "1",
  pages =        "259--268",
  day =          "1",
  month =        feb,
  year =         "2004",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:59:56 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042703008124",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Zeng:2004:AMM,
  author =       "Zhonggang Zeng",
  title =        "Algorithm 835: {MultRoot}---a {Matlab} package for
                 computing polynomial roots and multiplicities",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "218--236",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/992200.992209",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H05",
  MRnumber =     "MR2075984 (2005c:65041)",
  bibdate =      "Tue Mar 30 16:16:28 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "MultRoot is a collection of Matlab modules for
                 accurate computation of polynomial roots, especially
                 roots with non-trivial multiplicities. As a
                 blackbox-type software, MultRoot requires the
                 polynomial coefficients as the only input, and outputs
                 the computed roots, multiplicities, backward error,
                 estimated forward error, and the structure-preserving
                 condition number. The most significant features of
                 MultRoot are the multiplicity identification capability
                 and high accuracy on multiple roots without using
                 multiprecision arithmetic, even if the polynomial
                 coefficients are inexact. A comprehensive test suite of
                 polynomials that are collected from the literature is
                 included for numerical experiments and performance
                 comparison.",
  acknowledgement = ack-nhfb,
  fjournal =     "Association for Computing Machinery. Transactions on
                 Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Zhu:2004:ISR,
  author =       "Hufei Zhu and Zhongding Lei and F. P. S. Chin",
  title =        "An improved square-root algorithm for {BLAST}",
  journal =      j-IEEE-SIGNAL-PROCESS-LETT,
  volume =       "11",
  number =       "9",
  pages =        "772--775",
  month =        sep,
  year =         "2004",
  CODEN =        "ISPLEM",
  DOI =          "https://doi.org/10.1109/LSP.2004.833483",
  ISSN =         "1070-9908 (print), 1558-2361 (electronic)",
  ISSN-L =       "1070-9908",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Signal Processing Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=97",
  summary =      "In this letter, an improved square-root algorithm for
                 Bell Labs Layered Space-Time (BLAST) system is
                 proposed. It speeds up the original square-root
                 algorithm by 36\% in terms of the number of
                 multiplications and additions. Compared with the
                 \ldots{}",
}

@Article{Abad:2005:TNA,
  author =       "Julio Abad and Javier Sesma",
  title =        "Two new asymptotic expansions of the ratio of two
                 gamma functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "173",
  number =       "2",
  pages =        "359--363",
  day =          "15",
  month =        jan,
  year =         "2005",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:00:02 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042704001669",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Antelo:2005:LLD,
  author =       "Elisardo Antelo and Tom{\'a}s Lang and Paolo Montuschi
                 and Alberto Nannarelli",
  title =        "Low Latency Digit-Recurrence Reciprocal and
                 Square-Root Reciprocal Algorithm and Architecture",
  crossref =     "IEEE:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arith17.polito.it/final/paper-116.pdf",
  abstract =     "The reciprocal and square-root reciprocal operations
                 are important in several applications. For the
                 operations, we present algorithms that combine a
                 digit-by-digit module and one iteration of a
                 quadratic-convergence approximation. The latter is
                 implemented by a digit-recurrence, which uses the
                 digits produced by the digit-by-digit part. In this
                 way, both parts execute in an overlapped manner, so
                 that the total number of cycles is about half the
                 number that would be required by the digit-by-digit
                 part alone. Because of the approximation, correct
                 rounding of the result cannot be obtained directly in
                 all cases; we propose a variable-time implementation
                 that produces the correctly rounded result with a small
                 average overhead. Radix-4 implementations are described
                 and have been synthesized. They achieve the same cycle
                 time as the standard digit-by-digit implementation,
                 resulting in a speed-up of about 2 and, because of the
                 approximation part, the area factor is also about 2. We
                 also show a combined implementation for both operations
                 that has essentially the same complexity as that for
                 square-root reciprocal alone.",
  acknowledgement = ack-nhfb,
  pagecount =    "8",
}

@Book{Arfken:2005:MMP,
  author =       "George B. Arfken and Hans-J{\"u}rgen Weber",
  title =        "Mathematical Methods for Physicists",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  edition =      "Sixth",
  pages =        "xii + 1182",
  year =         "2005",
  ISBN =         "0-12-059876-0, 0-12-088584-0 (paperback)",
  ISBN-13 =      "978-0-12-059876-2, 978-0-12-088584-8 (paperback)",
  LCCN =         "QA37.3 .A74 2005",
  bibdate =      "Tue Feb 17 18:23:45 MST 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Mathematics; Mathematical physics",
  tableofcontents = "1. Vector Analysis \\
                 2. Vector Analysis in Curved Coordinates and Tensors
                 \\
                 3. Determinants and Matrices \\
                 4. Group Theory \\
                 5. Infinite Series \\
                 6. Functions of a Complex Variable I: Analytic
                 Properties, Mapping \\
                 7. Functions of a Complex Variable II \\
                 8. The Gamma Function (Factorial Function) \\
                 9. Differential Equations \\
                 10. Sturm--Liouville Theory-Orthogonal Functions \\
                 11. Bessel Functions \\
                 12. Legendre Functions \\
                 13. More Special Functions \\
                 14. Fourier Series \\
                 15. Integral Transforms \\
                 16. Integral Equations \\
                 17. Calculus of Variations \\
                 18. Nonlinear Methods and Chaos \\
                 19. Probability",
  xxauthor =     "George B. (George Brown) Arfken and Hans-J{\"u}rgen
                 Weber",
  xxURL =        "http://www.loc.gov/catdir/enhancements/fy0625/2005049844-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0625/2005049844-t.html",
}

@Article{Bonan-Hamada:2005:SCF,
  author =       "Catherine M. Bonan-Hamada and William B. Jones",
  title =        "{Stieltjes} continued fractions for polygamma
                 functions; speed of convergence",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "179",
  number =       "1--2",
  pages =        "47--55",
  day =          "1",
  month =        jul,
  year =         "2005",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:00:05 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704270400442X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Brisebarre:2005:NRR,
  author =       "Nicolas Brisebarre and David Defour and Peter Kornerup
                 and Jean-Michel Muller and Nathalie Revol",
  title =        "A New Range-Reduction Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "331--339",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.36",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Apr 27 18:04:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0331abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0331.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0331.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388197.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388197.pdf?isnumber=30205&prod=JNL&arnumber=1388197&arSt=+331&ared=+339&arAuthor=Brisebarre%2C+N.%3B+Defour%2C+D.%3B+Kornerup%2C+P.%3B+Muller%2C+J.-M.%3B+Revol%2C+N.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388197&count=13&index=8;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388197",
  abstract =     "Range-reduction is a key point for getting accurate
                 elementary function routines. We introduce a new
                 algorithm that is fast for input arguments belonging to
                 the most common domains, yet accurate over the full
                 double-precision range.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Carlson:2005:JEF,
  author =       "B. C. Carlson",
  title =        "{Jacobian} elliptic functions as inverses of an
                 integral",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "174",
  number =       "2",
  pages =        "355--359",
  day =          "15",
  month =        feb,
  year =         "2005",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:00:02 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042704002201",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Cheng:2005:SEEa,
  author =       "Howard Cheng and Barry Gergel and Ethan Kim and Eugene
                 Zima",
  title =        "Space-efficient evaluation of hypergeometric series",
  journal =      j-SIGSAM,
  volume =       "39",
  number =       "2",
  pages =        "41--52",
  month =        jun,
  year =         "2005",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Tue Nov 29 06:11:40 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin (ACM Special Interest Group on
                 Symbolic and Algebraic Manipulation)",
  issue =        "152",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Article{Cheng:2005:SEEb,
  author =       "Howard Cheng and Barry Gergel and Ethan Kim and Eugene
                 Zima",
  title =        "Space-efficient evaluation of hypergeometric series",
  journal =      j-SIGSAM,
  volume =       "39",
  number =       "3",
  pages =        "81--83",
  year =         "2005",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Sat Feb 4 09:52:36 MST 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  note =         "ISSAC 2005 poster abstract.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin (ACM Special Interest Group on
                 Symbolic and Algebraic Manipulation)",
  issue =        "153",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@InProceedings{deDinechin:2005:TPU,
  author =       "Florent de Dinechin and Alexey Ershov and Nicolas
                 Gast",
  title =        "Towards the Post-ultimate {\tt libm}",
  crossref =     "IEEE:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arith17.polito.it/final/paper-165.pdf",
  abstract =     "This article presents advances on the subject of
                 correctly rounded elementary functions since the
                 publication of the {\tt libultim} mathematical library
                 developed by Ziv at IBM. This library showed that the
                 average performance and memory overhead of correct
                 rounding could be made negligible. However, the
                 worst-case overhead was still a factor 1000 or more. It
                 is shown here that, with current processor technology,
                 this worst-case overhead can be kept within a factor of
                 2 to 10 of current best libms. This low overhead has
                 very positive consequences on the techniques for
                 implementing and proving correctly rounded functions,
                 which are also studied. These results lift the last
                 technical obstacles to a generalisation of (at least
                 some) correctly rounded double precision elementary
                 functions.",
  acknowledgement = ack-nhfb,
  pagecount =    "8",
}

@Article{Freitas:2005:IPF,
  author =       "Pedro Freitas",
  title =        "Integrals of polylogarithmic functions, recurrence
                 relations, and associated {Euler} sums",
  journal =      j-MATH-COMPUT,
  volume =       "74",
  number =       "251",
  pages =        "1425--1440",
  month =        jul,
  year =         "2005",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Aug 2 10:37:19 MDT 2005",
  bibsource =    "http://www.ams.org/mcom/2005-74-251;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2000.bib",
  URL =          "http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/home.html;
                 http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/S0025-5718-05-01747-3.dvi;
                 http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/S0025-5718-05-01747-3.pdf;
                 http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/S0025-5718-05-01747-3.ps;
                 http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01747-3/S0025-5718-05-01747-3.tex",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Hernandez:2005:ACN,
  author =       "M. A. Hern{\'a}ndez and N. Romero",
  title =        "Accelerated convergence in {Newton}'s method for
                 approximating square roots",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "177",
  number =       "1",
  pages =        "225--229",
  day =          "1",
  month =        may,
  year =         "2005",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/j.cam.2004.09.025",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:00:04 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042704004315",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Misc{IBM:2005:MAS,
  author =       "{IBM Corporation}",
  title =        "{Mathematical Acceleration Subsystem} for {Linux}",
  howpublished = "World Wide Web document",
  year =         "2005",
  bibdate =      "Mon Dec 05 18:59:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www-306.ibm.com/software/awdtools/mass/linux/mass-linux.html",
  abstract =     "Mathematical Acceleration Subsystem (MASS) for Linux
                 consists of libraries of mathematical intrinsic
                 functions tuned specifically for optimum performance on
                 POWER architectures.",
  acknowledgement = ack-nhfb,
  keywords =     "Mathematical Acceleration Subsystem (MASS)",
  remark =       "Scalar library functions: atan, atan2, cos, cosh,
                 dnint, exp, log, pow [Fortran **], rsqrt, sin, sinh,
                 sqrt, tan, and tanh.\par

                 Vector library double-precision function: vacos, vasin,
                 vatan2, vcbrt, vcos, vcosh, vcosisin, vdint, vdiv,
                 vdnint, vexp, vexpm1, vlog, vlog10, vlog1p, vpow,
                 vrcbrt, vrec, vrsqrt, vsin, vsincos, vsinh, vsqrt,
                 vtan, and vtanh.\par

                 Vector library single-precision functions: vsacos,
                 vsasin, vsatan2, vscbrt, vscos, vscosh, vscosisin,
                 vsdiv, vsexp, vsexpm1, vslog, vslog10, vslog1p, vspow,
                 vsrcbrt, vsrec, vsrsqrt, vssin, vssincos, vssinh,
                 vssqrt, vstan, and vstanh.",
}

@Article{Kornerup:2005:DSS,
  author =       "Peter Kornerup",
  title =        "Digit Selection for {SRT} Division and Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "294--303",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.47",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 19 09:20:54 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0294abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0294.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0294.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388194.pdf?isnumber=30205&prod=JNL&arnumber=1388194&arSt=+294&ared=+303&arAuthor=Kornerup%2C+P.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388194&count=13&index=5;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388194",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "The quotient digit selection in the SRT division
                 algorithm is based on a few most significant bits of
                 the remainder and divisor, where the remainder is
                 usually represented in a redundant representation. The
                 number of leading bits needed depends on \ldots{}",
}

@Article{Ledoux:2005:CME,
  author =       "V. Ledoux and M. {Van Daele} and G. {Vanden Berghe}",
  title =        "{CP} methods and the evaluation of negative energy
                 {Coulomb} {Whittaker} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "183",
  number =       "1",
  pages =        "168--176",
  day =          "1",
  month =        nov,
  year =         "2005",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:00:34 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042705000233",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Lee:2005:OHF,
  author =       "Dong-U. Lee and Altaf Abdul Gaffar and Oskar Mencer
                 and Wayne Luk",
  title =        "Optimizing hardware function evaluation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "12",
  pages =        "1520--1531",
  month =        dec,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.201",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue May 30 12:04:26 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  abstract =     "We present a methodology and an automated system for
                 function evaluation unit generation. Our system selects
                 the best function evaluation hardware for a given
                 function, accuracy requirements, technology mapping,
                 and optimization metrics, such as area, throughput, and
                 latency. Function evaluation $ f(x) $ typically
                 consists of range reduction and the actual evaluation
                 on a small convenient interval such as $ [0, \pi / 2) $
                 for $ \sin (x) $. We investigate the impact of hardware
                 function evaluation with range reduction for a given
                 range and precision of $x$ and $ f(x) $ on area and
                 speed. An automated bit-width optimization technique
                 for minimizing the sizes of the operators in the data
                 paths is also proposed. We explore a vast design space
                 for fixed-point $ \sin (x) $, $ \log (x) $, and $ \sqrt
                 {x} $ accurate to one unit in the last place using
                 MATLAB and ASC, a stream compiler for
                 field-programmable gate arrays (FPGAs). In this study,
                 we implement over 2,000 placed-and-routed FPGA designs,
                 resulting in over 100 million application-specific
                 integrated circuit (ASIC) equivalent gates. We provide
                 optimal function evaluation results for range and
                 precision combinations between 8 and 48 bits.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "application specific integrated circuits;
                 application-specific integrated circuit equivalent
                 gates; ASC; ASIC; automated bit-width optimization
                 technique; circuit optimisation; computer arithmetic;
                 elementary function approximation; field programmable
                 gate arrays; field-programmable gate arrays; fixed
                 point arithmetic; fixed-point arithmetic; FPGA;
                 hardware function evaluation optimisation; logic
                 design; MATLAB; minimax approximation; range reduction;
                 stream compiler",
}

@InProceedings{Lefevre:2005:NRD,
  author =       "Vincent Lef{\`e}vre",
  title =        "New Results on the Distance Between a Segment and {$
                 Z^2 $}. {Application} to the Exact Rounding",
  crossref =     "IEEE:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arith17.polito.it/final/paper-147.pdf",
  abstract =     "This paper presents extensions to Lef{\'e}vre's
                 algorithm that computes a lower bound on the distance
                 between a segment and a regular grid $ Z^2 $. This
                 algorithm and, in particular, the extensions are useful
                 in the search for worst cases for the exact rounding of
                 unary elementary functions or base-conversion
                 functions. The proof that is presented here is simpler
                 and less technical than the original proof. This paper
                 also gives benchmark results with various optimization
                 parameters, explanations of these results, and an
                 application to base conversion.",
  acknowledgement = ack-nhfb,
  pagecount =    "8",
}

@InProceedings{Markstein:2005:FSM,
  author =       "Peter Markstein",
  title =        "A Fast-Start Method for Computing the Inverse
                 Tangent",
  crossref =     "IEEE:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arith17.polito.it/final/paper-112.pdf",
  abstract =     "In a search for an algorithm to compute $ \atan (x) $
                 which has both low latency and few floating point
                 instructions, an interesting variant of familiar
                 trigonometry formulas was discovered that allow the
                 start of argument reduction to commence before any
                 references to tables stored in memory are needed. Low
                 latency makes the method suitable for a closed
                 subroutine, and few floating point operations make the
                 method advantageous for a software-pipelined
                 implementation.",
  acknowledgement = ack-nhfb,
  keywords =     "IA-64; Itanium-2",
  pagecount =    "6",
}

@Article{Merkle:2005:GRG,
  author =       "M. Merkle",
  title =        "{Gurland}'s ratio for the gamma function",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "49",
  number =       "2--3",
  pages =        "389--406",
  month =        jan # "\slash " # feb,
  year =         "2005",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:42 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122105000416",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Perram:2005:EFW,
  author =       "John W. Perram and Edgar R. Smith",
  title =        "Elliptic Functions of the Worst Kind: Non-linear
                 Quantisation of the Classical Spherical Pendulum",
  journal =      j-ADV-QUANTUM-CHEM,
  volume =       "48",
  pages =        "111--125",
  year =         "2005",
  CODEN =        "AQCHA9",
  DOI =          "https://doi.org/10.1016/S0065-3276(05)48008-9",
  ISSN =         "0065-3276",
  ISSN-L =       "0065-3276",
  bibdate =      "Thu Oct 13 11:45:04 MDT 2011",
  bibsource =    "http://www.sciencedirect.com/science/bookseries/00653276;
                 https://www.math.utah.edu/pub/tex/bib/advquantumchem.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0065327605480089",
  acknowledgement = ack-nhfb,
  ajournal =     "Adv. Quantum Chem.",
  fjournal =     "Advances in Quantum Chemistry",
  journal-URL =  "http://www.sciencedirect.com/science/bookseries/00653276",
}

@Article{Pineiro:2005:HSF,
  author =       "Jose-Alejandro Pi{\~n}eiro and Stuart F. Oberman and
                 Jean-Michel Muller and Javier D. Bruguera",
  title =        "High-Speed Function Approximation Using a Minimax
                 Quadratic Interpolator",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "304--318",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.52",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 19 09:20:54 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0304abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0304.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0304.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388195.pdf?isnumber=30205&prod=JNL&arnumber=1388195&arSt=+304&ared=+318&arAuthor=Pineiro%2C+J.-A.%3B+Oberman%2C+S.F.%3B+Muller%2C+J.-M.%3B+Bruguera%2C+J.D.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388195&count=13&index=6;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388195",
  abstract =     "A table-based method for high-speed function
                 approximation in single-precision floating-point format
                 is presented in this paper. Our focus is the
                 approximation of reciprocal, square root, square root
                 reciprocal, exponentials, logarithms, trigonometric
                 functions, powering (with a fixed exponent $p$ ), or
                 special functions. The algorithm presented here
                 combines table look-up, an enhanced minimax quadratic
                 approximation, and an efficient evaluation of the
                 second-degree polynomial (using a specialized squaring
                 unit, redundant arithmetic, and multioperand addition).
                 The execution times and area costs of an architecture
                 implementing our method are estimated, showing the
                 achievement of the fast execution times of linear
                 approximation methods and the reduced area requirements
                 of other second-degree interpolation algorithms.
                 Moreover, the use of an enhanced minimax approximation
                 which, through an iterative process, takes into account
                 the effect of rounding the polynomial coefficients to a
                 finite size allows for a further reduction in the size
                 of the look-up tables to be used, making our method
                 very suitable for the implementation of an elementary
                 function generator in state-of-the-art DSPs or graphics
                 processing units (GPUs).",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Shore:2005:ARB,
  author =       "Haim Shore",
  title =        "Accurate {RMM}-Based Approximations for the {CDF} of
                 the Normal Distribution",
  journal =      j-COMMUN-STAT-THEORY-METH,
  volume =       "34",
  number =       "3",
  pages =        "507--513",
  year =         "2005",
  CODEN =        "CSTMDC",
  DOI =          "https://doi.org/10.1081/STA-200052102",
  ISSN =         "0361-0926 (print), 1532-415X (electronic)",
  ISSN-L =       "0361-0926",
  bibdate =      "Wed Jan 27 05:42:00 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/communstattheorymeth2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Theory and Methods",
  journal-URL =  "http://www.tandfonline.com/loi/lsta20",
}

@Book{Simon:2005:DCF,
  author =       "Marvin Kenneth Simon and Mohamed-Slim Alouini",
  title =        "Digital communication over fading channels",
  publisher =    pub-WI,
  address =      pub-WI:adr,
  edition =      "Second",
  pages =        "xxxiv + 900",
  year =         "2005",
  ISBN =         "0-471-64953-8 (hardcover)",
  ISBN-13 =      "978-0-471-64953-3 (hardcover)",
  LCCN =         "TK5103.7 .S523 2005",
  bibdate =      "Sat Dec 16 17:34:06 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley series in telecommunications and signal
                 processing",
  URL =          "http://www.loc.gov/catdir/description/wiley042/2004042040.html;
                 http://www.loc.gov/catdir/enhancements/fy0617/2004042040-b.html;
                 http://www.loc.gov/catdir/toc/wiley041/2004042040.html",
  acknowledgement = ack-nhfb,
  author-dates = "1939--",
  subject =      "Digital communications; Reliability; Mathematics;
                 Radio; Transmitters and transmission; Fading",
}

@Article{Skorokhodov:2005:MCG,
  author =       "S. L. Skorokhodov",
  title =        "A method for computing generalized hypergeometric
                 function {$_p F_{p - 1}(a_1, \ldots {}, a_p; b_1,
                 \ldots {}, b_{p - 1}; 1)$} in terms of the {Riemann}
                 zeta function",
  journal =      j-COMPUT-MATH-MATH-PHYS,
  volume =       "45",
  number =       "4",
  pages =        "550--562",
  month =        "????",
  year =         "2005",
  CODEN =        "????",
  ISSN =         "0965-5425 (print), 1555-6662 (electronic)",
  ISSN-L =       "0965-5425",
  bibdate =      "Thu Dec 01 09:31:40 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "1077.33008",
  acknowledgement = ack-nhfb,
  classmath =    "33C20 (Generalized hypergeometric series, ${}_pF_q$)",
  fjournal =     "Computational Mathematics and Mathematical Physics",
  keywords =     "generalized hypergeometric functions; Hurwitz zeta
                 function; hypergeometric function; Riemann zeta
                 function",
  xxnote =       "Is the journal name correct??",
}

@InProceedings{Stehle:2005:GAT,
  author =       "Damien Stehl{\'e} and Paul Zimmermann",
  title =        "{Gal}'s Accurate Tables Method Revisited",
  crossref =     "IEEE:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arith17.polito.it/final/paper-152.pdf",
  abstract =     "Gal's accurate tables algorithm aims at providing an
                 efficient implementation of mathematical functions with
                 correct rounding as often as possible. This method
                 requires an expensive pre-computation of the values
                 taken by the function or by several related functions
                 at some distinguished points. Our improvements of Gal's
                 method are two-fold: on the one hand we describe what
                 is the arguably best set of distinguished values and
                 how it improves the efficiency and accuracy of the
                 function implementation, and on the other hand we give
                 an algorithm which drastically decreases the cost of
                 the pre-computation. These improvements are related to
                 the worst cases for the correct rounding of
                 mathematical functions and to the algorithms for
                 finding them. We demonstrate how the whole method can
                 be turned into practice for $ 2^x $ and $ \sin x $ for
                 $ x \in [1 / 2, 1) $, in double precision.",
  acknowledgement = ack-nhfb,
  pagecount =    "8",
}

@Article{Stehle:2005:SWC,
  author =       "Damien Stehl{\'e} and Vincent Lef{\`e}vre and Paul
                 Zimmermann",
  title =        "Searching Worst Cases of a One-Variable Function Using
                 Lattice Reduction",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "340--346",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.55",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 19 09:20:54 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0340abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0340.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0340.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388198.pdf?isnumber=30205&prod=JNL&arnumber=1388198&arSt=+340&ared=+346&arAuthor=Stehle%2C+D.%3B+Lefevre%2C+V.%3B+Zimmermann%2C+P.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388198&count=13&index=9;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388198",
  abstract =     "We propose a new algorithm to find worst cases for the
                 correct rounding of a mathematical function of one
                 variable. We first reduce this problem to the real
                 small value problem---i.e., for polynomials with real
                 coefficients. Then, we show that this second problem
                 can be solved efficiently by extending Coppersmith's
                 work on the integer small value problem---for
                 polynomials with integer coefficients---using lattice
                 reduction. For floating-point numbers with a mantissa
                 less than $N$ and a polynomial approximation of degree
                 $d$, our algorithm finds all worst cases at distance
                 less than $ N^{\frac {-d^2}{2d + 1}} $ from a machine
                 number in time $ O(N^{{\frac {d + 12d + 1}} +
                 \varepsilon }) $. For $ d = 2 $, a detailed study
                 improves on the $ O(N^{2 / 3 + \varepsilon }) $
                 complexity from Lef{\`e}vre's algorithm to $ O(N^{4 / 7
                 + \varepsilon }) $. For larger $d$, our algorithm can
                 be used to check that there exist no worst cases at
                 distance less than $ N^{-k} $ in time $ O(N^{1 / 2 +
                 \varepsilon }) $.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Computer arithmetic; correct rounding; multiple
                 precision arithmetic; special function approximations",
}

@Article{Uzer:2005:CAS,
  author =       "A. Uzer and T. Ege",
  title =        "On the Convergence Acceleration of Slowly Convergent
                 Sums Involving Oscillating Terms",
  journal =      j-COMPUTING,
  volume =       "75",
  number =       "4",
  pages =        "311--318",
  month =        aug,
  year =         "2005",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/s00607-005-0126-2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65F05; 65F30; 65F50",
  bibdate =      "Tue Jul 8 22:32:46 MDT 2008",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=75&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=75&issue=4&spage=311",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "convergence acceleration; Fourier series; infinite
                 sums; slowly convergent sums; zeta functions",
}

@InProceedings{Walters:2005:EFA,
  author =       "George Walters and Michael Schulte",
  title =        "Efficient Function Approximation Using Truncated
                 Multipliers and Squarers",
  crossref =     "IEEE:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arith17.polito.it/final/paper-190.pdf",
  abstract =     "This paper presents a technique for designing linear
                 and quadratic interpolators for function approximation
                 using truncated multipliers and squarers. Initial
                 coefficient values are found using a Chebyshev series
                 approximation, and then adjusted through exhaustive
                 simulation to minimize the maximum absolute error of
                 the interpolator output. This technique is suitable for
                 any function and any precision up to 24-bits (IEEE
                 single precision). Designs for linear and quadratic
                 interpolators that implement the reciprocal function, $
                 f(x) = 1 / x, $ are presented and analyzed as an
                 example. We show that a 24-bit truncated reciprocal
                 quadratic interpolator with a design specification of $
                 \pm 1 $ ulp error requires 24.1\% fewer partial
                 products to implement than a comparable standard
                 interpolator with the same error specification.",
  acknowledgement = ack-nhfb,
  pagecount =    "8",
}

@InProceedings{Wang:2005:DFPa,
  author =       "L.-K. Wang and M. J. Schulte",
  title =        "Decimal Floating-Point Square Root Using
                 {Newton--Raphson} Iteration",
  crossref =     "Vassiliadis:2005:IIC",
  pages =        "309--315",
  year =         "2005",
  bibdate =      "Sun Mar 04 10:19:28 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2005-05.pdf",
  abstract =     "With continued reductions in feature size, additional
                 functionality may be added to future microprocessors to
                 boost the performance of important application domains.
                 Due to growth in commercial, financial, and
                 Internet-based applications, decimal floating point
                 arithmetic is now attracting more attention and
                 hardware support for decimal operations is being
                 considered by various computer manufacturers. In order
                 to standardize decimal number formats and operations,
                 specifications for decimal floating-point arithmetic
                 have been added to the draft revision of the IEEE-754
                 Standard for Floating-Point Arithmetic (IEEE-754R).
                 This paper presents an efficient arithmetic algorithm
                 and hardware design for decimal floating-point square
                 root. This design uses an optimized piecewise linear
                 approximation, a modified Newton--Raphson iteration, a
                 specialized rounding technique, and a modified decimal
                 multiplier. Synthesis results show that a 64-bit
                 (16-digit) implementation of decimal square root, which
                 is compliant with IEEE-754R, has an estimated critical
                 path delay of 0.95 ns and a maximum latency of 210
                 clock cycles when implemented using a sequential
                 multiplier and LSI Logic's 0.11 micron Gflx-P standard
                 cell library.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Weber:2005:MIG,
  author =       "Kenneth Weber and Vilmar Trevisan and Luiz Felipe
                 Martins",
  title =        "A modular integer {GCD} algorithm",
  journal =      j-J-ALG,
  volume =       "54",
  number =       "2",
  pages =        "152--167",
  month =        feb,
  year =         "2005",
  CODEN =        "JOALDV",
  DOI =          "https://doi.org/10.1016/j.jalgor.2004.06.006",
  ISSN =         "0196-6774 (print), 1090-2678 (electronic)",
  ISSN-L =       "0196-6774",
  bibdate =      "Tue Dec 11 09:21:34 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jalg.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0196677404001075",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Algorithms",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01966774",
}

@Article{West:2005:BAC,
  author =       "G. West",
  title =        "Better approximations to cumulative normal functions",
  journal =      "Wilmott Magazine",
  volume =       "??",
  number =       "??",
  pages =        "70--76",
  month =        "????",
  year =         "2005",
  ISSN =         "1540-6962 (print), 1541-8286 (electronic)",
  ISSN-L =       "1540-6962",
  bibdate =      "Sat Dec 16 17:59:43 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1541-8286;
                 https://www.wilmott.com/category/magazine/",
  remark =       "No issues online at Wiley before year 2011, or at
                 Wilmott before 2006.",
}

@TechReport{Zimmermann:2005:XXX,
  author =       "Paul Zimmermann",
  title =        "5,341,321",
  type =         "Technical report",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "2",
  day =          "8",
  month =        jun,
  year =         "2005",
  bibdate =      "Sun Sep 10 07:32:04 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/papers/5341321.ps.gz",
  abstract =     "This short note shows the nasty effects of patents for
                 the development of free software, even for patents that
                 were not written with software applications in mind.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point division; Karp--Markstein patent on
                 modified Newton--Raphson iteration",
  remark =       "The title is the number of the U.S. Patent on the
                 algorithm described in the article, which is a
                 completely trivial modification of Newton--Raphson
                 iteration, published in \cite{Karp:1997:HPD}. The
                 patent itself is \cite{Karp:1994:FPA}, and it expired
                 on 5 May 2013.",
}

@InProceedings{Anderson:2006:AMF,
  author =       "Cristina S. Anderson and Shane Story and Nikita
                 Astafiev",
  title =        "Accurate Math Functions on the {Intel IA-32}
                 Architecture: a Performance-Driven Design",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions",
}

@TechReport{Bertot:2006:PGS,
  author =       "Yves Bertot and Nicolas Magaud and Paul Zimmermann",
  title =        "A proof of {GMP} square root using the {Coq}
                 assistant",
  type =         "Research Report",
  number =       "RR-4475",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "28",
  year =         "2006",
  bibdate =      "Sun Sep 10 08:34:35 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4475.pdf;
                 ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4475.ps.gz;
                 http://www.inria.fr/rrrt/rr-4475.html",
  abstract =     "We present a formal proof (at the implementation
                 level) of an efficient algorithm proposed in to compute
                 square roots of arbitrarily large integers. This
                 program, which is part of the GNU Multiple Precision
                 Arithmetic Library (GMP), is completely proven within
                 the system. Proofs are developed using the Correctness
                 tool to deal with imperative features of the program.
                 The formalization is rather large (more than 13000
                 lines) and requires some advanced techniques for proof
                 management and reuse.",
  acknowledgement = ack-nhfb,
}

@Article{Bogolubsky:2006:FEH,
  author =       "A. I. Bogolubsky and S. L. Skorokhodov",
  title =        "Fast evaluation of the hypergeometric function {$_p
                 F_{p - 1}(a; b; z)$} at the singular point $ z = 1 $ by
                 means of the {Hurwitz} zeta function $ \zeta (\alpha,
                 s) $",
  journal =      j-PROG-COMP-SOFT,
  volume =       "32",
  number =       "??",
  pages =        "145--153",
  month =        "????",
  year =         "2006",
  CODEN =        "PCSODA",
  ISSN =         "0361-7688 (print), 1608-3261 (electronic)",
  ISSN-L =       "0361-7688",
  bibdate =      "Thu Dec 01 09:34:31 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Programming and Computer Software; translation of
                 Programmirovaniye (Moscow, USSR) Plenum",
  journal-URL =  "http://link.springer.com/journal/11086",
}

@Article{Boldo:2006:PFF,
  author =       "Sylvie Boldo",
  editor =       "Ulrich Furbach and Natarajan Shankar",
  booktitle =    "{Automated Reasoning: Third International Joint
                 Conference, IJCAR 2006, Seattle, WA, USA, August
                 17--20, 2006, Proceedings}",
  title =        "Pitfalls of a full floating-point proof: Example on
                 the formal proof of the {Veltkamp\slash Dekker}
                 algorithms",
  journal =      j-LECT-NOTES-COMP-SCI,
  bookpages =    "xv + 680",
  pages =        "52--66",
  year =         "2006",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/11814771_6",
  ISBN =         "3-540-37187-7 (paperback), 3-540-37188-5",
  ISBN-13 =      "978-3-540-37187-8 (paperback), 978-3-540-37188-5",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  LCCN =         "QA76.9.A96 I33 2006eb",
  MRnumber =     "MR2354672",
  bibdate =      "Mon Jun 12 16:14:21 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/11814771",
  book-URL =     "http://www.springer.com/us/book/9783540371878",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@TechReport{Brent:2006:FAH,
  author =       "Richard P. Brent",
  title =        "Fast Algorithms for High-Precision Computation of
                 Elementary Functions",
  type =         "Report",
  number =       "??",
  institution =  "Australian National University",
  address =      "Canberra, ACT 0200, Australia",
  pages =        "61",
  day =          "12",
  month =        jul,
  year =         "2006",
  bibdate =      "Fri Sep 04 16:33:10 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://rnc7.loria.fr/brent_invited.pdf;
                 https://maths-people.anu.edu.au/~brent/pd/RNC7t.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "arithmetic-geometric mean",
  remark =       "From page 57: ``This talk is based on a chapter of a
                 book that Paul Zimmermann and I are writing''. That
                 book is entry \cite{Brent:2011:MCA}.",
}

@TechReport{Crandall:2006:NFP,
  author =       "Richard E. Crandall",
  title =        "Note on fast polylogarithm computation",
  type =         "Report",
  institution =  "Reed College",
  address =      "Portland, OR, USA",
  pages =        "6",
  month =        jan,
  year =         "2006",
  bibdate =      "Tue Mar 19 09:03:09 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://people.reed.edu/~crandall/papers/Polylog.pdf;
                 https://web.archive.org/web/20120916145721/http://people.reed.edu/~crandall/papers/Polylog.pdf",
  abstract =     "The polylogarithm function $ \Li_n(z) = \sum_{k =
                 1}^\infty z^k / k^n $, manifestly convergent for $ |z|
                 \eq 1 $, integer $ n > 1 $, is sometimes
                 numerically\slash symbolically relevant for $ |z| > 1
                 $, i.e., the analytic continuation may be required. By
                 exploiting analytic symmetry relations, we give, for
                 integer $n$, simple and efficient algorithms for
                 complete continuation in complex $z$.",
  acknowledgement = ack-nhfb,
}

@Article{Cuyt:2006:ERM,
  author =       "Annie Cuyt and Brigitte Verdonk and Haakon Waadeland",
  title =        "Efficient and Reliable Multiprecision Implementation
                 of Elementary and Special Functions",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "28",
  number =       "4",
  pages =        "1437--1462",
  month =        jan,
  year =         "2006",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/050629203",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Wed May 19 10:43:41 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/28/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@InProceedings{deDinechin:2006:STP,
  author =       "Florent de Dinechin and Sergey Maidanov",
  title =        "Software techniques for perfect elementary functions
                 in floating-point interval arithmetic",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions",
}

@Book{ElAttar:2006:SFO,
  author =       "Refaat A. {El Attar}",
  title =        "Special functions and orthogonal polynomials",
  volume =       "3",
  publisher =    "Lulu Press",
  address =      "Morrisville, NC, USA",
  pages =        "vi + 302",
  year =         "2006",
  ISBN =         "1-4116-6690-9 (paperback)",
  ISBN-13 =      "978-1-4116-6690-0 (paperback)",
  LCCN =         "QA404.5 .E5 2006; QA351 .E5 2006",
  bibdate =      "Sat Oct 30 17:42:31 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  series =       "Mathematical series",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Orthogonal polynomials; Polinomios
                 ortogonales; Series ortogonales",
  tableofcontents = "Series solutions of differential equations \\
                 Gamma and beta functions and others \\
                 Legendre polynomials \\
                 Hermite polynomials \\
                 Laguerre and other orthogonal polynomials \\
                 Bessel functions",
}

@Article{Ferreira:2006:GHF,
  author =       "C. Ferreira and J. L. L{\'o}pez and E. P.
                 Sinus{\'\i}a",
  title =        "The {Gauss} hypergeometric function {$ F(a; b; c; z)
                 $} for large $c$",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "197",
  number =       "2",
  pages =        "568--577",
  day =          "15",
  month =        jan,
  year =         "2006",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "33C05 (33F05 41A60)",
  MRnumber =     "MR2260426 (2007i:33012)",
  bibdate =      "Thu Dec 01 09:20:59 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  remark =       "$ F(a; b; c; z) = {}_2 F_1 (a, b + 1; c + 2; z) $",
}

@Article{Gil:2006:ARP,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 850}: {Real} parabolic cylinder functions
                 {$ U(a, x) $, $ V(a, x) $}",
  journal =      j-TOMS,
  volume =       "32",
  number =       "1",
  pages =        "102--112",
  month =        mar,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1132973.1132978",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri May 26 06:32:19 MDT 2006",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Fortran 90 programs for the computation of real
                 parabolic cylinder functions are presented. The code
                 computes the functions $ U(a, x) $, $ V(a, x) $ and
                 their derivatives for real $a$ and $ x (x \geq 0) $.
                 The code also computes scaled functions. The range of
                 computation for scaled PCFs is practically
                 unrestricted. The aimed relative accuracy for scaled
                 functions is better than $ 5 \times 10^{14} $.
                 Exceptions to this accuracy are the evaluation of the
                 functions near their zeros and the error caused by the
                 evaluation of trigonometric functions of large
                 arguments when $ |a| > x $. The routines always give
                 values for which the Wronskian relation for scaled
                 functions is verified with a relative accuracy better
                 than $ 5 \times 10^{14} $. The accuracy of the unscaled
                 functions is also better than $ 5 \times 10^{14} $ for
                 moderate values of $x$ and $a$ (except close to the
                 zeros), while for large $x$ and $a$ the error is
                 dominated by exponential and trigonometric function
                 evaluations. For IEEE standard double precision
                 arithmetic, the accuracy is better than $ 5 \times
                 10^{13} $ in the computable range of unscaled PCFs
                 (except close to the zeros).",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gil:2006:CRP,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Computing the real parabolic cylinder functions {$
                 U(a, x) $, $ V(a, x) $}",
  journal =      j-TOMS,
  volume =       "32",
  number =       "1",
  pages =        "70--101",
  month =        mar,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1132973.1132977",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri May 26 06:32:19 MDT 2006",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Methods for the computation of real parabolic cylinder
                 functions $ U(a, x) $, and $ V(a, x) $ and their
                 derivatives are described. We give details on power
                 series, asymptotic series, recursion and quadrature. A
                 combination of these methods can be used for computing
                 parabolic cylinder functions for unrestricted values of
                 the order $a$ and the variable $x$ except for the
                 overflow\slash underflow limitations. By factoring the
                 dominant exponential factor, scaled functions can be
                 computed without practical overflow\slash underflow
                 limitations. In an accompanying article we describe the
                 precise domains for these methods and we present the
                 Fortran 90 codes for the computation of these
                 functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Jones:2006:PCF,
  author =       "D. S. Jones",
  title =        "Parabolic cylinder functions of large order",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "190",
  number =       "1--2",
  pages =        "453--469",
  day =          "1",
  month =        jun,
  year =         "2006",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:11:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042705002463",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Kong:2006:IGA,
  author =       "Fanyu Kong and Zhun Cai and Jia Yu and Daxing Li",
  title =        "Improved generalized {Atkin} algorithm for computing
                 square roots in finite fields",
  journal =      j-INFO-PROC-LETT,
  volume =       "98",
  number =       "1",
  pages =        "1--5",
  day =          "15",
  month =        apr,
  year =         "2006",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Thu Mar 31 18:41:08 MDT 2011",
  bibsource =    "http://www.sciencedirect.com/science/journal/00200190;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@InProceedings{Muller:2006:GFA,
  author =       "Jean-Michel Muller",
  editor =       "Michael B. Matthews",
  booktitle =    "{2006 Fortieth Asilomar Conference on Signals, Systems
                 and Computers. October 29--November 1, 2006. Pacific
                 Grove, California}",
  title =        "Generating function approximations at compile time",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "328--331",
  year =         "2006",
  DOI =          "https://doi.org/10.1109/ACSSC.2006.354761",
  ISBN =         "1-4244-0785-0",
  ISBN-13 =      "978-1-4244-0785-9",
  bibdate =      "Fri Sep 29 10:57:58 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Nowak:2006:MCA,
  author =       "Rafal Nowak",
  title =        "A method of convergence acceleration of some continued
                 fractions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "41",
  number =       "3",
  pages =        "297--317",
  month =        mar,
  year =         "2006",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-005-9013-3",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "subject classification; 30B70; 40A15; 65B99",
  bibdate =      "Tue Jul 8 19:14:28 MDT 2008",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=41&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=41&issue=3&spage=297",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "continued fraction; convergence acceleration; modified
                 approximant; tail",
}

@Article{Ozban:2006:NMA,
  author =       "Ahmet Ya{\c{s}}ar {\"O}zban",
  title =        "New methods for approximating square roots",
  journal =      j-APPL-MATH-COMP,
  volume =       "175",
  number =       "1",
  pages =        "532--540",
  day =          "1",
  month =        apr,
  year =         "2006",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Jul 12 09:02:54 MDT 2008",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@InProceedings{Parks:2006:UTS,
  author =       "Michael Parks",
  title =        "Unifying Tests for Square Root",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions",
}

@Article{Qian:2006:HMP,
  author =       "Jianbo Qian and Cao An Wang",
  title =        "How much precision is needed to compare two sums of
                 square roots of integers?",
  journal =      j-INFO-PROC-LETT,
  volume =       "100",
  number =       "5",
  pages =        "194--198",
  day =          "16",
  month =        dec,
  year =         "2006",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Thu Mar 31 15:52:31 MDT 2011",
  bibsource =    "http://www.sciencedirect.com/science/journal/00200190;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@Article{Shi:2006:NAS,
  author =       "Xiquan Shi and Fengshan Liu and Minghan Hu",
  title =        "A new asymptotic series for the Gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "195",
  number =       "1--2",
  pages =        "134--154",
  day =          "15",
  month =        oct,
  year =         "2006",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/j.cam.2005.03.081",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:12:01 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042705004802",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Sidi:2006:CTC,
  author =       "Avram Sidi",
  title =        "A challenging test for convergence accelerators:
                 Summation of a series with a special sign pattern",
  journal =      "App. Math. E-Notes",
  volume =       "6",
  number =       "??",
  pages =        "225--234",
  month =        "????",
  year =         "2006",
  CODEN =        "????",
  ISSN =         "????",
  MRclass =      "40A99 (11M41 40A05 65B10)",
  MRnumber =     "MR2231748 (2007h:40009)",
  bibdate =      "Thu Dec 01 10:33:54 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration; Shanks transformation",
}

@InProceedings{Thakkar:2006:PDP,
  author =       "Anuja J. Thakkar and Abdel Ejnioui",
  title =        "Pipelining of double precision floating point division
                 and square root operations",
  crossref =     "Menezes:2006:PAS",
  pages =        "488--493",
  year =         "2006",
  DOI =          "https://doi.org/10.1145/1185448.1185555",
  bibdate =      "Sat Oct 9 13:04:49 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Space applications rely increasingly on high data rate
                 DSP algorithms. These algorithms use double precision
                 floating point arithmetic operations. While most DSP
                 applications can be compiled on DSP processors, high
                 data rate DSP computations require novel implementation
                 technologies to support their high throughputs. Only
                 recently, gate densities in FPGAs have reached a level
                 which makes them attractive platforms to implement
                 compute-intensive DSP applications. In this context,
                 this paper presents the sequential and pipelined
                 designs of a double precision floating point divider
                 and square root unit on FPGAs. Contrary to pipelined
                 parallel implementations, the pipelining of these units
                 is based on unrolling the iterations in low-radix digit
                 recurrence algorithms. These units are mapped on
                 generic FPGA reconfigurable fabric without taking
                 advantage of any advanced architectural components
                 available in high capacity FPGAs. The implementations
                 of these designs show that their performances are
                 comparable to, and sometimes higher than, the
                 performances of non-iterative designs based of high
                 radix numbers. The iterative divider and square root
                 unit occupy less than 1\% of an XC2V6000 FPGA chip
                 while their pipelined counterparts can produce
                 throughputs that reach the 100 MFLOPS mark by consuming
                 a modest 8\% of the chip area.",
  acknowledgement = ack-nhfb,
}

@Article{VanDeun:2006:ACI,
  author =       "Joris {Van Deun} and Ronald Cools",
  title =        "{Algorithm 858}: {Computing} infinite range integrals
                 of an arbitrary product of {Bessel} functions",
  journal =      j-TOMS,
  volume =       "32",
  number =       "4",
  pages =        "580--596",
  month =        dec,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1186785.1186790",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:57 MDT 2007",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present an algorithm to compute integrals of the
                 form $ \int_0^\infty x^m \prod^k_i = 1 J_{\nu_i}(a_i
                 x)d x $ with $ J_{\nu_i}(x) $ the Bessel function of
                 the first kind and (real) order $ \nu_i $. The
                 parameter $m$ is a real number such that $ \sum_i \nu_i
                 + m > - 1 $ and the coefficients $ a_i $ are strictly
                 positive real numbers. The main ingredients in this
                 algorithm are the well-known asymptotic expansion for $
                 J_{\nu_i}(x) $ and the observation that the infinite
                 part of the integral can be approximated using the
                 incomplete Gamma function $ \Gamma (a, z) $. Accurate
                 error estimates are included in the algorithm, which is
                 implemented as a MATLAB program.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{VanDeun:2006:SRI,
  author =       "Joris {Van Deun} and Ronald Cools",
  title =        "A stable recurrence for the incomplete gamma function
                 with imaginary second argument",
  journal =      j-NUM-MATH,
  volume =       "104",
  number =       "4",
  pages =        "445--456",
  month =        oct,
  year =         "2006",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s00211-006-0026-1",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Tue Jul 8 10:28:23 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Wires:2006:RRS,
  author =       "Kent E. Wires and Michael J. Schulte",
  title =        "Reciprocal and Reciprocal Square Root Units with
                 Operand Modification and Multiplication",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "42",
  number =       "3",
  pages =        "257--272",
  month =        mar,
  year =         "2006",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1007/s11265-006-4186-0",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Mon Mar 05 08:26:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://springerlink.metapress.com/content/t6027p6713727606/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@InProceedings{Barnett:2007:HPV,
  author =       "Ross Barnett and J. A. Youngman",
  booktitle =    "{1st Joint Meeting of the American Mathematical
                 Society and the New Zealand Mathematical Society,
                 Victoria University of Wellington, Wellington, New
                 Zealand, December 12--15, 2007}",
  title =        "High-Precision Values of the Gamma Function of real
                 argument",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "????",
  year =         "2007",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Mon Jul 14 11:57:00 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://homepages.mcs.vuw.ac.nz/~mathmeet/amsnzms2007/abstracts.pdf",
  abstract =     "A method is described to calculate values of $ \Gamma
                 (\nu) $, $ 0 \leq \nu \leq 1 $ to arbitrary precision
                 by combining a Bessel function with a $_0 F_1$
                 function. Steed's algorithm is used to compute the
                 regular Bessel function $ J_\nu (x) $, for a suitable
                 argument $x$ and real $ \nu $, to arbitrary accuracy.
                 Hence the gamma function is obtained. Example values
                 are given to 200D. Verification is by the 80D-results
                 of Frans{\'e}n and Wrigge, by the use of the
                 duplication formula, and by computing the closed form
                 results of Borwein and Zucker. A caveat is offered
                 concerning the coding of the Bessel functions in
                 Numerical Recipes and in the GSL library.",
  acknowledgement = ack-nhfb,
}

@Article{Batterman:2007:SSF,
  author =       "Robert W. Batterman",
  title =        "On the Specialness of Special Functions (The Nonrandom
                 Effusions of the Divine Mathematician)",
  journal =      j-BRITISH-J-PHILOS-SCI,
  volume =       "58",
  number =       "2",
  pages =        "263--286",
  month =        jun,
  year =         "2007",
  CODEN =        "BJPIA5",
  DOI =          "https://doi.org/10.1093/bjps/axm007",
  ISSN =         "0007-0882 (print), 1464-3537 (electronic)",
  ISSN-L =       "0007-0882",
  bibdate =      "Thu Oct 7 14:03:55 MDT 2010",
  bibsource =    "http://bjps.oxfordjournals.org/content/58/2.toc;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bjps.oxfordjournals.org/content/58/2/263.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "British Journal for the Philosophy of Science",
  journal-URL =  "http://www.jstor.org/journals/00070882.html",
  onlinedate =   "May 18, 2007",
}

@InProceedings{Burgess:2007:DAV,
  author =       "Neil Burgess and Chris N. Hinds",
  title =        "Design of the {ARM VFP11} Divide and Square Root
                 Synthesisable Macrocell",
  crossref =     "Kornerup:2007:PIS",
  pages =        "87--96",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.15",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents the detailed design of the ARM
                 VFP11 Divide and Square Root synthesisable macrocell.
                 The macrocell was designed using the minimum-redundancy
                 radix-4 SRT digit recurrence algorithm, and this paper
                 describes a novel acceleration technique employed to
                 achieve the required processor clock frequency of up to
                 750MHz in 90nm CMOS. Logical Effort theory is used to
                 provide a delay analysis of the unit, which
                 demonstrates the balanced nature of the two critical
                 paths therein.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Article{Cerone:2007:SFA,
  author =       "Pietro Cerone",
  title =        "Special functions: approximations and bounds",
  journal =      "Applicable Analysis and Discrete Mathematics",
  volume =       "1",
  number =       "1",
  pages =        "72--91",
  year =         "2007",
  DOI =          "https://doi.org/10.2298/AADM0701072C",
  ISSN =         "1452-8630 (print), 2406-100X (electronic)",
  ISSN-L =       "1452-8630",
  MRclass =      "26D15 (26D20 33B15 33C05)",
  MRnumber =     "2316589",
  MRreviewer =   "Pierpaolo Natalini",
  bibdate =      "Thu Jul 29 07:41:55 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://pefmath.etf.rs/accepted/AADM-Vol1-No1-72-91.pdf",
  abstract =     "The Steffensen inequality and bounds for the
                 {\v{C}}eby{\v{s}}ev functional are utilised to obtain
                 bounds for some classical special functions. The
                 technique relies on determining bounds on integrals of
                 products of functions. The above techniques are used to
                 obtain novel and useful bounds for the Bessel function
                 of the first kind, the Beta function, and the Zeta
                 function.",
  acknowledgement = ack-nhfb,
  ajournal =     "Appl. Anal. Discrete Math.",
  fjournal =     "Applicable Analysis and Discrete Mathematics",
}

@Book{Chakraborty:2007:VSF,
  author =       "Kalyan Chakraborty and Shigeru Kanemitsu and Haruo
                 Tsukada",
  title =        "Vistas of special functions {II}",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "xii + 215",
  year =         "2007",
  ISBN =         "981-270-774-3",
  ISBN-13 =      "978-981-270-774-1",
  LCCN =         "QA351 .K35 2007",
  bibdate =      "Sat Oct 30 17:02:07 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  abstract =     "This is a unique book for studying special functions
                 through zeta-functions. Many important formulas of
                 special functions scattered throughout the literature
                 are located in their proper positions and readers get
                 enlightened access to them in this book. The areas
                 covered include: Bernoulli polynomials, the gamma
                 function (the beta and the digamma function), the
                 zeta-functions (the Hurwitz, the Lerch, and the Epstein
                 zeta-function), Bessel functions, an introduction to
                 Fourier analysis, finite Fourier series, Dirichlet
                 L-functions, the rudiments of complex functions and
                 summation formulas. The Fourier series for the (first)
                 periodic Bernoulli polynomial is effectively used,
                 familiarizing the reader with the relationship between
                 special functions and zeta-functions.",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Bernoulli polynomials",
  tableofcontents = "The theory of Bernoulli and allied polynomials \\
                 The theory of the gamma and related functions \\
                 The theory of the Hurwitz--Lerch zeta-functions \\
                 The theory of Bernoulli polynomials via zeta-functions
                 \\
                 The theory of the gamma and related functions via
                 zeta-functions \\
                 The theory of Bessel functions and the Epstein
                 zeta-functions \\
                 Fourier series and Fourier transforms \\
                 Around Dirichlet's $L$-functions \\
                 Appendix A: Complex functions \\
                 Appendix B: Summation formulas and convergence
                 theorems",
}

@Article{Dyer:2007:AEF,
  author =       "Stephen Dyer and Justin Dyer",
  title =        "Approximations to Error Functions",
  journal =      "IEEE Instrumentation \& Measurement Magazine",
  volume =       "10",
  number =       "6",
  pages =        "45--48",
  month =        dec,
  year =         "2007",
  DOI =          "https://doi.org/10.1109/mim.2007.4428581",
  bibdate =      "Sat Dec 16 16:26:38 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/abstract/document/4428581/",
  acknowledgement = ack-nhfb,
}

@Article{Ercegovac:2007:CSR,
  author =       "Milo{\v{s}} D. Ercegovac and Jean-Michel Muller",
  title =        "Complex Square Root with Operand Prescaling",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "49",
  number =       "1",
  pages =        "19--30",
  month =        oct,
  year =         "2007",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1007/s11265-006-0029-2",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Mon Nov 05 19:24:36 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We propose a radix-$r$ digit-recurrence algorithm for
                 complex square-root. The operand is prescaled to allow
                 the selection of square-root digits by rounding of the
                 residual. This leads to a simple hardware
                 implementation of digit selection. Moreover, the use of
                 digit recurrence approach allows correct rounding of
                 the result if needed. The algorithm, compatible with
                 the complex division presented in Ercegovac and Muller
                 (``Complex Division with Prescaling of the Operands,''
                 in Proc. Application-Specific Systems, Architectures,
                 and Processors (ASAP'03), The Hague, The Netherlands,
                 June 24---26, 2003), and its design are described. We
                 also give rough estimates of its latency and cost with
                 respect to implementation based on standard
                 floating-point instructions as used in software
                 routines for complex square root.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@Article{Ferraro:2007:FAG,
  author =       "Giovanni Ferraro",
  title =        "The foundational aspects of {Gauss}'s work on the
                 hypergeometric, factorial and digamma functions",
  journal =      j-ARCH-HIST-EXACT-SCI,
  volume =       "61",
  number =       "5",
  pages =        "457--518",
  month =        sep,
  year =         "2007",
  CODEN =        "AHESAN",
  DOI =          "https://doi.org/10.1007/s00407-007-0004-8",
  ISSN =         "0003-9519 (print), 1432-0657 (electronic)",
  ISSN-L =       "0003-9519",
  MRclass =      "33-03 (01A50 33B15 33C05)",
  MRnumber =     "2329096 (2009d:33002)",
  MRreviewer =   "M. E. Muldoon",
  bibdate =      "Fri Feb 4 21:50:42 MST 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=61&issue=5;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=61&issue=5&spage=457",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for History of Exact Sciences",
  journal-URL =  "http://link.springer.com/journal/407",
  MRtitle =      "The foundational aspects of {Gauss}'s work on the
                 hypergeometric, factorial and digamma functions",
}

@Article{Fousse:2007:MMP,
  author =       "Laurent Fousse and Guillaume Hanrot and Vincent
                 Lef{\`e}vre and Patrick P{\'e}lissier and Paul
                 Zimmermann",
  title =        "{MPFR}: a multiple-precision binary floating-point
                 library with correct rounding",
  journal =      j-TOMS,
  volume =       "33",
  number =       "2",
  pages =        "1--15",
  month =        jun,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1236463.1236468",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G99",
  MRnumber =     "MR2326955",
  bibdate =      "Thu Jul 26 17:36:59 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article presents a multiple-precision binary
                 floating-point library, written in the ISO C language,
                 and based on the GNU MP library. Its particularity is
                 to extend to arbitrary-precision, ideas from the IEEE
                 754 standard, by providing correct rounding and
                 exceptions. We demonstrate how these strong semantics
                 are achieved---with no significant slowdown with
                 respect to other arbitrary-precision tools---and
                 discuss a few applications where such a library can be
                 useful.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Book{Gil:2007:NMS,
  author =       "Amparo Gil and Javier Segura and N. M. Temme",
  title =        "Numerical methods for special functions",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xvi + 415",
  year =         "2007",
  ISBN =         "0-89871-634-9",
  ISBN-13 =      "978-0-89871-634-4",
  LCCN =         "QA351 .G455 2007",
  bibdate =      "Fri Sep 14 10:24:22 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$99.00",
  acknowledgement = ack-nhfb,
  remark =       "To be published October 2007.",
  subject =      "functions, special; data processing; numerical
                 analysis; asymptotic expansions; approximation theory",
}

@Article{Gil:2007:NSS,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Numerically satisfactory solutions of hypergeometric
                 recursions",
  journal =      j-MATH-COMPUT,
  volume =       "76",
  number =       "259",
  pages =        "1449--1468",
  month =        jul,
  year =         "2007",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Jul 8 06:24:22 MDT 2008",
  bibsource =    "http://www.ams.org/mcom/2007-76-259;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2000.bib",
  URL =          "http://www.ams.org/mcom/2007-76-259/S0025-5718-07-01918-7/home.html;
                 http://www.ams.org/mcom/2007-76-259/S0025-5718-07-01918-7/S0025-5718-07-01918-7.dvi;
                 http://www.ams.org/mcom/2007-76-259/S0025-5718-07-01918-7/S0025-5718-07-01918-7.pdf;
                 http://www.ams.org/mcom/2007-76-259/S0025-5718-07-01918-7/S0025-5718-07-01918-7.ps",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Glaser:2007:FAC,
  author =       "Andreas Glaser and Xiangtao Liu and Vladimir Rokhlin",
  title =        "A Fast Algorithm for the Calculation of the Roots of
                 Special Functions",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "29",
  number =       "4",
  pages =        "1420--1438",
  month =        "????",
  year =         "2007",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/06067016X",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Wed May 19 10:43:53 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/29/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "We describe a procedure for the determination of the
                 roots of functions satisfying second-order ordinary
                 differential equations, including the classical special
                 functions. The scheme is based on a combination of the
                 Pr{\"u}fer transform with the classical Taylor series
                 method for the solution of ordinary differential
                 equations and requires $ O(1) $ operations for the
                 determination of each root. When the functions in
                 question are classical orthogonal polynomials
                 (Legendre, Hermite, etc.), the techniques presented
                 here also provide tools for the evaluation of the
                 weights for the associated Gaussian quadratures. The
                 performance of the scheme for several classical special
                 functions (prolate spheroidal wave functions, Bessel
                 functions, and Legendre, Hermite, and Laguerre
                 polynomials) is illustrated with numerical examples.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@Article{Guseinov:2007:UTE,
  author =       "I. I. Guseinov and B. A. Mamedov",
  title =        "Unified treatment for the evaluation of generalized
                 complete and incomplete gamma functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "202",
  number =       "2",
  pages =        "435--439",
  day =          "15",
  month =        may,
  year =         "2007",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:13:14 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042706001506",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Hernandez:2007:MPO,
  author =       "M. A. Hern{\'a}ndez and N. Romero",
  title =        "Methods with prefixed order for approximating square
                 roots with global and general convergence",
  journal =      j-APPL-MATH-COMP,
  volume =       "194",
  number =       "2",
  pages =        "346--353",
  day =          "15",
  month =        dec,
  year =         "2007",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Jul 12 09:03:09 MDT 2008",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Kalmykov:2007:AOEa,
  author =       "M. Y. Kalmykov and B. F. L. Ward and Y. Yost",
  title =        "All order $ \epsilon $-expansion of {Gauss}
                 hypergeometric functions with integer and half\slash
                 integer values of parameters",
  journal =      j-J-HIGH-ENERGY-PHYS,
  volume =       "2007",
  number =       "02",
  pages =        "040--??",
  month =        "????",
  year =         "2007",
  CODEN =        "JHEPAB",
  ISSN =         "1126-6708",
  ISSN-L =       "1029-8479",
  MRclass =      "33C05 (33B30)",
  MRnumber =     "MR2318011 (2009g:33004)",
  bibdate =      "Thu Dec 01 09:16:04 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "JHEP",
  fjournal =     "Journal of High Energy Physics",
  pagecount =    "21",
}

@Article{Kalmykov:2007:AOEb,
  author =       "M. Y. Kalmykov and B. F. L. Ward and Y. Yost",
  title =        "On the all-order $ \epsilon $-expansion of generalized
                 hypergeometric functions with integer values of
                 parameters",
  journal =      j-J-HIGH-ENERGY-PHYS,
  volume =       "2007",
  number =       "11",
  pages =        "009",
  month =        "????",
  year =         "2007",
  CODEN =        "JHEPAB",
  ISSN =         "1126-6708",
  ISSN-L =       "1029-8479",
  MRclass =      "33C20 (33B30 41A58)",
  MRnumber =     "MR2362140 (2008m:33016)",
  bibdate =      "Thu Dec 01 09:16:04 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "JHEP",
  fjournal =     "Journal of High Energy Physics",
  pagecount =    "13",
}

@Article{Karagiannidis:2007:IAG,
  author =       "George Karagiannidis and Athanasios Lioumpas",
  title =        "An Improved Approximation for the {Gaussian}
                 {$Q$}-Function",
  journal =      j-IEEE-COMMUN-LET,
  volume =       "11",
  number =       "8",
  pages =        "644--646",
  month =        aug,
  year =         "2007",
  CODEN =        "ICLEF6",
  DOI =          "https://doi.org/10.1109/lcomm.2007.070470",
  ISSN =         "1089-7798 (print), 1558-2558 (electronic)",
  ISSN-L =       "1089-7798",
  bibdate =      "Sat Dec 16 16:49:58 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See corrections and comments \cite{Dyer:2008:CCI}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Communications Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}

@Book{King:2007:DNC,
  author =       "Louis Vessot King",
  title =        "On the Direct Numerical Calculation of Elliptic
                 Functions and Integrals",
  publisher =    "Mellon Press",
  address =      "",
  pages =        "56",
  year =         "2007",
  ISBN =         "1-4067-4226-0",
  ISBN-13 =      "978-1-4067-4226-8",
  LCCN =         "",
  bibdate =      "Wed Feb 03 08:53:04 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  remark =       "The AGM method for Jacobian elliptic was discovered by
                 this book's author at McGill University in 1913, first
                 published in \cite{King:1921:SNF}, and then in a 1924
                 monograph, of which this is a reprint.",
}

@Article{Kodama:2007:RA,
  author =       "Masao Kodama",
  title =        "Remark on {Algorithm 644}",
  journal =      j-TOMS,
  volume =       "33",
  number =       "4",
  pages =        "28:1--28:3",
  month =        aug,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1268776.1268783",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Dec 17 18:09:13 MST 2007",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Amos:1986:APP,Amos:1990:RPP,Amos:1995:RAP}.",
  abstract =     "This remark details correction for errors in the
                 functions which compute the modified Bessel function of
                 the second kind and the log of the gamma function. In
                 both cases these errors cause a loss of precision for a
                 small range of values of the $ \nu $ argument. These
                 routines are used in the calculation of a number of
                 other functions within the package whose accuracy is
                 thus similarly affected.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kuijlaars:2007:TIH,
  author =       "A. B. J. Kuijlaars and H. Stahl and W. {Van Assche}
                 and F. Wielonsky",
  title =        "{Type II} {Hermite--Pad{\'e}} approximation to the
                 exponential function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "207",
  number =       "2",
  pages =        "227--244",
  day =          "15",
  month =        oct,
  year =         "2007",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:13:18 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042706005978",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Kuliamin:2007:STI,
  author =       "V. V. Kuliamin",
  title =        "Standardization and testing of implementations of
                 mathematical functions in floating point numbers",
  journal =      j-PROG-COMP-SOFT,
  volume =       "33",
  number =       "3",
  pages =        "154--173",
  year =         "2007",
  CODEN =        "PCSODA",
  DOI =          "https://doi.org/10.1134/S036176880703005X",
  ISSN =         "0361-7688 (print), 1608-3261 (electronic)",
  ISSN-L =       "0361-7688",
  bibdate =      "Fri Aug 08 09:01:30 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Requirements definition and test suites development
                 for implementations of mathematical functions in
                 floating point arithmetic in the framework of the IEEE
                 754 standard are considered. A method based on this
                 standard is proposed for defining requirements for such
                 functions. This method can be used for the
                 standardization of implementations of such functions;
                 this kind of standardization extends IEEE 754. A method
                 for designing test suites for the verification of those
                 requirements is presented. The proposed methods are
                 based on specific properties of the representation of
                 floating point numbers and on some features of the
                 functions under examination.",
  acknowledgement = ack-nhfb,
  fjournal =     "Programming and Computer Software; translation of
                 Programmirovaniye (Moscow, USSR) Plenum",
  journal-URL =  "http://link.springer.com/journal/11086",
  keywords =     "floating-point function testing and verification",
}

@TechReport{Lefevre:2007:SNP,
  author =       "Vincent Lef{\'e}vre and Jean-Michel Muller",
  title =        "Some notes on the possible under\slash overflow of the
                 most common elementary functions",
  type =         "Report",
  institution =  "LIP, {\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "Lyon, France",
  pages =        "7",
  year =         "2007",
  bibdate =      "Fri May 25 16:18:32 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://prunel.ccsd.cnrs.fr/ensl-00149414",
  abstract =     "The purpose of this short note is not to describe when
                 underflow or overflow must be signalled (it is quite
                 clear that the rules are the same as for the basic
                 arithmetic operations). We just want to show that for
                 some of the most common functions and floating-point
                 formats, in many cases, we can know in advance that the
                 results will always lie in the range of the numbers
                 that are representable by normal floating-point
                 numbers, so that in these cases there is no need to
                 worry about underflow or overflow. Note that when it is
                 not the case, an implementation is still possible using
                 a run-time test.",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions; floating-point arithmetic;
                 overflow; underflow",
}

@Article{Neher:2007:CSF,
  author =       "Markus Neher",
  title =        "Complex standard functions and their implementation in
                 the {CoStLy} library",
  journal =      j-TOMS,
  volume =       "33",
  number =       "1",
  pages =        "2:1--2:27",
  month =        mar,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1206040.1206042",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:58 MDT 2007",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The practical calculation of range bounds for some
                 complex standard functions is addressed in this
                 article. The functions under consideration are root and
                 power functions, the exponential, trigonometric and
                 hyperbolic functions, and their inverse functions. For
                 such a function $f$ and a given rectangular complex
                 interval $z$, some interval $w$ is computed that
                 contains all function values of $f$ in $z$. This is
                 done by expressing the real and the imaginary part of
                 $f$ as compositions of real standard functions and then
                 estimating the ranges of these compositions. In many
                 cases, the inclusions are optimal, such that $w$ is the
                 smallest rectangular interval containing the range of
                 $f$.

                 The algorithms presented in this article have been
                 implemented in a C++ class library called CoStLy
                 (Complex Standard Functions License), which is
                 distributed under the conditions of the GNU General
                 Public License.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Book{Press:2007:NRA,
  author =       "William H. Press and Saul A. Teukolsky and William T.
                 Vetterling and Brian P. Flannery",
  title =        "Numerical Recipes --- The Art of Scientific
                 Computing",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Third",
  pages =        "xxi + 1235",
  year =         "2007",
  ISBN =         "0-521-88068-8 (hardcover), 0-521-88407-1 (with source
                 code CD ROM), 0-521-70685-8 (source code CD ROM)",
  ISBN-13 =      "978-0-521-88068-8 (hardcover), 978-0-521-88407-5 (with
                 source code CD ROM), 978-0-521-70685-8 (source code CD
                 ROM)",
  LCCN =         "QA297 .N866 2007",
  bibdate =      "Wed Dec 15 10:40:52 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2000.bib",
  URL =          "http://www.cambridge.org/numericalrecipes",
  acknowledgement = ack-nhfb,
  subject =      "numerical analysis; computer programs; science;
                 mathematics; C++ (computer program language)",
  tableofcontents = "1. Preliminaries \\
                 2. Solution of linear algebraic equations \\
                 3. Interpolation and extrapolation \\
                 4. Integration of functions \\
                 5. Evaluation of functions \\
                 6. Special functions \\
                 7. Random numbers \\
                 8. Sorting and selection \\
                 9. Root finding and nonlinear sets of equations \\
                 10. Minimization or maximization of functions \\
                 11. Eigensystems \\
                 12. Fast Fourier Transform \\
                 13. Fourier and spectral applications \\
                 14. Statistical description of data \\
                 15. Modeling of data \\
                 16. Classification and inference \\
                 17. Integration of ordinary differential equations \\
                 18. Two-point boundary value problems \\
                 19. Integral equations and inverse theory \\
                 20. Partial differential equations \\
                 21. Computational geometry \\
                 22. Less-numerical algorithms",
}

@Article{Ren:2007:CFA,
  author =       "C. Ren and A. R. MacKenzie",
  title =        "Closed-form approximations to the error and
                 complementary error functions and their applications in
                 atmospheric science",
  journal =      j-ATMOS-SCI-LETT,
  volume =       "8",
  number =       "3",
  pages =        "70--73",
  month =        "????",
  year =         "2007",
  DOI =          "https://doi.org/10.1002/asl.154",
  ISSN =         "1530-261X",
  ISSN-L =       "1530-261X",
  bibdate =      "Sat Dec 16 17:25:42 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/asl.154/full",
  acknowledgement = ack-nhfb,
  fjournal =     "Atmospheric Science Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/1530261X;
                 http://rmets.onlinelibrary.wiley.com/hub/journal/10.1002/(ISSN)1530-261X/",
}

@Article{Rokhlin:2007:AFC,
  author =       "Vladimir Rokhlin and Hong Xiao",
  title =        "Approximate formulae for certain prolate spheroidal
                 wave functions valid for large values of both order and
                 band-limit",
  journal =      j-APPL-COMPUT-HARMON-ANAL,
  volume =       "22",
  number =       "1",
  pages =        "105--123",
  month =        jan,
  year =         "2007",
  DOI =          "https://doi.org/10.1016/j.acha.2006.05.004",
  ISSN =         "1063-5203 (print), 1096-603x (electronic)",
  ISSN-L =       "1063-5203",
  bibdate =      "Sun Oct 31 10:00:51 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "We construct asymptotic formulae for the approximation
                 of certain prolate spheroidal wave functions and of the
                 corresponding eigenvalues. We investigate two regimes:
                 when the ratio $ c / m $ decays, and when both $c$ and
                 $m$ grow, but the ratio $ c / m $ stays bounded. Both
                 the regions of validity and the accuracies of the
                 obtained expansions are illustrated with numerical
                 examples.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied and Computational Harmonic Analysis.
                 Time-Frequency and Time-Scale Analysis, Wavelets,
                 Numerical Algorithms, and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/10635203",
  keywords =     "approximation; asymptotic; band-limit; prolate
                 spheroidal wave functions",
}

@Article{Schmelzer:2007:CGF,
  author =       "Thomas Schmelzer and Lloyd N. Trefethen",
  title =        "Computing the Gamma Function Using Contour Integrals
                 and Rational Approximations",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "45",
  number =       "2",
  pages =        "558--571",
  month =        "????",
  year =         "2007",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/050646342",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  bibdate =      "Mon Nov 24 18:03:07 MST 2008",
  bibsource =    "http://siamdl.aip.org/dbt/dbt.jsp?KEY=SJNAAM&Volume=45&Issue=2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}

@Book{Slavjanov:2007:SFU,
  author =       "Sergej J. Slavjanov and Wolfgang Lay",
  title =        "Special Functions: a Unified Theory Based on
                 Singularities",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xvi + 293",
  year =         "2007",
  ISBN =         "0-19-850573-6",
  ISBN-13 =      "978-0-19-850573-0",
  LCCN =         "????",
  bibdate =      "Tue Dec 5 11:27:46 MST 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Oxford mathematical monographs; Oxford science
                 publications",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "1: Linear second-order ODEs with polynomial
                 coefficients \\
                 2: The hypergeometric class of equations \\
                 3: The Heun class of equations \\
                 4: Application to physical sciences \\
                 5: The Painlev{\'e} class of equations \\
                 Appendix A: The gamma function and related functions
                 \\
                 Appendix B: CTCPs Heun equations in general form \\
                 Appendix C: Multipole Matrix elements \\
                 Appendix D: SFTools \\
                 Database of the special functions",
  subject =      "Functions, Special; Fonctions sp{\'e}ciales;
                 Functions, Special",
  tableofcontents = "1: Linear second-order ODEs with polynomial
                 coefficients \\
                 Regular singularities and Fuchsian equations \\
                 Regular and Fuchsian singularities \\
                 Fuchsian equations and their transformations \\
                 Characteristic exponents \\
                 Frobenius solutions \\
                 Irregular singularities and confluent equations \\
                 The $s$-rank of a singularity \\
                 Confluent and reduced confluent equations \\
                 The $s$-homotopic transformation \\
                 Asymptotic solutions at irregular singularities \\
                 Canonical forms \\
                 A generalization of Fuchs's theorem \\
                 Confluence and reduction processes \\
                 Strong and weak confluence. A confluence theorem \\
                 A confluence principle \\
                 Reduction of an equation \\
                 Classes and types of equations \\
                 Standard forms of equations \\
                 Invariants of $s$-homotopic transformations \\
                 Types of solutions \\
                 Eigenfunctions of singular Sturm--Liouville problems
                 \\
                 Central and lateral connection problems \\
                 Stokes lines at singularities. Stokes matrices \\
                 Generalized Riemann scheme \\
                 Applications \\
                 Central two-point connection problems (CTCPs) \\
                 Two regular singularities as relevant endpoints \\
                 One regular singularity and one irregular singularity
                 as the endpoints \\
                 A proof \\
                 Two irregular singularities \\
                 2: The hypergeometric class of equations \\
                 Classification scheme \\
                 General presentation \\
                 Hypergeometric equation \\
                 Confluent equations \\
                 Reduced confluent equations \\
                 Difference equations \\
                 General consideration \\
                 Difference equations for hypergeometric functions \\
                 Confluent hypergeometric functions \\
                 \ldots{}",
}

@Article{Srinivasan:2007:GFE,
  author =       "Gopala Krishna Srinivasan",
  title =        "The Gamma Function: An Eclectic Tour",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "114",
  number =       "4",
  pages =        "297--315",
  month =        apr,
  year =         "2007",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jan 30 12:00:28 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00029890.html;
                 http://www.jstor.org/stable/i27642189;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/27642193",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Temme:2007:NAS,
  author =       "Nico M. Temme",
  title =        "Numerical aspects of special functions",
  journal =      j-ACTA-NUMERICA,
  volume =       "16",
  pages =        "379--478",
  year =         "2007",
  CODEN =        "ANUMFU",
  DOI =          "https://doi.org/10.1017/S0962492906330012",
  ISBN =         "0-521-87743-1",
  ISBN-13 =      "978-0-521-87743-5",
  ISSN =         "0962-4929 (print), 1474-0508 (electronic)",
  ISSN-L =       "0962-4929",
  MRclass =      "33F05 (65D20)",
  MRnumber =     "2417932 (2009g:33027)",
  MRreviewer =   "Amparo Gil",
  bibdate =      "Sat Sep 24 11:37:18 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/actanumerica.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This paper describes methods that are important for
                 the numerical evaluation of certain functions that
                 frequently occur in applied mathematics, physics and
                 mathematical statistics. This includes what we consider
                 to be the basic methods, such as recurrence relations,
                 series expansions (both convergent and asymptotic), and
                 numerical quadrature. Several other methods are
                 available and some of these will be discussed in less
                 detail. Examples will be given on the use of special
                 functions in certain problems from mathematical physics
                 and mathematical statistics (integrals and series with
                 special functions).",
  acknowledgement = ack-nhfb,
  ajournal =     "Acta Numer.",
  fjournal =     "Acta Numerica",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANU",
  onlinedate =   "24 April 2007",
}

@InCollection{Weniger:2007:AAT,
  author =       "Ernst Joachim Weniger",
  title =        "Asymptotic approximations to truncation errors of
                 series representations for special functions",
  crossref =     "Iske:2007:AAP",
  pages =        "331--348",
  year =         "2007",
  MRclass =      "33F05",
  MRnumber =     "MR2335174 (2008h:33051)",
  bibdate =      "Thu Dec 01 09:38:02 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Bernoulli numbers; Euler--MacLaurin formula;
                 exponential integer $E_1(z)$; Gaussian hypergeometric
                 series $_2F_1(a / b / c / z)$; Riemann zeta function",
  remark =       "Available as math.CA/0511074.",
}

@Book{Agarwal:2008:OPD,
  author =       "Ravi P. Agarwal and Donal O'Regan",
  title =        "Ordinary and partial differential equations: with
                 special functions, {Fourier} series, and boundary value
                 problems",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xiv + 410",
  year =         "2008",
  ISBN =         "0-387-79145-0 (paperback)",
  ISBN-13 =      "978-0-387-79145-6 (paperback)",
  LCCN =         "????",
  bibdate =      "Sat Oct 30 17:22:04 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  series =       "Universitext",
  acknowledgement = ack-nhfb,
  subject =      "differential equations; differential equations,
                 partial; Fourier analysis; boundary value problems",
}

@Article{Alzer:2008:GFI,
  author =       "Horst Alzer",
  title =        "Gamma function inequalities",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "49",
  number =       "1--4",
  pages =        "53--84",
  month =        dec,
  year =         "2008",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon May 17 14:08:26 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=49&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=49&issue=1&spage=53",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Ancarani:2008:DOC,
  author =       "L. U. Ancarani and G. Gasaneo",
  title =        "Derivatives of any order of the confluent
                 hypergeometric function {$_1 F_1 (a, b, z)$} with
                 respect to the parameter $a$ or $b$",
  journal =      j-J-MATH-PHYS,
  volume =       "49",
  number =       "6",
  pages =        "063508",
  month =        jun,
  year =         "2008",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.2939395",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Wed Oct 26 09:06:03 MDT 2011",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2005.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v49/i6/p063508_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  onlinedate =   "20 June 2008",
  pagecount =    "16",
}

@Article{Borwein:2008:EBF,
  author =       "David Borwein and Jonathan M. Borwein and O-Yeat
                 Chan",
  title =        "The evaluation of {Bessel} functions via exp--arc
                 integrals",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "341",
  number =       "1",
  pages =        "478--500",
  month =        may,
  year =         "2008",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1016/j.jmaa.2007.10.003",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "33C10 (33F05 65D20)",
  MRnumber =     "2394100",
  MRreviewer =   "Richard B. Paris",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://adsabs.harvard.edu/abs/2008JMAA..341..478B;
                 http://docserver.carma.newcastle.edu.au/1231/;
                 http://www.sciencedirect.com/science/article/pii/S0022247X07012346",
  abstract =     "A standard method for computing values of Bessel
                 functions has been to use the well-known ascending
                 series for small argument, and to use an asymptotic
                 series for large argument; with the choice of the
                 series changing at some appropriate argument magnitude,
                 depending on the number of digits required. In a recent
                 paper, D. Borwein, J. Borwein, and R. Crandall [D.
                 Borwein, J. M. Borwein, R. Crandall, Effective Laguerre
                 asymptotics, preprint at
                 http://locutus.cs.dal.ca:8088/archive/00000334/]
                 derived a series for an ``exp-arc'' integral which gave
                 rise to an absolutely convergent series for the J and I
                 Bessel functions with integral order. Such series can
                 be rapidly evaluated via recursion and elementary
                 operations, and provide a viable alternative to the
                 conventional ascending-asymptotic switching. In the
                 present work, we extend the method to deal with Bessel
                 functions of general (non-integral) order, as well as
                 to deal with the Y and K Bessel functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "Bessel function; Exponential-hyperbolic expansions;
                 Uniform series expansion",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}

@Article{Borwein:2008:ELA,
  author =       "David Borwein and Jonathan M. Borwein and Richard E.
                 Crandall",
  title =        "Effective {Laguerre} asymptotics",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "46",
  number =       "6",
  pages =        "3285--3312",
  year =         "2008",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/07068031X",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "33C65 (30E20 34E05)",
  MRnumber =     "2448665",
  MRreviewer =   "Yu-Qiu Zhao",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/334/",
  abstract =     "It is known that the generalized Laguerre polynomials
                 can enjoy subexponential growth for large primary
                 index. In particular, for certain fixed parameter pairs
                 (a, z) one has the large-n asymptotic behavior
                 L-n((-a)) (-z) similar to C(a, z)(n)(-a)/2-1/ (4)e(2)
                 root nz. We introduce a computationally motivated
                 contour integral that allows efficient numerical
                 Laguerre evaluations yet also leads to the complete
                 asymptotic series over the full parameter domain of
                 subexponential behavior. We present a fast algorithm
                 for symbolic generation of the rather formidable
                 expansion coefficients. Along the way we address the
                 difficult problem of establishing effective (i. e.,
                 rigorous and explicit) error bounds on the general
                 expansion. A primary tool for these developments is an
                 ``exp-arc'' method giving a natural bridge between
                 converging series and effective asymptotics.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Borwein, Jonathan/A-6082-2009",
  unique-id =    "Borwein:2008:ELA",
}

@InProceedings{Brisebarre:2008:EME,
  author =       "Nicolas Brisebarre and Sylvain Chevillard and
                 Milo{\v{s}} D. Ercegovac and Jean-Michel Muller and
                 Serge Torres",
  title =        "An Efficient Method for Evaluating Polynomial and
                 Rational Function Approximations",
  crossref =     "IEEE:2008:ICA",
  pages =        "233--238",
  year =         "2008",
  DOI =          "https://doi.org/10.1109/ASAP.2008.4580185",
  bibdate =      "Mon Feb 10 07:28:25 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Chatterjee:2008:CNT,
  author =       "S. Chatterjee and D. Roy",
  title =        "A class of new transforms tailored for the
                 hypergeometric series",
  journal =      j-COMP-PHYS-COMM,
  volume =       "179",
  number =       "8",
  pages =        "555--561",
  day =          "15",
  month =        oct,
  year =         "2008",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2008.05.001",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Dec 01 09:09:57 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  xxauthor =     "S. Charterjee and D. Roy",
}

@Book{Cuyt:2008:HCF,
  author =       "Annie Cuyt and Vigdis B. Petersen and Brigitte Verdonk
                 and Haakon Waadeland and William B. Jones",
  title =        "Handbook of Continued Fractions for Special
                 Functions",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xx + 440",
  year =         "2008",
  DOI =          "https://doi.org/10.1007/978-1-4020-6949-9",
  ISBN =         "1-4020-6948-0",
  ISBN-13 =      "978-1-4020-6948-2",
  LCCN =         "QA295 .H275 2008",
  bibdate =      "Tue Jun 24 07:17:37 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  keywords =     "applying the limit process; associated continued
                 fraction; asymptotic series expansion; basic
                 hypergeometric functions; canonical contraction;
                 combination with property; complementary incomplete
                 gamma function; complex error function; confluent
                 hypergeometric series; continued fraction converges;
                 continued fraction representations; fraction
                 approximants; modified approximant; monic orthogonal
                 polynomial sequence; normed field; nth approximant; nth
                 denominator; nth numerator; nth tail; oval sequence
                 theorem; parabola theorem; partial numerators; strong
                 moment distribution function; successive approximants;
                 truncation error bounds",
  shorttableofcontents = "General considerations \\
                 Part 1, Basic Theory \\
                 1. Basics \\
                 2. Continued fraction representation of functions \\
                 3. Convergence criteria \\
                 4. Pade approximants \\
                 5. Moment theory and orthogonal functions \\
                 Part 2, Numerics \\
                 6. Continued fraction construction \\
                 7. Truncation error bounds \\
                 8. Continued fraction evaluation \\
                 Part 3, Special Functions \\
                 9. On tables and graphs \\
                 10. Mathematical constants \\
                 11. Elementary functions \\
                 12. Gamma function and related functions \\
                 13. Error function and related integrals \\
                 14. Exponential integrals and related functions \\
                 15. Hypergeometric functions \\
                 16. Confluent hypergeometric functions, \\
                 17. Bessel functions \\
                 18. Probability functions \\
                 19. Basic hypergeometric functions",
  tableofcontents = "Preface / xi \\
                 Notation / xiii \\
                 0 General considerations \\
                 / 1 \\
                 0.1 Part one / 1 \\
                 0.2 Part two / 2 \\
                 0.3 Part three / 2 \\
                 \\
                 Part I: Basic Theory \\
                 \\
                 1 Basics / 9 \\
                 1.1 Symbols and notation \\
                 1.2 Definitions / 10 \\
                 1.3 Recurrence relations / 13 \\
                 1.4 Equivalence transformations / 15 \\
                 1.5 Contractions and extensions / 16 \\
                 1.6 Continued fractions with prescribed approximants /
                 18 \\
                 1.7 Connection between continued fractions and series /
                 19 \\
                 1.8 Periodic and limit periodic continued fractions /
                 21 \\
                 1.9 Tails of continued fractions / 23 \\
                 1.10 Continued fractions over normed fields / 26 \\
                 1.11 Generalisations of continued fractions / 28 \\
                 \\
                 2 Continued fraction representation of functions / 29
                 \\
                 2.1 Symbols and notation / 29 \\
                 2.2 Correspondence / 30 \\
                 2.3 Families of continued fractions / 35 \\
                 2.4 Correspondence of C-fractions / 39 \\
                 2.5 Correspondence of P-fractions / 40 \\
                 2.6 Correspondence of J-fractions and T-fractions / 41
                 \\
                 2.7 Correspondence and three-term recurrences / 42 \\
                 \\
                 3 Convergence criteria / 45 \\
                 3.1 Some classical theorems / 45 \\
                 3.2 Convergence sets and value sets / 47 \\
                 3.3 Parabola and oval theorems / 49 \\
                 3.4 Correspondence and uniform convergence / 52 \\
                 3.5 Periodic and limit periodic continued fractions /
                 53 \\
                 3.6 Convergence and minimal solutions / 56 \\
                 \\
                 4 Pad{\'e} approximants / 59 \\
                 4.1 Definition and notation / 59 \\
                 4.2 Fundamental properties / 60 \\
                 4.3 Connection with regular C-fractions / 64 \\
                 4.4 Connection with P-fractions / 65 \\
                 4.5 Extension of the Pad{\'e} table / 67 \\
                 4.6 Connection with M-fractions and the M-table / 68
                 \\
                 4.7 Convergence of Pad{\'e} approximants / 70 \\
                 4.8 Formal orthogonality property / 72 \\
                 \\
                 5 Moment theory and orthogonal functions / 77 \\
                 5.1 Moment theory / 77 \\
                 5.2 Stieltjes transforms / 85 \\
                 5.3 Construction of solutions / 90 \\
                 5.4 Orthogonal polynomials / 91 \\
                 5.5 Monic orthogonal polynomials on $\mathbb{R}$ and
                 J-fractions / 92 \\
                 5.6 Szeg{\H{o}} polynomials and PPC-fractions / 100 \\
                 5.7 Orthogonal Laurent polynomials and APT-fractions /
                 102 \\
                 \\
                 Part II: Numerics \\
                 \\
                 6 Continued fraction construction / 107 \\
                 6.1 Regular C-fractions / 107 \\
                 6.2 C-fractions / 113 \\
                 6.3 S-fractions / 114 \\
                 6.4 P-fractions / 114 \\
                 6.5 J-fractions / 120 \\
                 6.6 M-fractions / 122 \\
                 6.7 Positive T-fractions / 124 \\
                 6.8 Thiele fractions / 125 \\
                 \\
                 7 Truncation error bounds / 129 \\
                 7.1 Parabola theorems / 129 \\
                 7.2 The oval sequence theorem / 131 \\
                 7.3 The interval sequence theorem / 136 \\
                 7.4 Specific a priori bounds for S-fractions / 138 \\
                 7.5 A posteriori truncation error bounds / 140 \\
                 7.6 Tails and truncation error bounds / 143 \\
                 7.7 Choice of modification / 143 \\
                 \\
                 8 Continued fraction evaluation / 149 \\
                 8.1 The effect of finite precision arithmetic / 149 \\
                 8.2 Evaluation of approximants / 152 \\
                 8.3 The forward recurrence and minimal solutions / 154
                 \\
                 8.4 Round-off error in the backward recurrence / 156
                 \\
                 \\
                 Part III: Special Functions \\
                 \\
                 9 On tables and graphs / 163 \\
                 9.1 Introduction / 163 \\
                 9.2 Comparative tables / 163 \\
                 9.3 Reliable graphs / 168 \\
                 \\
                 10 Mathematical constants / 175 \\
                 10.1 Regular continued fractions / 175 \\
                 10.2 Archimedes' constant, symbol $\pi$ / 176 \\
                 10.3 Euler's number, base of the natural logarithm /
                 178 \\
                 10.4 Integer powers and roots of $\pi$ and $e$ / 180
                 \\
                 10.5 The natural logarithm, $\ln(2)$ / 181 \\
                 10.6 Pythagoras' constant, the square root of two / 183
                 \\
                 10.7 The cube root of two / 183 \\
                 10.8 Euler's constant, symbol $\gamma$ / 185 \\
                 10.9 Golden ratio, symbol $\phi$ / 185 \\
                 10.10 The rabbit constant, symbol $\rho$ / 186 \\
                 10.11 Ap{\'e}ry's constant, $\zeta(3)$ / 188 \\
                 10.12 Catalan's constant, symbol $C$ / 189 \\
                 10.13 Gompertz' constant, symbol $G$ / 190 \\
                 10.14 Khinchin's constant, symbol $K$ / 190 \\
                 \\
                 11 Elementary functions / 193 \\
                 11.1 The exponential function / 193 \\
                 11.2 The natural logarithm / 196 \\
                 11.3 Trigonometric functions / 200 \\
                 11.4 Inverse trigonometric functions / 204 \\
                 11.5 Hyperbolic functions / 210 \\
                 11.6 Inverse hyperbolic functions / 213 \\
                 11.7 The power function / 217 \\
                 \\
                 12 Gamma function and related functions / 221 \\
                 12.1 Gamma function / 221 \\
                 12.2 Binet function / 224 \\
                 12.3 Polygamma functions / 229 \\
                 12.4 Trigamma function / 232 \\
                 12.5 Tetragamma function / 235 \\
                 12.6 Incomplete gamma functions / 238 \\
                 \\
                 13 Error function and related integrals / 253 \\
                 13.1 Error function and Dawson's integral / 253 \\
                 13.2 Complementary and complex error function / 261 \\
                 13.3 Repeated integrals / 268 \\
                 13.4 Fresnel integrals / 269 \\
                 \\
                 14 Exponential integrals and related functions / 275
                 \\
                 14.7 Exponential integrals / 275 \\
                 14.2 Related functions / 285 \\
                 \\
                 15 Hypergeometric functions / 291 \\
                 15.1 Definition and basic properties / 291 \\
                 15.2 Stieltjes transform / 295 \\
                 15.3 Continued fraction representations / 295 \\
                 15.4 Pad{\'e} approximants / 309 \\
                 15.5 Monotonicity properties / 313 \\
                 15.6 Hypergeometric series $_pF_q$ / 315 \\
                 \\
                 16 Confluent hypergeometric functions / 319 \\
                 16.1 Kummer functions / 319 \\
                 16.2 Confluent hypergeometric series $_2F_0$ / 330 \\
                 16.3 Confluent hypergeometric limit function / 333 \\
                 16.4 Whittaker functions / 334 \\
                 16.5 Parabolic cylinder functions / 337 \\
                 \\
                 17 Bessel functions / 334 \\
                 17.7 Bessel functions / 334 \\
                 17.2 Modified Bessel functions / 356 \\
                 \\
                 18 Probability functions / 371 \\
                 18.1 Definitions and elementary properties / 371 \\
                 18.2 Normal and log-normal distributions / 373 \\
                 18.3 Repeated integrals / 377 \\
                 18.4 Gamma and chi-square distribution / 378 \\
                 18.5 Beta, $F$- and Student's $t$-distributions / 382
                 \\
                 \\
                 19 Basic hypergeometric functions / 391 \\
                 19.1 Definition and basic properties / 391 \\
                 19.2 Continued fraction representations / 395 \\
                 19.3 Higher order basic hypergeometric functions / 399
                 \\
                 \\
                 Bibliography / 401 \\
                 \\
                 Index / 421",
}

@Article{Dyer:2008:CCI,
  author =       "J. S. Dyer and S. A. Dyer",
  title =        "Corrections to, and comments on, {``An improved
                 approximation for the Gaussian $Q$-Function''}",
  journal =      j-IEEE-COMMUN-LET,
  volume =       "12",
  number =       "4",
  pages =        "231--231",
  month =        apr,
  year =         "2008",
  CODEN =        "ICLEF6",
  DOI =          "https://doi.org/10.1109/lcomm.2008.080009",
  ISSN =         "1089-7798 (print), 1558-2558 (electronic)",
  ISSN-L =       "1089-7798",
  bibdate =      "Sat Dec 16 18:08:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Karagiannidis:2007:IAG}.",
  URL =          "http://ieeexplore.ieee.org/document/4489650/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Communications Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}

@Article{Elbert:2008:ZCE,
  author =       "{\'A}rp{\'a}d Elbert and Andrea Laforgia",
  title =        "The zeros of the complementary error function",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "49",
  number =       "1--4",
  pages =        "153--157",
  month =        dec,
  year =         "2008",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon May 17 14:08:26 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=49&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=49&issue=1&spage=153",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Gabutti:2008:EQG,
  author =       "Bruno Gabutti and Giampietro Allasia",
  title =        "Evaluation of $q$-gamma function and $q$-analogues by
                 iterative algorithms",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "49",
  number =       "1--4",
  pages =        "159--168",
  month =        dec,
  year =         "2008",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon May 17 15:07:19 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=49&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=49&issue=1&spage=159",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Gautschi:2008:LGW,
  author =       "Walter Gautschi and Carla Giordano",
  title =        "{Luigi Gatteschi}'s work on asymptotics of special
                 functions and their zeros",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "49",
  number =       "1--4",
  pages =        "11--31",
  month =        dec,
  year =         "2008",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon May 17 14:08:26 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=49&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=49&issue=1&spage=11",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Harris:2008:IBG,
  author =       "Frank E. Harris",
  title =        "Incomplete {Bessel}, generalized incomplete gamma, or
                 leaky aquifer functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "215",
  number =       "1",
  pages =        "260--269",
  year =         "2008",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/j.cam.2007.04.008",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "33B10 (33C10 41A58); 33B20",
  MRnumber =     "2400632 (2009d:33003)",
  MRreviewer =   "Necdet Batir",
  bibdate =      "Wed Dec 4 07:03:09 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042707002014",
  ZMnumber =     "Zbl 1135.33002",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Isukapalli:2008:ATA,
  author =       "Yogananda Isukapalli and Bhaskar D. Rao",
  title =        "An Analytically Tractable Approximation for the
                 {Gaussian} {$Q$}-Function",
  journal =      j-IEEE-COMMUN-LET,
  volume =       "12",
  number =       "9",
  pages =        "669--671",
  month =        sep,
  year =         "2008",
  CODEN =        "ICLEF6",
  DOI =          "https://doi.org/10.1109/lcomm.2008.080815",
  ISSN =         "1089-7798 (print), 1558-2558 (electronic)",
  ISSN-L =       "1089-7798",
  bibdate =      "Sat Dec 16 16:44:42 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Communications Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}

@Article{Kiani:2008:AND,
  author =       "M. Kiani and J. Panaretos and S. Psarakis and M.
                 Saleem",
  title =        "Approximations to the normal distribution function and
                 an extended table for the mean range of the normal
                 variables",
  journal =      "J. Iran. Stat. Soc.",
  volume =       "7",
  number =       "1",
  pages =        "57--72",
  month =        "????",
  year =         "2008",
  DOI =          "",
  bibdate =      "Sat Dec 16 16:56:03 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
}

@Article{Kodama:2008:ASP,
  author =       "Masao Kodama",
  title =        "{Algorithm 877}: a Subroutine Package for Cylindrical
                 Functions of Complex Order and Nonnegative Argument",
  journal =      j-TOMS,
  volume =       "34",
  number =       "4",
  pages =        "22:1--22:21",
  month =        jul,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377596.1377602",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 16 11:30:01 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The algorithm presented provides a package of
                 subroutines for calculating the cylindrical functions $
                 J_\nu (x) $, $ N_\nu (x) $, $ H_\nu^1 (x) $, $ H_\nu^2
                 (x) $ where the order $ \nu $ is complex and the real
                 argument $x$ is nonnegative. The algorithm is written
                 in Fortran 95 and calculates the functions using
                 single, double, or quadruple precision according to the
                 value of a parameter defined in the algorithm. The
                 methods of calculating the functions are based on a
                 series expansion, Debye's asymptotic expansions,
                 Olver's asymptotic expansions, and recurrence methods
                 (Miller's algorithms). The relative errors of the
                 functional values computed by this algorithm using
                 double precision are less than $ 2.4 \times 10^{-13} $
                 in the region $ 0 \leq \mbox {Re}(\nu) \leq 64 $, $ 0
                 \leq \mbox {Im}(\nu) \leq 63 $, $ 0.024 \leq x \leq 97
                 $.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Bessel functions; complex order; Cylindrical
                 functions; Debye's asymptotic expansions; Hankel
                 functions; Miller's algorithms; Neumann functions;
                 nonnegative argument; numerical calculation; Olver's
                 asymptotic expansions",
}

@Article{Lefevre:2008:WCE,
  author =       "Vincent Lef{\`e}vre and Damien Stehl{\'e} and Paul
                 Zimmermann",
  title =        "Worst Cases for the Exponential Function in the {IEEE
                 754r decimal64} Format",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "5045",
  pages =        "114--126",
  year =         "2008",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-540-85521-7_7",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Thu Oct 1 11:29:36 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2008a.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-540-85521-7_7.pdf",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-540-85521-7",
  book-URL =     "http://www.springerlink.com/content/978-3-540-85521-7",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  remark =       "From the abstract: ``the worst case for $ |x| \geq 3
                 \times 10^{-11} $ is exp(9.407822313572878e-2) =
                 1.09864568206633850000000000000000278.''",
}

@Article{Lorch:2008:MSR,
  author =       "Lee Lorch and Martin E. Muldoon",
  title =        "Monotonic sequences related to zeros of {Bessel}
                 functions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "49",
  number =       "1--4",
  pages =        "221--233",
  month =        dec,
  year =         "2008",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon May 17 15:07:19 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=49&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=49&issue=1&spage=221",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Book{Mathai:2008:SFA,
  author =       "A. M. Mathai and H. J. Haubold",
  title =        "Special functions for applied scientists",
  publisher =    "Springer Science+Business Media",
  address =      "New York, NY, USA",
  pages =        "xxv + 464",
  year =         "2008",
  ISBN =         "0-387-75893-3",
  ISBN-13 =      "978-0-387-75893-0",
  LCCN =         "QA351 .M37X 2008",
  bibdate =      "Sat Oct 30 17:02:02 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Fractional calculus; Wavelets
                 (Mathematics)",
}

@Article{Nam:2008:PAE,
  author =       "Byeong-Gyu Nam and Hyejung Kim and Hoi-Jun Yoo",
  title =        "Power and Area-Efficient Unified Computation of Vector
                 and Elementary Functions for Handheld {$3$D} Graphics
                 Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "57",
  number =       "4",
  pages =        "490--504",
  month =        apr,
  year =         "2008",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.12",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 12:17:40 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4432232",
  abstract =     "A unified computation method of vector and elementary
                 functions is proposed for handheld 3D graphics systems.
                 It unifies vector operations like vector multiply,
                 multiply-and-add, divide, divide-by-square-root, and
                 dot product and elementary functions like
                 trigonometric, inverse trigonometric, hyperbolic,
                 inverse hyperbolic, power ($ x^y $ with two variables),
                 and logarithm to an arbitrary base into a single
                 four-way arithmetic platform. A number system called
                 the fixed-point hybrid number system (FXP-HNS), which
                 combines the fixed-point number system (FXP) and the
                 logarithmic number system (LNS), is proposed for the
                 power and area-efficient unification. Power and
                 area-efficient logarithmic and antilogarithmic
                 conversion schemes are also proposed for the data
                 conversions between fixed-point and logarithmic numbers
                 in the FXP-HNS and achieve 0.41 percent and 0.08
                 percent maximum conversion errors, respectively. The
                 unified arithmetic unit based on the proposed schemes
                 is presented with less than 6.3 percent operation
                 error. Its fully pipelined architecture achieves
                 single-cycle throughput with maximum four-cycle latency
                 for all of the supported operations. Comparison results
                 show that the proposed arithmetic unit achieves 30
                 percent power and 10.9 percent area reductions and runs
                 two times faster than the previous approach.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Paszkowski:2008:CAO,
  author =       "Stefan Paszkowski",
  title =        "Convergence acceleration of orthogonal series",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "47",
  number =       "1",
  pages =        "35--62",
  month =        jan,
  year =         "2008",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-007-9146-7",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "subject classification (2000); 33C45; 42A32; 42C10;
                 42C20; 65B10",
  bibdate =      "Tue Jul 8 19:14:30 MDT 2008",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=47&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=47&issue=1&spage=35",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Convergence acceleration; convergence acceleration;
                 Orthogonal polynomials; Orthogonal series;
                 Trigonometric series",
}

@Article{Pinchon:2008:NEL,
  author =       "Didier Pinchon and Philip E. Hoggan and Frank E.
                 Harris",
  title =        "A new expansion of the leaky aquifer function",
  journal =      j-IJQC,
  volume =       "108",
  number =       "15",
  pages =        "3042--3046",
  month =        "????",
  year =         "2008",
  CODEN =        "IJQCB2",
  DOI =          "https://doi.org/10.1002/qua.21448;
                 https://doi.org/10.1002/qua.21835",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  MRclass =      "86A05 80A20 33C10 82B80",
  bibdate =      "Sat Oct 1 14:02:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc2000.bib",
  ZMnumber =     "Zbl 1189.86005",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Quantum Chem.",
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  onlinedate =   "4 Aug 2008",
}

@Article{Pineiro:2008:RDD,
  author =       "J.-A. Pineiro and J. D. Bruguera and F. Lamberti and
                 P. Montuschi",
  title =        "A Radix-2 Digit-by-Digit Architecture for Cube Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "57",
  number =       "4",
  pages =        "562--566",
  month =        apr,
  year =         "2008",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.70848",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 12:17:41 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4407683",
  abstract =     "A radix-2 digit-recurrence algorithm and architecture
                 for the computation of the cube root are presented in
                 this paper. The original recurrence based on the
                 concept of completing the cube is modified to allow an
                 efficient implementation of the algorithm and the cycle
                 time and area cost of the resulting architecture are
                 estimated as 7.5 times the delay of a full adder and
                 around 9,000 nand2 cells, respectively, for
                 double-precision computations.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Piso:2008:NRA,
  author =       "D. Piso and J. D. Bruguera",
  editor =       "Luca Fanucci",
  booktitle =    "Proceedings: {11th Euromicro Symposium on Digital
                 Systems Design: Architectures, Methods and Tools (DSD
                 2008), Parma, Italy, September 3--5, 2008}",
  title =        "A New Rounding Algorithm for Variable Latency Division
                 and Square Root Implementations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "760--767",
  year =         "2008",
  DOI =          "https://doi.org/10.1109/DSD.2008.28.",
  ISBN =         "0-7695-3277-2",
  ISBN-13 =      "978-0-7695-3277-6",
  bibdate =      "Sun Dec 10 13:55:38 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The aim of this work is to present a method for
                 rounding quadratically converging algorithms that
                 improves their performance. This method is able to
                 reduce significantly the number of cases where the
                 remainder calculation is necessary. It is based on
                 previous methods and incorporates additional bits of
                 the result approximation to be checked. This work
                 includes the result of exhaustive simulations that
                 permit us to measure exactly how many calculations are
                 avoided. Using these simulations, it is concluded that
                 the presented method is able to reduce by half the
                 number of remainder calculations. Using adequate result
                 approximations the remainder calculation is necessary
                 in only 5\% of the total cases",
  acknowledgement = ack-nhfb,
}

@Article{Rodriguez-Henriquez:2008:LCB,
  author =       "F. Rodriguez-Henriquez and G. Morales-Luna and J.
                 Lopez",
  title =        "Low-Complexity Bit-Parallel Square Root Computation
                 over {$ \mathrm {GF}(2^m) $} for All Trinomials",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "57",
  number =       "4",
  pages =        "472--480",
  month =        apr,
  year =         "2008",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.70822",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 12:17:40 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4358282",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Sablonniere:2008:BSH,
  author =       "Paul Sablonni{\`e}re",
  title =        "{B}-splines and {Hermite--Pad{\'e}} approximants to
                 the exponential function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "219",
  number =       "2",
  pages =        "509--517",
  day =          "1",
  month =        oct,
  year =         "2008",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:13:26 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704270700252X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Schreier:2008:OIR,
  author =       "Franz Schreier and Dieter Kohlert",
  title =        "Optimized implementations of rational approximations
                 --- a case study on the {Voigt} and complex error
                 function",
  journal =      j-COMP-PHYS-COMM,
  volume =       "179",
  number =       "7",
  pages =        "457--465",
  day =          "1",
  month =        oct,
  year =         "2008",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2008.04.012",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 23:42:36 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465508001495",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Segura:2008:IZC,
  author =       "Javier Segura",
  title =        "Interlacing of the zeros of contiguous hypergeometric
                 functions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "49",
  number =       "1--4",
  pages =        "387--407",
  month =        dec,
  year =         "2008",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon May 17 15:07:19 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=49&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=49&issue=1&spage=387",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Misc{Steele:2008:FPSb,
  author =       "Guy L. {Steele Jr.}",
  title =        "Floating point square root provider with embedded
                 status information",
  howpublished = "US Patent 7430576",
  day =          "30",
  month =        sep,
  year =         "2008",
  bibdate =      "Tue Dec 23 15:06:43 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7430576/fulltext.html",
  abstract =     "A system for providing a floating point square root
                 comprises an analyzer circuit configured to determine a
                 first status of a first floating point operand based
                 upon data within the first floating point operand. In
                 addition, the system comprises a results circuit
                 coupled to the analyzer circuit. The results circuit is
                 configured to assert a resulting floating point operand
                 containing the square root of the first floating point
                 operand and a resulting status embedded within the
                 resulting floating point operand.",
  acknowledgement = ack-nhfb,
}

@Article{Vepstas:2008:EAA,
  author =       "Linas Vepstas",
  title =        "An efficient algorithm for accelerating the
                 convergence of oscillatory series, useful for computing
                 the polylogarithm and {Hurwitz} zeta functions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "47",
  number =       "3",
  pages =        "211--252",
  month =        mar,
  year =         "2008",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-007-9153-8",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon May 17 15:49:34 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=47&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=47&issue=3&spage=211",
  abstract =     "This paper sketches a technique for improving the rate
                 of convergence of a general oscillatory sequence, and
                 then applies this series acceleration algorithm to the
                 polylogarithm and the Hurwitz zeta function. As such,
                 it may be taken as an extension of the techniques given
                 by Borwein's ``An efficient algorithm for computing the
                 Riemann zeta function'' by Borwein for computing the
                 Riemann zeta function, to more general series. The
                 algorithm provides a rapid means of evaluating $
                 \operatorname {Li}_s(z) $ for general values of complex
                 $s$ and a kidney-shaped region of complex $z$ values
                 given by $ |z^2 / (z - 1)| < 4 $. By using the
                 duplication formula and the inversion formula, the
                 range of convergence for the polylogarithm may be
                 extended to the entire complex $z$-plane, and so the
                 algorithms described here allow for the evaluation of
                 the polylogarithm for all complex $s$ and $z$ values.
                 Alternatively, the Hurwitz zeta can be very rapidly
                 evaluated by means of an Euler Maclaurin series. The
                 polylogarithm and the Hurwitz zeta are related, in that
                 two evaluations of the one can be used to obtain a
                 value of the other; thus, either algorithm can be used
                 to evaluate either function. The Euler Maclaurin series
                 is a clear performance winner for the Hurwitz zeta,
                 while the Borwein algorithm is superior for evaluating
                 the polylogarithm in the kidney-shaped region. Both
                 algorithms are superior to the simple Taylor's series
                 or direct summation. The primary, concrete result of
                 this paper is an algorithm allows the exploration of
                 the Hurwitz zeta in the critical strip, where fast
                 algorithms are otherwise unavailable. A discussion of
                 the monodromy group of the polylogarithm is included.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "convergence acceleration",
}

@Book{Ware:2008:RIE,
  author =       "Willis H. Ware",
  title =        "{RAND} and the information evolution: a history in
                 essays and vignettes",
  publisher =    "Rand Corporation",
  address =      "Santa Monica, CA",
  pages =        "xxvi + 201",
  year =         "2008",
  DOI =          "https://doi.org/10.7249/cp537rc",
  ISBN =         "0-8330-4513-X, 0-8330-4816-3, 1-282-45123-5",
  ISBN-13 =      "978-0-8330-4513-3, 978-0-8330-4816-5,
                 978-1-282-45123-0",
  LCCN =         "QA76.27",
  bibdate =      "Tue Jun 2 19:14:18 MDT 2020",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  URL =          "http://www.jstor.org/stable/10.7249/cp537rc;
                 https://www.rand.org/content/dam/rand/pubs/corporate_pubs/2008/RAND_CP537.pdf",
  abstract =     "This professional memoir describes RAND's
                 contributions to the evolution of computer science,
                 particularly during the first decades following World
                 War II, when digital computers succeeded slide rules,
                 mechanical desk calculators, electric accounting
                 machines, and analog computers. The memoir includes
                 photographs and vignettes that reveal the collegial,
                 creative, and often playful spirit in which the
                 groundbreaking research was conducted at RAND.",
  acknowledgement = ack-nhfb,
  keywords =     "JOHNNIAC; JOSS; JOSS-1; JOSS-2; RAND tablet",
  remark-1 =     "Page 13 has a photograph of the JOHNNIAC, and on the
                 wall of its room, a photograph of John von Neumann.",
  remark-2 =     "From page 15: ``\ldots{} the JOHNNIAC, which
                 nonetheless was the basis of a continuing series of
                 engineering advances, each making important
                 contributions to the art of the time. Among them were
                 the first commercially produced magnetic core memory,
                 which, for a while, was the largest in existence [4096
                 40-bit words]; a transistor-based adder and logic which
                 caused the JOHNNIAC to become a hybrid
                 transistor-vacuum tube device; the first high-speed
                 impact printer 140 columns wide (manufactured by
                 Anderson--Nichols, an engineering contracting firm);
                 and the first machine with extensive trouble-diagnostic
                 capability from the operating console.''",
  remark-3 =     "From page 53: ``the only bright spot was the Princeton
                 development at IAS, and thus it was that a working
                 alliance between RAND and IAS came into being. RAND
                 would build a machine patterned in the likeness of the
                 Princeton one. So JOHNNIAC came from an illustrious
                 ancestor --- the so-called von Neumann machine
                 developed at Princeton's IAS.''",
  remark-4 =     "Page 57 has a photograph of the JOHNNIAC's 256-word
                 Selectron high-speed memory. Page 59, a picture of its
                 140-column drum printer. Page 61 has an inside view of
                 the JOHNNIAC. Page 73 shows a step in the installation
                 of the JOHNNIAC. Page 162 has a photograph of the
                 JOHNNIAC console.",
  remark-5 =     "From page 66: ``RAND purchased the first commercially
                 available license for UNIX.''",
  remark-6 =     "Page 84 has a photo of a young Cecil Hastings, an
                 early pioneer of function approximation on digital
                 computers, and a few paragraphs about his work and its
                 influence.",
  remark-7 =     "Pages 87--90 discuss the preparation of RAND's famous
                 book of one million random digits, computed in Spring
                 1947, tested for two years after that before
                 publication in 1955. About 7000 copies of the book were
                 sold over three printings and fifteen years, and the
                 book was reprinted in 1966 and 2001.",
  remark-8 =     "From page 138: ``In the 1950s, RAND was involved in
                 designing and building one of the first stored-program
                 digital computers, the JOHNNIAC (named after John von
                 Neumann, a RAND consultant in the late 1940s and early
                 1950s). It was in operation from 1953 to 1966,
                 \ldots{}.''",
  shorttableofcontents = "Introduction \\
                 The department \\
                 RAND's first computer people \\
                 RAND's early computers \\
                 A building for people with computers \\
                 Project essays \\
                 Lore, snippets, and snapshots \\
                 Epilogue",
  tableofcontents = "Dedication / v \\
                 Preface / vii \\
                 Figures / xiii \\
                 Photographs / xv \\
                 Tables / xvii \\
                 Acknowledgments / xix \\
                 Abbreviations / xxiii \\
                 CHAPTER ONE \\
                 Introduction / 1 \\
                 Purpose and Scope / 1 \\
                 Organization of the Document / 3 \\
                 CHAPTER TWO \\
                 The Department / 5 \\
                 The Genesis of RAND / 5 \\
                 The Need for a New Kind of Organization / 6 \\
                 The Douglas Years / 7 \\
                 An Independent, Private Nonprofit Organization / 8 \\
                 The Nature of RAND's Contributions / 9 \\
                 RAND Contributions to the Development of Computing / 10
                 \\
                 In the Beginning / 10 \\
                 An Early Computing Success / 11 \\
                 The Move to Electronic Machines / 11 \\
                 The Middle Years / 14 \\
                 The JOHNNIAC Open-Shop System / 15 \\
                 The Tablet / 16 \\
                 Videographic System / 16 \\
                 The Later Years / 17 \\
                 RAND and the USAF Computing Evolution / 18 \\
                 The Bottom Line / 19 \\
                 CHAPTER THREE \\
                 RAND's First Computer People / 21 \\
                 The Legacy of Wartime Collaboration / 21 \\
                 Early RAND Leaders / 22 \\
                 Early Technical Staff / 24 \\
                 The Douglas Thread / 24 \\
                 The Wartime Thread / 26 \\
                 The University Thread / 28 \\
                 The Recruiting Thread / 30 \\
                 Departmental Growth / 36 \\
                 CHAPTER FOUR \\
                 RAND's Early Computers / 45 \\
                 Mid-20th Century Computation / 45 \\
                 Reeves Electronic Analog Computer / 47 \\
                 Plug-Board Interconnections / 50 \\
                 Chopper-Stabilized Amplifiers / 50 \\
                 Arbitrary Function Input / 51 \\
                 The JOHNNIAC Digital Computer / 53 \\
                 JOHNNIAC's ``Obituary'' / 63 \\
                 IBM Mainframes / 64 \\
                 Other Machinery. / 66 \\
                 CHAPTER FIVE \\
                 A Building for People with Computers / 67 \\
                 A New Building and Campus. / 68 \\
                 The Machine Room. / 72 \\
                 Two-Story Installation / 72 \\
                 REAC Installation. / 73 \\
                 Raised-Floor Installation / 73 \\
                 Air Conditioning. / 74 \\
                 Configurations of the Machine Room / 75 \\
                 Open House. / 75 \\
                 Later Enhancements / 79 \\
                 The Camera / 79 \\
                 Kevershan's Trough / 80 \\
                 Programmer-Alert Lights / 80 \\
                 CHAPTER SIX \\
                 Project Essays / 83 \\
                 Approximations / 83 \\
                 Random Digits and Normal Deviates / 87 \\
                 The Bombing Simulator (aka Pinball Machine) / 90 \\
                 The Air-Combat Room / 94 \\
                 System Research Laboratory / 94 \\
                 The RAND Tablet, Videographics, and Related Projects /
                 98 \\
                 The RAND Tablet / 98 \\
                 Handwriting Recognition / 99 \\
                 Chinese-Character Lookup / 100 \\
                 Map Annotation / 100 \\
                 Videographic System / 103 \\
                 GRAIL / 105 \\
                 BIOMOD / 105 \\
                 CLINFO / 107 \\
                 Time-Shared Computing: JOSS / 109 \\
                 JOSS-1 / 110 \\
                 JOSS-2 / 113 \\
                 Networked Computing: Packet Switching and Distributed
                 Communications / 115 \\
                 The Beginnings of Packet Switching: Some Underlying
                 Concepts / 116 \\
                 Text Editors (NED and e) / 122 \\
                 Word Processing / 126 \\
                 The Mail Handler / 128 \\
                 The Original MH-Proposal Memorandum / 129 \\
                 Implementation / 132 \\
                 Another Perspective / 134 \\
                 A User's Perspective / 135 \\
                 The Developers' Present Views / 137 \\
                 Artificial-Intelligence Research / 138 \\
                 The Beginnings of Artificial Intelligence / 138 \\
                 Newell, Shaw, and Simon: The Development of
                 List-Processing Languages / 138 \\
                 Expert Systems / 140 \\
                 Knowledge-Based Simulation / 142 \\
                 Computational Linguistics / 143 \\
                 The Perfect Buddy / 144 \\
                 Department of Defense Computer Institute / 147 \\
                 Officer Career Paths / 149 \\
                 Software / 150 \\
                 Security and Privacy / 152 \\
                 Security / 152 \\
                 Privacy / 154 \\
                 Fair Information Practices / 155 \\
                 CHAPTER SEVEN \\
                 Lore, Snippets, and Snapshots / 159 \\
                 The Great Machine Fire / 159 \\
                 The Gavel Caper / 159 \\
                 Department-Head-Office Decor / 161 \\
                 Oliver Alfred Gross and JOSS-1 / 162 \\
                 The Soviet ``Threat'' / 163 \\
                 Social Events / 164 \\
                 The One-Way Wire / 166 \\
                 Soviet Cybernetics / 166 \\
                 Inter/Exhume / 167 \\
                 The RAND Computer Symposia / 168 \\
                 Professional Societies / 169 \\
                 Microvignettes / 170 \\
                 The Marchant March / 170 \\
                 Getting Out the Documents / 171 \\
                 Hero of the Week / 171 \\
                 The Chiquita Banana War / 171 \\
                 The Mengel Joint / 171 \\
                 John Williams' Jaguar / 172 \\
                 Programmer Sweepstakes / 173 \\
                 CHAPTER EIGHT \\
                 Epilogue / 175 \\
                 Bibliography / 177 \\
                 Index / 191",
}

@Article{Zhu:2008:SNR,
  author =       "Ling Zhu and Jinju Sun",
  title =        "Six new {Redheffer}-type inequalities for circular and
                 hyperbolic functions",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "56",
  number =       "2",
  pages =        "522--529",
  month =        jul,
  year =         "2008",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:50:15 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122108000813",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Anand:2009:OCS,
  author =       "C. K. Anand and W. Kahl",
  title =        "An Optimized {Cell BE} Special Function Library
                 Generated by {Coconut}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "8",
  pages =        "1126--1138",
  month =        aug,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.223",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4731241",
  abstract =     "Coconut, a tool for developing high-assurance,
                 high-performance kernels for scientific computing,
                 contains an extensible domain-specific language (DSL)
                 embedded in Haskell. The DSL supports interactive
                 prototyping and unit testing, simplifying the process
                 of designing efficient implementations of common
                 patterns. Unscheduled C and scheduled assembly language
                 output are supported. Using the patterns, even
                 nonexpert users can write efficient function
                 implementations, leveraging special hardware features.
                 A production-quality library of elementary functions
                 for the cell BE SPU compute engines has been developed.
                 Coconut-generated and -scheduled vector functions were
                 more than four times faster than commercially
                 distributed functions written in C with intrinsics (a
                 nicer syntax for in-line assembly), wrapped in loops
                 and scheduled by {\tt spuxlc}. All Coconut functions
                 were faster, but the difference was larger for
                 hard-to-approximate functions for which register-level
                 SIMD lookups made a bigger difference. Other helpful
                 features in the language include facilities for
                 translating interval and polynomial descriptions
                 between GHCi, a Haskell interpreter used to prototype
                 in the DSL, and Maple, used for exploration and minimax
                 polynomial generation. This makes it easier to match
                 mathematical properties of the functions with efficient
                 calculational patterns in the SPU ISA. By using single,
                 literate source files, the resulting functions are
                 remarkably readable.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Backeljauw:2009:ACF,
  author =       "Franky Backeljauw and Annie Cuyt",
  title =        "{Algorithm 895}: a continued fractions package for
                 special functions",
  journal =      j-TOMS,
  volume =       "36",
  number =       "3",
  pages =        "15:1--15:20",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1527286.1527289",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Jul 21 14:09:07 MDT 2009",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The continued fractions for special functions package
                 (in the sequel abbreviated as CFSF package) complements
                 a systematic study of continued fraction
                 representations for special functions. It provides all
                 the functionality to create continued fractions, in
                 particular $k$-periodic or limit $k$-periodic
                 fractions, to compute approximants, make use of
                 continued fraction tails, perform equivalence
                 transformations and contractions, and much more. The
                 package, developed in Maple, includes a library of more
                 than 200 representations of special functions, of which
                 only 10\% can be found in the 1964 NBS {\em Handbook of
                 Mathematical Functions with Formulas, Graphs and
                 Mathematical Tables\/} by M. Abramowitz and I.
                 Stegun.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "CAS software; continued fractions; Maple; special
                 functions",
}

@Article{Blomquist:2009:MSC,
  author =       "Frithjof Blomquist and Werner Hofschuster and Walter
                 Kr{\"a}mer",
  title =        "A Modified Staggered Correction Arithmetic with
                 Enhanced Accuracy and Very Wide Exponent Range",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "5492",
  pages =        "41--67",
  year =         "2009",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-01591-5_4",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Apr 10 08:32:19 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/content/k038294004403504/",
  acknowledgement = ack-nhfb,
  author-dates = "1952--2014 (WK)",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "C-XSC; complex interval functions; interval
                 computation; multiple precision; reliable numerical
                 computations; staggered correction; wide exponent
                 range",
  remark =       "Conference on Numerical Validation in Current Hardware
                 Architectures",
  remark-2 =     "Includes algorithms for division, $\exp(x)$, $(1 +
                 x)^n$, $\log(x)$, $\log(1 + x)$, and $\sqrt{x}$.
                 Staggered arithmetic represents numbers with tuples
                 $(e, x_1, x_2, \ldots{}, x_n)$ where $e$ is either
                 integer or a floating-point whole number, the $x_k$ are
                 floating-point, and a number has the value $2^e \sum_{k
                 = 1}^n x_k$. For interval arithmetic, the last element
                 is a pair of lower and upper bounds.",
}

@Article{Boldo:2009:FVA,
  author =       "S. Boldo and M. Daumas and Ren-Cang Li",
  title =        "Formally Verified Argument Reduction with a Fused
                 Multiply-Add",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "8",
  pages =        "1139--1145",
  month =        aug,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.216",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4711042",
  abstract =     "The Cody and Waite argument reduction technique works
                 perfectly for reasonably large arguments, but as the
                 input grows, there are no bits left to approximate the
                 constant with enough accuracy. Under mild assumptions,
                 we show that the result computed with a fused
                 multiply-add provides a fully accurate result for many
                 possible values of the input with a constant almost
                 accurate to the full working precision. We also present
                 an algorithm for a fully accurate second reduction step
                 to reach full double accuracy (all the significand bits
                 of two numbers are accurate) even in the worst cases of
                 argument reduction. Our work recalls the common
                 algorithms and presents proofs of correctness. All the
                 proofs are formally verified using the Coq automatic
                 proof checker.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Bowling:2009:LAC,
  author =       "Shannon R. Bowling and Mohammad T. Khasawneh and
                 Sittichai Kaewkuekool and Byung Rae Cho",
  title =        "A logistic approximation to the cumulative normal
                 distribution",
  journal =      "Journal of Industrial Engineering and Management",
  volume =       "2",
  number =       "1",
  pages =        "114--127",
  month =        "",
  year =         "2009",
  DOI =          "https://doi.org/10.3926/jiem..v2n1.p114-127",
  bibdate =      "Sat Dec 16 15:22:05 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jiem.org/index.php/jiem/article/view/60",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Ind. Eng. Manage.",
  fjournal =     "Journal of Industrial Engineering and Management",
  journal-URL =  "http://www.jiem.org/index.php/jiem/",
}

@Article{Boyd:2009:AAC,
  author =       "John P. Boyd",
  title =        "Acceleration of algebraically-converging {Fourier}
                 series when the coefficients have series in powers of $
                 1 / n $",
  journal =      j-J-COMPUT-PHYS,
  volume =       "228",
  number =       "5",
  pages =        "1404--1411",
  day =          "20",
  month =        mar,
  year =         "2009",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/j.jcp.2008.10.039",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Thu Dec 01 10:35:35 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
  keywords =     "Bernoulli polynomials; Clausen functions; convergence
                 acceleration; Lanczos--Krylov (LK) functions",
}

@Article{Bunck:2009:FAE,
  author =       "Benjamin F. Bunck",
  title =        "A fast algorithm for evaluation of normalized
                 {Hermite} functions",
  journal =      j-BIT-NUM-MATH,
  volume =       "49",
  number =       "2",
  pages =        "281--295",
  month =        jun,
  year =         "2009",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Mon May 24 15:36:43 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=49&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=49&issue=2&spage=281",
  abstract =     "An algorithm for computing the normalized Hermite
                 Functions, $ h_n(x) $, in floating point arithmetic is
                 presented. The algorithm is based on an efficient
                 numerical evaluation of certain closed contour
                 integrals in the complex plane. For large degree $n$,
                 the algorithm is significantly faster than the $ O(n) $
                 complexity of the well known three-term recurrence
                 relation. Comparable accuracy is achieved in no more $
                 O(\sqrt {n}) $ than operations, and for arguments
                 bounded away from $ \pm \sqrt {2n} $, only $ O(\sqrt
                 {\log n}) $ operations.",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT. Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "fast algorithm; Hermite functions; numerical
                 integration; recursion",
}

@Article{Chen:2009:SPA,
  author =       "Yunfei Chen and Norman C. Beaulieu",
  title =        "A simple polynomial approximation to the {Gaussian}
                 {$Q$}-function and its application",
  journal =      j-IEEE-COMMUN-LET,
  volume =       "13",
  number =       "2",
  pages =        "124--126",
  month =        feb,
  year =         "2009",
  CODEN =        "ICLEF6",
  DOI =          "https://doi.org/10.1109/lcomm.2009.081754",
  ISSN =         "1089-7798 (print), 1558-2558 (electronic)",
  ISSN-L =       "1089-7798",
  bibdate =      "Sat Dec 16 15:46:17 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/4783779/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Communications Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}

@InProceedings{Chevillard:2009:CFC,
  author =       "Sylvain Chevillard and Mioara Joldes and Christoph
                 Lauter",
  title =        "Certified and Fast Computation of Supremum Norms of
                 Approximation Errors",
  crossref =     "Bruguera:2009:PIS",
  pages =        "169--176",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "In many numerical programs there is a need for a
                 high-quality floating-point approximation of useful
                 functions $f$, such as such as $ \exp $, $ \sin $, $
                 \erf $. In the actual implementation, the function is
                 replaced by a polynomial $p$, which leads to an
                 approximation error (absolute or relative) $ \epsilon =
                 p - f $ or $ \epsilon = p / f - 1 $. The tight yet
                 certain bounding of this error is an important step
                 towards safe implementations. The problem is difficult
                 mainly because that approximation error is very small
                 and the difference $ p - f $ is subject to high
                 cancellation. Previous approaches for computing the
                 supremum norm in this degenerate case, have proven to
                 be unsafe, not sufficiently tight or too tedious in
                 manual work. We present a safe and fast algorithm that
                 computes a tight lower and upper bound for the supremum
                 norms of approximation errors. The algorithm is based
                 on a combination of several techniques, including
                 enhanced interval arithmetic, automatic differentiation
                 and isolation of the roots of a polynomial. We have
                 implemented our algorithm and give timings on several
                 examples.",
  acknowledgement = ack-nhfb,
  keywords =     "approximation error; ARITH-19; automatic/algorithmic
                 differentiation; certified computation; elementary
                 function; interval arithmetic; roots isolation
                 technique.; supremum/infinity norm",
}

@TechReport{Chevillard:2009:FEE,
  author =       "S. Chevillard",
  title =        "The functions {ERF} and {ERFC} computed with arbitrary
                 precision",
  type =         "Report",
  number =       "RRLIP2009-04",
  institution =  "HAL",
  address =      "????",
  pages =        "32",
  year =         "2009",
  bibdate =      "Mon Jun 12 16:09:53 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Daumas:2009:VRN,
  author =       "M. Daumas and D. Lester and C. Muoz",
  title =        "Verified Real Number Calculations: a Library for
                 Interval Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "2",
  pages =        "226--237",
  month =        feb,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.213",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 12 08:51:00 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Real number calculations on elementary functions are
                 remarkably difficult to handle in mechanical proofs. In
                 this paper, we show how these calculations can be
                 performed within a theorem prover or proof assistant in
                 a convenient and highly automated as well as
                 interactive way. First, we formally establish upper and
                 lower bounds for elementary functions. Then, based on
                 these bounds, we develop a rational interval arithmetic
                 where real number calculations take place in an
                 algebraic setting. In order to reduce the dependency
                 effect of interval arithmetic, we integrate two
                 techniques: interval splitting and Taylor series
                 expansions. This pragmatic approach has been developed,
                 and formally verified, in a theorem prover. The formal
                 development also includes a set of customizable
                 strategies to automate proofs involving explicit
                 calculations over real numbers. Our ultimate goal is to
                 provide guaranteed proofs of numerical properties with
                 minimal human theorem-prover interaction.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "interval arithmetic; proof checking; real number
                 calculations; theorem proving",
  remark =       "Extended version of ARITH-18 article
                 \cite{Daumas:2009:VRN}.",
}

@Article{Deano:2009:MAS,
  author =       "Alfredo Dea{\~n}o and Nico M. Temme",
  title =        "On modified asymptotic series involving confluent
                 hypergeometric functions",
  journal =      j-ELECTRON-TRANS-NUMER-ANAL,
  volume =       "35",
  pages =        "88--103",
  year =         "2009",
  CODEN =        "????",
  ISSN =         "1068-9613 (print), 1097-4067 (electronic)",
  ISSN-L =       "1068-9613",
  bibdate =      "Mon Sep 6 12:28:30 MDT 2010",
  bibsource =    "http://etna.mcs.kent.edu/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://etna.mcs.kent.edu/vol.35.2009/pp88-103.dir/pp88-103.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Transactions on Numerical Analysis",
  journal-URL =  "http://etna.mcs.kent.edu/",
}

@Article{FreitasDeAbreu:2009:JCU,
  author =       "Giuseppe Thadeu {Freitas De Abreu}",
  title =        "{Jensen--Cotes} upper and lower bounds on the
                 {Gaussian} {$Q$}-function and related functions",
  journal =      j-IEEE-TRANS-COMM,
  volume =       "57",
  number =       "11",
  pages =        "3328--3338",
  month =        nov,
  year =         "2009",
  CODEN =        "IECMBT",
  DOI =          "https://doi.org/10.1109/tcomm.2009.11.080479",
  ISSN =         "0090-6778 (print), 1558-0857 (electronic)",
  ISSN-L =       "0090-6778",
  bibdate =      "Sat Dec 16 15:12:46 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Communications",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=26",
}

@Article{Fukushima:2009:FCC,
  author =       "Toshio Fukushima",
  title =        "Fast computation of complete elliptic integrals and
                 {Jacobian} elliptic functions",
  journal =      j-CELEST-MECH-DYN-ASTR,
  volume =       "105",
  number =       "4",
  pages =        "305--328",
  month =        dec,
  year =         "2009",
  CODEN =        "CLMCAV",
  DOI =          "https://doi.org/10.1007/s10569-009-9228-z",
  ISSN =         "0923-2958 (print), 1572-9478 (electronic)",
  ISSN-L =       "0923-2958",
  MRclass =      "33E05 (33F05 65E05)",
  MRnumber =     "2559416",
  MRreviewer =   "Mehdi Hassani",
  bibdate =      "Wed Oct 20 21:29:31 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/content/0923-2958/",
  abstract =     "As a preparation step to compute Jacobian elliptic
                 functions efficiently, we created a fast method to
                 calculate the complete elliptic integral of the first
                 and second kinds, $ K(m) $ and $ E(m) $, for the
                 standard domain of the elliptic parameter, $ 0 < m < 1
                 $. For the case $ 0 < m < 0.9 $, the method utilizes $
                 10 $ pairs of approximate polynomials of the order of
                 $9$--$ 19 $ obtained by truncating Taylor series
                 expansions of the integrals. Otherwise, the associate
                 integrals, $ K(1 - m) $ and $ E(1 - m) $, are first
                 computed by a pair of the approximate polynomials and
                 then transformed to $ K(m) $ and $ E(m) $ by means of
                 Jacobi's nome, $q$, and Legendre's identity relation.
                 In average, the new method runs more-than-twice faster
                 than the existing methods including Cody's Chebyshev
                 polynomial approximation of Hastings type and Innes'
                 formulation based on $q$-series expansions. Next, we
                 invented a fast procedure to compute simultaneously
                 three Jacobian elliptic functions, {\tt sn(u|m)}, {\tt
                 cn(u|m)}, and {\tt dn(u|m)}, by repeated usage of the
                 double argument formulae starting from the Maclaurin
                 series expansions with respect to the elliptic
                 argument, $u$, after its domain is reduced to the
                 standard range, $ 0 \leq u < K(m) / 4 $, with the help
                 of the new method to compute K(m). The new procedure is
                 25--70\% faster than the methods based on the Gauss
                 transformation such as Bulirsch's algorithm, sncndn,
                 quoted in the Numerical Recipes even if the
                 acceleration of computation of $ K(m) $ is not taken
                 into account.",
  acknowledgement = ack-nhfb,
  fjournal =     "Celestial Mechanics \& Dynamical Astronomy. An
                 International Journal of Space Dynamics",
  keywords =     "complete elliptic integrals; Encke's method; Innes'
                 method; Jacobian elliptic functions; nome expansion;
                 numerical methods",
}

@Article{Fukushima:2009:FCJ,
  author =       "Toshio Fukushima",
  title =        "Fast computation of {Jacobian} elliptic functions and
                 incomplete elliptic integrals for constant values of
                 elliptic parameter and elliptic characteristic",
  journal =      j-CELEST-MECH-DYN-ASTR,
  volume =       "105",
  number =       "1--3",
  pages =        "245--260",
  year =         "2009",
  CODEN =        "CLMCAV",
  DOI =          "https://doi.org/10.1007/s10569-008-9177-y",
  ISSN =         "0923-2958 (print), 1572-9478 (electronic)",
  ISSN-L =       "0923-2958",
  MRclass =      "33E05 (33F05 65D20 70M20)",
  MRnumber =     "2551836",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/content/0923-2958/",
  abstract =     "In order to accelerate the numerical evaluation of
                 torque-free rotation of triaxial rigid bodies, we
                 present a fast method to compute various kinds of
                 elliptic functions for a series of the elliptic
                 argument when the elliptic parameter and the elliptic
                 characteristic are fixed. The functions we evaluate are
                 the Jacobian elliptic functions and the incomplete
                 elliptic integral of the second and third kinds
                 regarded as a function of that of the first kind. The
                 key technique is the utilization of the Maclaurin
                 series expansion and the addition theorems with respect
                 to the elliptic argument. The new method is around 25
                 times faster than the method using the incomplete
                 elliptic integral of general kind and around 70 times
                 faster than the method using mathematical libraries
                 given in the latest version of Numerical Recipes.",
  acknowledgement = ack-nhfb,
  fjournal =     "Celestial Mechanics \& Dynamical Astronomy. An
                 International Journal of Space Dynamics",
  keywords =     "elliptic integrals; extended body dynamics; Jacobian
                 elliptic functions; numerical method; rotation",
}

@Article{Guo:2009:CLC,
  author =       "Senlin Guo and Feng Qi",
  title =        "A class of logarithmically completely monotonic
                 functions associated with the gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "224",
  number =       "1",
  pages =        "127--132",
  day =          "1",
  month =        feb,
  year =         "2009",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:13:29 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042708001829",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Guralnik:2009:ISV,
  author =       "Elena Guralnik and Ariel J. Birnbaum and Anatoly
                 Koyfman and Avi Kaplan",
  title =        "Implementation Specific Verification of Divide and
                 Square Root Instructions",
  crossref =     "Bruguera:2009:PIS",
  pages =        "114--121",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating point operations such as divide and square
                 root are typically implemented in microcode rather than
                 dedicated logic. Bugs in these operations missed by
                 generic black-box verification tools, were analyzed.
                 This led to the conclusion that the corner cases, in
                 addition to being implementation dependent, could not
                 be characterized in terms of special input or output
                 values in a straightforward manner.\par

                 However, many of those cases can be easily generalized
                 for many known implementations. The typical
                 implementation uses a known iterative approximation
                 algorithm, such as the Newton--Raphson method, to
                 calculate the desired result; thus, it is sufficient to
                 produce the corner cases associated with the specific
                 algorithm.\par

                 We investigated the following problem: given an
                 iterative algorithm to compute a binary floating point
                 operation, the iteration number, and an interval, find
                 random inputs for the operation that, after the
                 requested iteration, yield a relative error within the
                 specified interval. This paper describes a method to
                 solve this problem. This method was implemented in a
                 floating-point test generator and is currently being
                 used to verify the floating-point units of several
                 processors.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@Article{Han:2009:ICS,
  author =       "Dong-Guk Han and Dooho Choi and Howon Kim",
  title =        "Improved Computation of Square Roots in Specific
                 Finite Fields",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "2",
  pages =        "188--196",
  month =        feb,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.201",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4663058",
  abstract =     "In this paper, we study exponentiation in the specific
                 finite fields $ F_q $ with very special exponents such
                 as those that occur in algorithms for computing square
                 roots. Here, $q$ is a prime power, $ q = p^k $, where $
                 k > 1 $, and $k$ is odd. Our algorithmic approach
                 improves the corresponding exponentiation resulted from
                 the better rewritten exponent. To the best of our
                 knowledge, it is the first major improvement to the
                 Tonelli--Shanks algorithm, for example, the number of
                 multiplications can be reduced to at least 60 percent
                 on the average when $ p \equiv 1 \pmod 16 $. Several
                 numerical examples are given that show the speedup of
                 the proposed methods.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "cryptography; efficient computation; finite fields;
                 square roots",
}

@Article{Harris:2009:MIB,
  author =       "Frank E. Harris and J. G. Fripiat",
  title =        "Methods for incomplete {Bessel} function evaluation",
  journal =      j-IJQC,
  volume =       "109",
  number =       "8",
  pages =        "1728--1740",
  month =        feb,
  year =         "2009",
  CODEN =        "IJQCB2",
  DOI =          "https://doi.org/10.1002/qua.21972",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Fri Mar 27 07:41:18 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Presented here are detailed methods for evaluating the
                 incomplete Bessel functions arising when Gaussian-type
                 orbitals are used for systems periodic in one spatial
                 dimension. The scheme is designed to yield these
                 incomplete Bessel functions with an absolute accuracy
                 of $ \pm 1 \times 10^{-10} $, for the range of integer
                 orders $ 0 \leq n \leq 12 $ [a range sufficient for a
                 basis whose members have angular momenta of up to three
                 units ($s$, $p$, $d$, or $f$ atomic functions)]. To
                 reach this accuracy level within acceptable computation
                 times, new rational approximations were developed to
                 compute the special functions involved, namely, the
                 exponential integral $ E_1 (x) $ and the modified
                 Bessel functions $ K_0 (x) $ and $ K_1 (x) $, to
                 absolute accuracy $ \pm 1 \times 10^{-15} $.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  keywords =     "E1(x); exponential integral; incomplete Bessel
                 function; K0(x); K1(x); leaky aquifer function;
                 modified Bessel function; numerical methods",
}

@InProceedings{Harrison:2009:DTB,
  author =       "John Harrison",
  title =        "Decimal Transcendentals via Binary",
  crossref =     "Bruguera:2009:PIS",
  pages =        "187--194",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ARITH.2009.32",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "We describe the design and implementation of a
                 comprehensive library of transcendental functions for
                 the new IEEE decimal floating-point formats. In
                 principle, such functions are very much analogous to
                 their binary counterparts, though with a few additional
                 subtleties connected with `scale' (preferred exponent).
                 But our approach has been not to employ direct
                 techniques, but rather to re-use existing binary
                 functions as much as possible, both for greater
                 efficiency and ease of implementation. For some
                 functions the most straightforward approach (convert
                 from decimal to binary, perform binary operation,
                 convert back) works well. In many cases, however, these
                 are insufficiently accurate, and subtler approaches
                 must be used.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@InProceedings{Harrison:2009:FAB,
  author =       "John Harrison",
  title =        "Fast and Accurate {Bessel} Function Computation",
  crossref =     "Bruguera:2009:PIS",
  pages =        "104--113",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The Bessel functions are considered relatively
                 difficult to compute. Although they have a simple power
                 series expansion that is everywhere convergent, they
                 exhibit approximately periodic behavior which makes the
                 direct use of the power series impractically slow and
                 numerically unstable. We describe an alternative method
                 based on systematic expansion around the zeros,
                 refining existing techniques based on Hankel
                 expansions, which mostly avoids the use of
                 multiprecision arithmetic while yielding accurate
                 results.",
  acknowledgement = ack-nhfb,
  keywords =     "$J0(x), J1(1), Y0(x), Y1(1)$; ARITH-19; ordinary
                 Bessel functions of the first and second kinds",
}

@Book{Henner:2009:MMP,
  author =       "Victor Henner and Tatyana Belozerova and Kyle
                 Forinash",
  title =        "Mathematical methods in physics: partial differential
                 equations, {Fourier} series, and special functions",
  publisher =    pub-A-K-PETERS,
  address =      pub-A-K-PETERS:adr,
  pages =        "xviii + 841",
  year =         "2009",
  ISBN =         "1-56881-335-X",
  ISBN-13 =      "978-1-56881-335-6",
  LCCN =         "QC20 .H487 2009",
  bibdate =      "Sat Oct 30 17:39:29 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Mathematical physics; Textbooks",
}

@Article{Lauter:2009:ERB,
  author =       "C. Q. Lauter and V. Lefevre",
  title =        "An Efficient Rounding Boundary Test for {\tt pow(x,
                 y)} in Double Precision",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "2",
  pages =        "197--207",
  month =        feb,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.202",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 12 08:51:00 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The correct rounding of the function $ \textrm {pow} :
                 (x, y) \rightarrow x^y $ is currently based on Ziv's
                 iterative approximation process. In order to ensure its
                 termination, cases when $ x^y $ falls on a
                 rounding-boundary must be filtered out. Such
                 rounding-boundaries are floating-point numbers and
                 midpoints between two consecutive floating-point
                 numbers. Detecting rounding-boundaries for pow is a
                 difficult problem. Previous approaches use repeated
                 square root extraction followed by repeated square and
                 multiply. This paper presents a new rounding-boundary
                 test for pow in double precision, which reduces this to
                 a few comparisons with precomputed constants. These
                 constants are deduced from worst cases for the Table
                 Maker's Dilemma, searched over a small subset of the
                 input domain. This is a novel use of such worst-case
                 bounds. The resulting algorithm has been designed for a
                 fast-on-average correctly rounded implementation of
                 pow, considering the scarcity of rounding-boundary
                 cases. It does not stall average computations for
                 rounding-boundary detection. This paper includes its
                 correctness proof and experimental results.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "correct rounding; floating-point arithmetic; power
                 function.",
}

@Article{Linhart:2009:ACL,
  author =       "Jean Marie Linhart",
  title =        "{Algorithm 885}: Computing the Logarithm of the Normal
                 Distribution",
  journal =      j-TOMS,
  volume =       "35",
  number =       "3",
  pages =        "20:1--20:10",
  month =        oct,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1391989.1391993",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 1 19:57:00 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present and compare three C functions to compute
                 the logarithm of the cumulative standard normal
                 distribution. The first is a new algorithm derived from
                 Algorithm 304's calculation of the standard normal
                 distribution via a series or continued fraction
                 approximation, and it is good to the accuracy of the
                 machine. The second is based on Algorithm 715's
                 calculation of the standard normal distribution via
                 rational Chebyshev approximation. This is related to,
                 and an improvement on, the algorithm for the logarithm
                 of the normal distribution available in the software
                 package R. The third is a new and simple algorithm that
                 uses the compiler's implementation of the error
                 function, and complement of the error function, to
                 compute the log of the normal distribution.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "error function; logarithm of the standard normal
                 distribution; Normal distribution; normal integral",
}

@Article{Loskot:2009:PPA,
  author =       "P. Loskot and N. C. Beaulieu",
  title =        "{Prony} and Polynomial Approximations for Evaluation
                 of the Average Probability of Error Over Slow-Fading
                 Channels",
  journal =      j-IEEE-TRANS-VEH-TECHNOL,
  volume =       "58",
  number =       "3",
  pages =        "1269--1280",
  month =        mar,
  year =         "2009",
  CODEN =        "ITUTAB",
  DOI =          "https://doi.org/10.1109/tvt.2008.926072",
  ISSN =         "0018-9545 (print), 1939-9359 (electronic)",
  ISSN-L =       "0018-9545",
  bibdate =      "Sat Dec 16 18:08:41 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/4529094/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Vehicular Technology",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=25",
}

@Article{Nagayama:2009:CGB,
  author =       "S. Nagayama and T. Sasao",
  title =        "Complexities of Graph-Based Representations for
                 Elementary Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "1",
  pages =        "106--119",
  month =        jan,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.134",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4599569",
  abstract =     "This paper analyzes complexities of decision diagrams
                 for elementary functions such as polynomial,
                 trigonometric, logarithmic, square root, and reciprocal
                 functions. These real functions are converted into
                 integer-valued functions by using fixed-point
                 representation. This paper presents the numbers of
                 nodes in decision diagrams representing the
                 integer-valued functions. First, complexities of
                 decision diagrams for polynomial functions are
                 analyzed, since elementary functions can be
                 approximated by polynomial functions. A theoretical
                 analysis shows that binary moment diagrams (BMDs) have
                 low complexity for polynomial functions. Second, this
                 paper analyzes complexity of edge-valued binary
                 decision diagrams (EVBDDs) for monotone functions,
                 since many common elementary functions are monotone. It
                 introduces a new class of integer functions,
                 Mp-monotone increasing function, and derives an upper
                 bound on the number of nodes in an EVBDD for the
                 Mp-monotone increasing function. A theoretical analysis
                 shows that EVBDDs have low complexity for Mp-monotone
                 increasing functions. This paper also presents the
                 exact number of nodes in the smallest EVBDD for the
                 n-bit multiplier function, and a variable order for the
                 smallest EVBDD.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "binary moment diagram; decision diagrams; edge-valued
                 binary decision diagram; elementary function;
                 elementary function approximation; fixed-point
                 representation; general representations; graph-based
                 representation; integer-valued function; monotone
                 function; polynomial function; trees",
}

@Book{Oldham:2009:AF,
  editor =       "Keith B. Oldham and Jan Myland and Jerome Spanier",
  title =        "An Atlas of Functions: With Equator, the Atlas
                 Function Calculator",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xi + 748",
  year =         "2009",
  DOI =          "https://doi.org/10.1007/978-0-387-48807-3",
  ISBN =         "0-387-48807-3 (softcover), 0-387-48806-5 (hardcover)",
  ISBN-13 =      "978-0-387-48807-3 (softcover), 978-0-387-48806-6
                 (hardcover)",
  LCCN =         "QA331 .S685 2009",
  bibdate =      "Fri Aug 31 16:20:13 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/canjstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$129.95",
  acknowledgement = ack-nhfb,
  subject =      "Functions",
  tableofcontents = "Front Matter / i--xi \\
                 General Considerations / 1--11 \\
                 The Constant Function $c$ / 13--19 \\
                 The Factorial Function $n!$ / 21--27 \\
                 The Zeta Numbers and Related Functions / 29--38 \\
                 The Bernoulli Numbers $B_n$ / 39--44 \\
                 The Euler Numbers $E_n$ / 45--48 \\
                 The Binomial Coefficients $\binom{\nu}{m}$ / 49--56 \\
                 The Linear Function $b x + c$ and Its Reciprocal /
                 57--65 \\
                 Modifying Functions / 67--74 \\
                 The Heaviside $u(x - a)$ And Dirac $\delta(x - a)$
                 Functions / 75--80 \\
                 The Integer Powers $x^n$ and $(b x + c)^n$ / 81--93 \\
                 The Square-Root Function $\sqrt{b x + c}$ and Its
                 Reciprocal / 95--102 \\
                 The Noninteger Powers $x^\nu$ / 103--112 \\
                 The Semielliptic Function $(b / a)\sqrt{a^2 - x^2}$ and
                 Its Reciprocal / 113--120 \\
                 The Semihyperbolic Functions $(b / a) \sqrt{x^2 \pm
                 a^2}$ and Their Reciprocals / 121--130 \\
                 The Quadratic Function $a x^2 + b x + c$ and Its
                 Reciprocal / 131--138 \\
                 The Cubic Function $x^3 + a x^2 + b x + c$ / 139--146
                 \\
                 Polynomial Functions / 147--158 \\
                 The Pochhammer Polynomials $(x)_n$ / 159--174 \\
                 The Bernoulli Polynomials $B_n(x)$ / 175--180 \\
                 The Euler Polynomials $E_n(x)$ / 181--186 \\
                 The Legendre Polynomials $P_n(x)$ / 187--196 \\
                 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ /
                 197--208 \\
                 The Laguerre Polynomials $L_n(x)$ / 209--216 \\
                 The Hermite Polynomials $H_n(x)$ / 217--227 \\
                 The Logarithmic Function $\ln(x)$ / 229--239 \\
                 The Exponential Function $\exp(\pm x)$ / 241--253 \\
                 Exponentials of Powers $\exp(\pm x^\nu)$ / 255--267 \\
                 The Hyperbolic Cosine $\cosh(x)$ and Sine $\sinh(x)$
                 Functions / 269--279 \\
                 The Hyperbolic Secant $\sech(x)$ and Cosecant
                 $\csch(x)$ Functions / 281--288 \\
                 The Hyperbolic Tangent $\tanh(x)$ and Cotangent
                 $\coth(x)$ Functions / 289--296 \\
                 The Inverse Hyperbolic Functions / 297--307 \\
                 The Cosine $\cos(x)$ and Sine $\sin(x)$ Functions /
                 309--328 \\
                 The Secant $\sec(x)$ and Cosecant $\csc(x)$ Functions /
                 329--338 \\
                 The Tangent $\tan(x)$ and Cotangent $\cot(x)$ Functions
                 / 339--350 \\
                 The Inverse Circular Functions / 351--366 \\
                 Periodic Functions / 367--374 \\
                 The Exponential Integrals $\Ei(x)$ and $\Ein(x)$ /
                 375--383 \\
                 Sine and Cosine Integrals / 385--394 \\
                 The Fresnel Integrals $C(x)$ and $S(x)$ / 395--404 \\
                 The Error Function $\erf(x)$ and Its Complement
                 $\erfc(x)$ / 405--415 \\
                 The $\exp(x)\erfc(\sqrt{x})$ and Related Functions /
                 417--426 \\
                 Dawson's Integral $\daw(x)$ / 427--433 \\
                 The Gamma Function $\Gamma(\nu)$ / 435--448 \\
                 The Digamma Function $\psi(\nu)$ / 449--460 \\
                 The Incomplete Gamma Functions / 461--470 \\
                 The Parabolic Cylinder Function $D_\nu(x)$ / 471--484
                 \\
                 The Kummer Function $M(a, c, x)$ / 485--496 \\
                 The Tricomi Function $U(a, c, x)$ / 497--506 \\
                 The Modified Bessel Functions $I_n(x)$ of Integer Order
                 / 507--517 \\
                 The Modified Bessel Function $I_\nu(x)$ of Arbitrary
                 Order / 519--526 \\
                 The Macdonald Function $K_\nu(x)$ / 527--536 \\
                 The Bessel Functions $J_n(x)$ of Integer Order /
                 537--552 \\
                 The Bessel Function $J_\nu(x)$ of Arbitrary Order /
                 553--565 \\
                 The Neumann Function $Y_\nu(x)$ / 567--576 \\
                 The Kelvin Functions / 577--584 \\
                 The Airy Functions $\Ai(x)$ and $\Bi(x)$ / 585--592 \\
                 The Struve Function $h_\nu(x)$ / 593--601 \\
                 The Incomplete Beta Function $B(\nu, \mu, x)$ /
                 603--609 \\
                 The Legendre Functions $P_\nu(x)$ and $Q_\nu(x)$ /
                 611--626 \\
                 The Gauss Hypergeometric Function $F(a, b, c, x)$ /
                 627--636 \\
                 The Complete Elliptic Integrals $K(k)$ and $E(k)$ /
                 637--651 \\
                 The Incomplete Elliptic Integrals $F(k, \phi)$ and
                 $E(k, \phi)$ / 653--669 \\
                 The Jacobian Elliptic Functions / 671--684 \\
                 The Hurwitz Function $\zeta(\nu, u)$ / 685--695 \\
                 Back Matter / 697--748",
}

@Article{Opps:2009:RFA,
  author =       "Sheldon B. Opps and Nasser Saad and H. M. Srivastava",
  title =        "Recursion formulas for {Appell}'s hypergeometric
                 function {$ F_2 $} with some applications to radiation
                 field problems",
  journal =      j-APPL-MATH-COMP,
  volume =       "207",
  number =       "2",
  pages =        "545--558",
  day =          "15",
  month =        jan,
  year =         "2009",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Sep 3 10:53:24 MDT 2010",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Paris:2009:HPE,
  author =       "R. B. Paris",
  title =        "High-precision evaluation of the {Bessel} functions
                 via {Hadamard} series",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "224",
  number =       "1",
  pages =        "84--100",
  day =          "1",
  month =        feb,
  year =         "2009",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:13:29 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042708001799",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@MastersThesis{Pearson:2009:CHF,
  author =       "J. Pearson",
  title =        "Computation of hypergeometric functions",
  type =         "{Master}'s thesis",
  school =       "Oxford University",
  address =      "Oxford, UK",
  year =         "2009",
  bibdate =      "Thu Dec 01 09:05:26 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Talman:2009:NSC,
  author =       "J. D. Talman",
  title =        "{NumSBT}: a subroutine for calculating spherical
                 {Bessel} transforms numerically",
  journal =      j-COMP-PHYS-COMM,
  volume =       "180",
  number =       "2",
  pages =        "332--338",
  month =        feb,
  year =         "2009",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2008.10.003",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 23:42:39 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465508003329",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Temme:2009:AER,
  author =       "Nico M. Temme and Vladimir Varlamov",
  title =        "Asymptotic expansions for {Riesz} fractional
                 derivatives of {Airy} functions and applications",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "232",
  number =       "2",
  pages =        "201--215",
  day =          "15",
  month =        oct,
  year =         "2009",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:24:17 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042709003410",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Vazquez:2009:CDT,
  author =       "{\'A}lvaro V{\'a}zquez and Julio Villalba and Elisardo
                 Antelo",
  title =        "Computation of Decimal Transcendental Functions Using
                 the {CORDIC} Algorithm",
  crossref =     "Bruguera:2009:PIS",
  pages =        "179--186",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "In this work we propose new decimal floating-point
                 CORDIC algorithms for transcendental function
                 evaluation. We show how these algorithms are mapped to
                 a state of the art Decimal Floating-Point Unit (DFPU),
                 both considering the use of a carry-propagate adder or
                 a carry-save redundant adder. We compared with previous
                 decimal CORDIC proposals and with table-driven
                 algorithms, and we concluded that our approach have
                 significant potential advantages for transcendental
                 function evaluation in state of the art DFPUs with
                 minor modifications of the hardware.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@Article{Weniger:2009:SHF,
  author =       "Ernst Joachim Weniger",
  title =        "The strange history of {$B$} functions or how
                 theoretical chemists and mathematicians do (not)
                 interact",
  journal =      j-IJQC,
  volume =       "109",
  number =       "8",
  pages =        "1728--1740",
  month =        feb,
  year =         "2009",
  CODEN =        "IJQCB2",
  DOI =          "https://doi.org/10.1002/qua.22014",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Fri Mar 27 07:47:31 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "$B$ functions are a class of relatively complicated
                 exponentially decaying basis functions. Because the
                 molecular multicenter integrals of the much simpler
                 Slater-type functions are notoriously difficult, it is
                 not at all obvious why $B$ functions should offer any
                 advantages. However, $B$ functions have Fourier
                 transforms of exceptional simplicity, which greatly
                 simplifies many of their molecular multicenter
                 integrals. This article discusses the historical
                 development of $B$ functions from the perspective of
                 the interaction between mathematics and theoretical
                 chemistry, which traditionally has not been very good.
                 Nevertheless, future progress in theoretical chemistry
                 depends very much on a fertile interaction with
                 neighboring disciplines.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  keywords =     "B functions; electronic structure theory;
                 exponentially decaying basis functions;
                 interdisciplinary collaboration; multicenter
                 integrals",
}

@Article{Wozny:2009:MSS,
  author =       "Pawe{\l} Wo{\'z}ny and Rafa{\l} Nowak",
  title =        "Method of summation of some slowly convergent series",
  journal =      j-APPL-MATH-COMP,
  volume =       "215",
  number =       "4",
  pages =        "1622--1645",
  month =        "????",
  year =         "2009",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  MRclass =      "65B10",
  MRnumber =     "MR2571650",
  bibdate =      "Thu Dec 01 09:25:02 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "convergence acceleration",
}

@Article{Yun:2009:ACN,
  author =       "Beong In Yun",
  title =        "Approximation to the cumulative normal distribution
                 using hyperbolic tangent based functions",
  journal =      "Journal of the Korean Mathematical Society",
  volume =       "46",
  number =       "6",
  pages =        "1267--1276",
  year =         "2009",
  DOI =          "https://doi.org/10.4134/JKMS.2009.46.6.1267",
  ISSN =         "0304-9914",
  MRclass =      "62E17 (65C60)",
  MRnumber =     "2572515",
  bibdate =      "Sat Dec 16 18:04:41 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Korean Math. Soc.",
  fjournal =     "Journal of the Korean Mathematical Society",
}

@Article{Ahmadi:2010:LCC,
  author =       "O. Ahmadi and F. R. Henr{\'\i}quez",
  title =        "Low Complexity Cubing and Cube Root Computation over
                 {$ F_3^m $} in Polynomial Basis",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "59",
  number =       "10",
  pages =        "1297--1308",
  month =        oct,
  year =         "2010",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2009.183",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 3 11:52:32 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5374372",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Akbarpour:2010:VSI,
  author =       "Behzad Akbarpour and Amr T. Abdel-Hamid and
                 Sofi{\`e}ne Tahar and John Harrison",
  title =        "Verifying a Synthesized Implementation of {IEEE-754}
                 Floating-Point Exponential Function using {HOL}",
  journal =      j-COMP-J,
  volume =       "53",
  number =       "4",
  pages =        "465--488",
  month =        may,
  year =         "2010",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxp023",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Wed Apr 28 14:33:36 MDT 2010",
  bibsource =    "http://comjnl.oxfordjournals.org/content/vol53/issue4/index.dtl;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://comjnl.oxfordjournals.org/cgi/content/abstract/53/4/465;
                 http://comjnl.oxfordjournals.org/cgi/reprint/53/4/465",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Alimohammad:2010:UAA,
  author =       "A. Alimohammad and S. F. Fard and B. F. Cockburn",
  title =        "A Unified Architecture for the Accurate and
                 High-Throughput Implementation of Six Key Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "59",
  number =       "4",
  pages =        "449--456",
  month =        "????",
  year =         "2010",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2009.169",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 3 11:52:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5313801",
  abstract =     "This paper presents a unified architecture for the
                 compact implementation of several key elementary
                 functions, including reciprocal, square root, and
                 logarithm, in single-precision floating-point
                 arithmetic. The proposed high-throughput design is
                 based on uniform domain segmentation and curve fitting
                 techniques. Numerically accurate least-squares
                 regression is utilized to calculate the polynomial
                 coefficients. The architecture is optimized by
                 analyzing the trade-off between the size of the
                 required memory and the precision of intermediate
                 variables to achieve the minimum 23-bit accuracy
                 required for single-precision floating-point
                 representation. The efficiency of the proposed unified
                 data path is demonstrated on a common
                 field-programmable gate array.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Alzer:2010:EFI,
  author =       "Horst Alzer",
  title =        "Error function inequalities",
  journal =      j-ADV-COMPUT-MATH,
  volume =       "33",
  number =       "3",
  pages =        "349--379",
  month =        oct,
  year =         "2010",
  CODEN =        "ACMHEX",
  DOI =          "https://doi.org/10.1007/s10444-009-9139-2",
  ISSN =         "1019-7168 (print), 1572-9044 (electronic)",
  ISSN-L =       "1019-7168",
  MRclass =      "33B20 (26D07 26D15)",
  MRnumber =     "2718103",
  MRreviewer =   "Feng Qi",
  bibdate =      "Sat Feb 3 18:22:50 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/s10444-009-9139-2",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in Computational Mathematics",
  journal-URL =  "http://link.springer.com/journal/10444",
}

@Article{Anand:2010:UTE,
  author =       "Christopher Kumar Anand and Anuroop Sharma",
  title =        "Unified Tables for Exponential and Logarithm
                 Families",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "28:1--28:23",
  month =        sep,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1824806",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Accurate table methods allow for very accurate and
                 efficient evaluation of elementary functions. We
                 present new single-table approaches to logarithm and
                 exponential evaluation, by which we mean that a single
                 table of values works for both $ \log (x) $ and $ l o
                 g(1 + x) $, and a single table for $ e^x $ and $ e^x -
                 1 $. This approach eliminates special cases normally
                 required to evaluate $ \log (1 + x) $ and $ e^x - 1 $
                 accurately near zero, which will significantly improve
                 performance on architectures which use SIMD
                 parallelism, or on which data-dependent branching is
                 expensive.\par

                 We have implemented it on the Cell/B.E. SPU (SIMD
                 compute engine) and found the resulting functions to be
                 up to twice as fast as the conventional implementations
                 distributed in the IBM Mathematical Acceleration
                 Subsystem (MASS). We include the literate code used to
                 generate all the variants of exponential and log
                 functions in the article, and discuss relevant language
                 and hardware features.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Accurate tables method; Cell/B.E; IEEE arithmetic;
                 SIMD; vector library",
}

@Book{Baricz:2010:GBF,
  author =       "{\'A}rp{\'a}d Baricz",
  title =        "Generalized {Bessel} Functions of the First Kind",
  volume =       "1994",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xiv + 206",
  year =         "2010",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/978-3-642-12230-9",
  ISBN =         "3-642-12229-9 (print), 3-642-12230-2 (e-book)",
  ISBN-13 =      "978-3-642-12229-3 (print), 978-3-642-12230-9
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  LCCN =         "QA3 .L28 no. 1994",
  MRclass =      "33C10 (33-02 33C05 33C75)",
  MRnumber =     "2656410 (2011f:33007)",
  MRreviewer =   "Matti Vuorinen",
  bibdate =      "Tue May 6 14:56:34 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm2010.bib",
  series =       ser-LECT-NOTES-MATH,
  URL =          "http://link.springer.com/book/10.1007/978-3-642-12230-9;
                 http://www.springerlink.com/content/978-3-642-12230-9",
  acknowledgement = ack-nhfb,
  series-URL =   "http://link.springer.com/bookseries/304",
}

@Article{Baricz:2010:GPG,
  author =       "{\'A}rp{\'a}d Baricz",
  title =        "Geometric Properties of Generalized {Bessel}
                 Functions",
  journal =      j-LECT-NOTES-MATH,
  volume =       "1994",
  pages =        "23--69",
  year =         "2010",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/978-3-642-12230-9_2",
  ISBN =         "3-642-12229-9 (print), 3-642-12230-2 (e-book)",
  ISBN-13 =      "978-3-642-12229-3 (print), 978-3-642-12230-9
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  bibdate =      "Fri May 9 19:06:58 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm2010.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-12230-9_2.pdf",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-12230-9",
  book-URL =     "http://www.springerlink.com/content/978-3-642-12230-9",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
}

@Book{Beals:2010:SFG,
  author =       "Richard Beals and R. (Roderick) Wong",
  title =        "Special functions: a graduate text",
  volume =       "126",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "ix + 456",
  year =         "2010",
  ISBN =         "0-521-19797-X",
  ISBN-13 =      "978-0-521-19797-7",
  LCCN =         "QA351 .B34 2010; QA351 BEA 2010",
  bibdate =      "Sat Oct 30 16:43:46 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 library.ox.ac.uk:210/ADVANCE",
  series =       "Cambridge studies in advanced mathematics",
  URL =          "http://assets.cambridge.org/97805211/97977/cover/9780521197977.jpg;
                 http://www.loc.gov/catdir/enhancements/fy1009/2010017815-b.html;
                 http://www.loc.gov/catdir/enhancements/fy1009/2010017815-d.html;
                 http://www.loc.gov/catdir/enhancements/fy1009/2010017815-t.html",
  abstract =     "From the Publisher: The subject of special functions
                 is often presented as a collection of disparate
                 results, which are rarely organised in a coherent way.
                 This book answers the need for a different approach to
                 the subject. The authors' main goals are to emphasise
                 general unifying principles coherently and to provide
                 clear motivation, efficient proofs, and original
                 references for all of the principal results. The book
                 covers standard material, but also much more, including
                 chapters on discrete orthogonal polynomials and
                 elliptic functions. The authors show how a very large
                 part of the subject traces back to two equations ---
                 the hypergeometric equation and the confluent
                 hypergeometric equation --- and describe the various
                 ways in which these equations are canonical and
                 special. Providing ready access to theory and formulas,
                 this book serves as an ideal graduate-level textbook as
                 well as a convenient reference.",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Textbooks",
  tableofcontents = "Preface; 1. Orientation\\
                 2. Gamma, beta, zeta\\
                 3. Second order differential equations\\
                 4. Orthogonal polynomials\\
                 5. Discrete orthogonal polynomials\\
                 6. Confluent hypergeometric functions\\
                 7. Cylinder functions\\
                 8. Hypergeometric functions\\
                 9. Spherical functions\\
                 10. Asymptotics\\
                 11. Elliptic functions\\
                 References\\
                 Index",
}

@InProceedings{Benoit:2010:DDM,
  author =       "Alexandre Benoit and Fr{\'e}d{\'e}ric Chyzak and
                 Alexis Darrasse and Stefan Gerhold and Marc Mezzarobba
                 and Bruno Salvy",
  title =        "The Dynamic Dictionary of Mathematical Functions
                 {(DDMF)}",
  crossref =     "Fukuda:2010:MSI",
  pages =        "35--41",
  year =         "2010",
  DOI =          "https://doi.org/10.1007/978-3-642-15582-6_7",
  bibdate =      "Sat Sep 23 06:20:46 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Borghi:2010:AFE,
  author =       "Riccardo Borghi",
  title =        "Asymptotic and factorial expansions of {Euler} series
                 truncation errors via exponential polynomials",
  journal =      j-APPL-NUM-MATH,
  volume =       "60",
  number =       "12",
  pages =        "1242--1250",
  month =        dec,
  year =         "2010",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65B10 (33F05 40A25)",
  MRnumber =     "MR2735157",
  bibdate =      "Thu Dec 01 09:47:34 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
}

@Article{Brent:2010:UAE,
  author =       "Richard P. Brent",
  title =        "Unrestricted algorithms for elementary and special
                 functions",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--13",
  month =        apr,
  year =         "2010",
  bibdate =      "Sat Feb 25 10:56:45 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://arxiv.org/abs/1004.3621",
  abstract =     "We describe some ``unrestricted'' algorithms which are
                 useful for the computation of elementary and special
                 functions when the precision required is not known in
                 advance. Several general classes of algorithms are
                 identified and illustrated by examples. The topics
                 include: power series methods, use of halving
                 identities, asymptotic expansions, continued fractions,
                 recurrence relations, Newton's method, numerical
                 contour integration, and the arithmetic-geometric mean.
                 Most of the algorithms discussed are implemented in the
                 MP package.",
  acknowledgement = ack-nhfb,
}

@Article{Celledoni:2010:AFF,
  author =       "Elena Celledoni and Antonella Zanna",
  title =        "{Algorithm 903}: {FRB} --- {Fortran} routines for the
                 exact computation of free rigid body motions",
  journal =      j-TOMS,
  volume =       "37",
  number =       "2",
  pages =        "23:1--23:24",
  month =        apr,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1731022.1731033",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Apr 21 11:39:57 MDT 2010",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present two algorithms and their corresponding
                 Fortran routines for the exact computation of free
                 rigid body motions. The methods use the same
                 description of the angular momentum part $m$ by Jacobi
                 elliptic functions, and suitably chosen frames for the
                 attitude matrix\slash quaternion $ Q / q $,
                 respectively. The frame transformation requires the
                 computation of elliptic integrals of the third kind.
                 Implementation and usage of the routines are described,
                 and some examples of drivers are included. Accuracy and
                 performance are also tested to provide reliable
                 numerical results.",
  acknowledgement = ack-nhfb,
  articleno =    "23",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "attitude rotation; Jacobi elliptic integrals;
                 numerical methods; Rigid body; splitting methods",
}

@Article{Cuyt:2010:VSF,
  author =       "Annie Cuyt and Franky Backeljauw and Stefan Becuwe and
                 Joris {Van Deun}",
  title =        "Validated Special Functions Software",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "6327",
  pages =        "32--34",
  year =         "2010",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-15582-6_6",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Aug 9 15:34:11 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2010a.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-15582-6_6.pdf",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-15582-6",
  book-URL =     "http://www.springerlink.com/content/978-3-642-15582-6",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{deDinechin:2010:FPE,
  author =       "Florent de Dinechin and Bogdan Pasca",
  editor =       "Jinian Bian and Qiang Zhou and Kang Zhao",
  booktitle =    "{Proceedings 2010 International Conference on
                 Field-Programmable Technology, 8--10 December 2010,
                 Beijing, China}",
  title =        "Floating-point exponential functions for {DSP}-enabled
                 {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "110--117",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1109/FPT.2010.5681764",
  bibdate =      "Sat Feb 08 09:35:06 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Dumbgen:2010:BSG,
  author =       "L. D{\"u}mbgen",
  title =        "Bounding standard {Gaussian} tail probabilities",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "9",
  month =        dec,
  year =         "2010",
  bibdate =      "Sat Dec 16 16:24:48 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://arxiv.org/abs/1012.2063",
  acknowledgement = ack-nhfb,
}

@InProceedings{Erocal:2010:SPU,
  author =       "Bur{\c{c}}in Er{\"o}cal and William Stein",
  title =        "The {Sage Project}: Unifying Free Mathematical
                 Software to Create a Viable Alternative to {Magma},
                 {Maple}, {Mathematica} and {MATLAB}",
  crossref =     "Fukuda:2010:MSI",
  pages =        "12--27",
  year =         "2010",
  DOI =          "https://doi.org/10.1007/978-3-642-15582-6_4",
  bibdate =      "Sat Sep 23 06:20:46 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/magma.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  acknowledgement = ack-nhfb,
}

@Article{Fukushima:2010:FCI,
  author =       "Toshio Fukushima",
  title =        "Fast computation of incomplete elliptic integral of
                 first kind by half argument transformation",
  journal =      j-NUM-MATH,
  volume =       "116",
  number =       "4",
  pages =        "687--719",
  month =        oct,
  year =         "2010",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s00211-010-0321-8",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sat Oct 16 16:02:41 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=116&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=116&issue=4&spage=687",
  abstract =     "We developed a new method to calculate the incomplete
                 elliptic integral of the first kind, $ F(\varphi |m) $,
                 by using the half argument formulas of Jacobian
                 elliptic functions. The method reduces the magnitude of
                 $ \varphi $ by repeated usage of the formulas while
                 fixing $m$. The method is sufficiently precise in the
                 sense that the maximum relative error is $3$--$5$
                 machine epsilons at most. Thanks to the simplicity of
                 the half argument formulas, the new procedure is
                 significantly faster than the existing procedures. For
                 example, it runs 20--60\% faster than Bulirsch's
                 function, {\tt el1}, and 1.9--2.2 times faster than the
                 method using Carlson's function, $ R_F $.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Book{ISO:2010:IIIa,
  author =       "{ISO}",
  title =        "{ISO\slash IEC 29124:2010}: Information technology ---
                 Programming languages, their environments and system
                 software interfaces --- Extensions to the {C++ Library}
                 to support mathematical special functions",
  publisher =    pub-ISO,
  address =      pub-ISO:adr,
  year =         "2010",
  LCCN =         "????",
  bibdate =      "Thu Nov 25 08:56:44 2010",
  bibsource =    "http://www.iso.org/iso/search.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/isostd.bib",
  series =       "Technical report",
  URL =          "http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=50511",
  acknowledgement = ack-nhfb,
  subject =      "programming languages (electronic computers)",
}

@Article{Li:2010:NRB,
  author =       "Rong Li and Pooi Yuen Kam and Hua Fu",
  title =        "New representations and bounds for the generalized
                 {Marcum} {$Q$}-function via a geometric approach, and
                 an application",
  journal =      j-IEEE-TRANS-COMM,
  volume =       "58",
  number =       "1",
  pages =        "157--169",
  month =        jan,
  year =         "2010",
  CODEN =        "IECMBT",
  DOI =          "https://doi.org/10.1109/tcomm.2010.01.070426",
  ISSN =         "0090-6778 (print), 1558-0857 (electronic)",
  ISSN-L =       "0090-6778",
  bibdate =      "Sat Dec 16 16:52:49 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/5397910/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Communications",
}

@Article{Nandagopal:2010:NEF,
  author =       "Mohankumar Nandagopal and Soubhadra Sen and Ajay
                 Rawat",
  title =        "A Note on the Error Function",
  journal =      j-COMPUT-SCI-ENG,
  volume =       "12",
  number =       "4",
  pages =        "84--88",
  month =        jul # "\slash " # aug,
  year =         "2010",
  CODEN =        "CSENFA",
  DOI =          "https://doi.org/10.1109/MCSE.2010.79",
  ISSN =         "1521-9615 (print), 1558-366X (electronic)",
  ISSN-L =       "1521-9615",
  bibdate =      "Tue Jul 27 16:37:11 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See improvements \cite{Iacono:2021:BEF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing in Science and Engineering",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}

@Article{Paszkowski:2010:UMC,
  author =       "Stefan Paszkowski",
  title =        "Untypical methods of convergence acceleration",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "54",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2010",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-010-9381-1",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon May 17 14:24:01 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=0&issue=0;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=0&issue=0&spage=??",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "convergence acceleration",
  remark =       "Article in press, not yet assigned to an issue.",
}

@Article{Prevost:2010:RVZ,
  author =       "Marc Pr{\'e}vost",
  title =        "Recurrence for values of the zeta function",
  journal =      j-APPL-NUM-MATH,
  volume =       "60",
  number =       "12",
  pages =        "1382--1394",
  month =        dec,
  year =         "2010",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1016/j.apnum.2010.05.011",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Sat Oct 16 16:17:49 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Using the Pad{\'e} approximation of the exponential
                 function, we obtain a general recurrence relation for
                 values of the zeta function which contains, as
                 particular cases, many relations already proved.
                 Applications to Bernoulli polynomials are given.
                 Finally, we derive some new recurrence relations with
                 gap of length 4 for zeta numbers.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "Pad{\'e} approximants; zeta function",
}

@Article{Qi:2010:CMS,
  author =       "Feng Qi and Senlin Guo and Bai-Ni Guo",
  title =        "Complete monotonicity of some functions involving
                 polygamma functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "233",
  number =       "9",
  pages =        "2149--2160",
  day =          "1",
  month =        mar,
  year =         "2010",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:24:22 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042709006682",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Safouhi:2010:BSC,
  author =       "Hassan Safouhi",
  title =        "{Bessel}, sine and cosine functions and extrapolation
                 methods for computing molecular multi-center
                 integrals",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "54",
  number =       "1",
  pages =        "141--167",
  month =        may,
  year =         "2010",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon May 17 14:08:57 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=54&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=54&issue=1&spage=141",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Slevinsky:2010:RAT,
  author =       "Richard M. Slevinsky and Hassan Safouhi",
  title =        "A recursive algorithm for the {$G$} transformation and
                 accurate computation of incomplete {Bessel} functions",
  journal =      j-APPL-NUM-MATH,
  volume =       "60",
  number =       "12",
  pages =        "1411--1417",
  month =        dec,
  year =         "2010",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1016/j.apnum.2010.04.005",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Sat Oct 16 16:17:49 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "In the present contribution, we develop an efficient
                 algorithm for the recursive computation of the $
                 G_n^{(1)} $ source transformation for the approximation
                 of infinite-range integrals. Previous to this
                 contribution, the theoretically powerful $ G_n^{(1)} $
                 transformation was handicapped by the lack of an
                 algorithmic implementation. Our proposed algorithm
                 removes this handicap by introducing a recursive
                 computation of the successive $ G_n^{(1)} $
                 transformations with respect to the order $n$. This
                 recursion, however, introduces the $ (x^2 d / d x) $
                 source operator applied to the integrand. Consequently,
                 we employ the Slevinsky--Safouhi formula I for the
                 analytical and numerical developments of these required
                 successive derivatives.\par

                 Incomplete Bessel functions, which pose as a numerical
                 challenge, are computed to high pre-determined
                 accuracies using the developed algorithm. The numerical
                 results obtained show the high efficiency of the new
                 method, which does not resort to any numerical
                 integration in the computation.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "Extrapolation methods; Incomplete Bessel functions;
                 Nonlinear transformations; Slevinsky--Safouhi
                 formulae",
}

@InProceedings{Sofotasios:2010:NEM,
  author =       "Paschalis C. Sofotasios and Steven Freear",
  booktitle =    "2010 7th International Symposium on Wireless
                 Communication Systems",
  title =        "Novel expressions for the {Marcum} and one dimensional
                 {$Q$}-functions",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "",
  month =        sep,
  year =         "2010",
  DOI =          "https://doi.org/10.1109/iswcs.2010.5624374",
  ISBN =         "1-4244-6315-7 (print), 1-4244-6317-3 (e-book),
                 1-4244-6316-5 (CD-ROM)",
  ISBN-13 =      "978-1-4244-6315-2 (print), 978-1-4244-6317-6 (e-book),
                 978-1-4244-6316-9 (CD-ROM)",
  ISSN =         "2154-0217 (print), 2154-0225 (electronic)",
  ISSN-L =       "2154-0225",
  bibdate =      "Sat Dec 16 17:36:08 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/5624374/",
  acknowledgement = ack-nhfb,
}

@Book{Vallee:2010:AFA,
  author =       "Olivier Vall{\'e}e and Manuel Soares",
  title =        "{Airy} Functions and Applications to Physics",
  publisher =    "Imperial College Press",
  address =      "London WC26 9HE, UK",
  edition =      "Second",
  pages =        "x + 202",
  year =         "2010",
  ISBN =         "1-84816-548-X, 1-84816-550-1",
  ISBN-13 =      "978-1-84816-548-9, 978-1-84816-550-2",
  LCCN =         "QA351",
  bibdate =      "Tue Dec 5 10:05:10 MST 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Addressed mainly to physicist and chemical physicist,
                 this textbook is the result of a broad compilation of
                 current knowledge on analytical properties of Airy
                 functions. In particular, the calculus implying the
                 Airy functions is developed with care. In the latter
                 chapters, examples are given to succinctly illustrate
                 the use of Airy functions in classical and quantum
                 physics. The physicist, for instance in fluid
                 mechanics, can find what he is looking for, in the
                 references for works of molecular physics or in physics
                 of surfaces, and vice versa. The knowledge on Airy
                 functions is frequently reviewed. The reason may be
                 found in the need to express a physical phenomenon in
                 terms of an effective and comprehensive analytical form
                 for the whole scientific community.",
  acknowledgement = ack-nhfb,
  remark =       "See also first edition \cite{Vallee:2004:AFA}",
  subject =      "Airy functions; Airy-Funktion; Mathematische Physik",
  tableofcontents = "Preface / x \\
                 1: A Historical Introduction: Sir George Biddell Airy /
                 1 \\
                 2: Definitions and Properties / 5 \\
                 2.1: Homogeneous Airy functions \\
                 2.1.1: The Airy equation \\
                 2.1.2: Elementary properties \\
                 2.1.3: Integral representations \\
                 2.1.4: Ascending and asymptotic series \\
                 2.2: Properties of Airy functions \\
                 2.2.1: Zeros of Airy functions \\
                 2.2.2: The spectral zeta function \\
                 2.2.3: Inequalities \\
                 2.2.4: Connection with Bessel functions \\
                 2.2.5: Modulus and phase of Airy functions \\
                 2.3: Inhomogeneous Airy functions \\
                 2.3.1: Definitions \\
                 2.3.2: Properties of inhomogeneous Airy functions \\
                 2.3.3: Ascending series and asymptotic expansion \\
                 2.3.4: Zeros of the Scorer functions \\
                 2.4: Squares and products of Airy functions \\
                 2.4.1: Differential equation and integral
                 representation \\
                 2.4.2: A remarkable identity \\
                 2.4.3: The product $\Ai(x) \Ai(-x)$: Airy wavelets \\
                 3: Primitives and Integrals of Airy Functions / 37 \\
                 3.1: Primitives containing one Airy function \\
                 3.1.1: In terms of Airy functions \\
                 3.1.2: Ascending series \\
                 3.1.3: Asymptotic expansions \\
                 3.1.4: Primitives of Scorer functions \\
                 3.1.5: Repeated primitives \\
                 3.2: Product of Airy functions \\
                 3.2.1: The method of Albright \\
                 3.2.2: Some primitives \\
                 3.3: Other primitives \\
                 3.4: Miscellaneous \\
                 3.5: Elementary integrals \\
                 3.5.1: Particular integrals \\
                 3.5.2: Integrals containing a single Airy function \\
                 3.5.3: Integrals of products of two Airy functions \\
                 3.6: Other integrals \\
                 3.6.1: Integrals involving the Volterra $\mu$-function
                 \\
                 3.6.2: Canonisation of cubic forms \\
                 3.6.3: Integrals with three Airy functions \\
                 3.6.4: Integrals with four Airy functions \\
                 3.6.5: Double integrals \\
                 4: Transformations of Airy functions / 69 \\
                 4.1: Causal properties of Airy functions \\
                 4.1.1: Causal relations \\
                 4.1.2: Green's function of the Airy equation \\
                 4.1.3: Fractional derivatives of Airy functions \\
                 4.2: The Airy transform \\
                 4.2.1: Definitions and elementary properties \\
                 4.2.2: Some examples \\
                 4.2.3: Airy polynomials \\
                 4.2.4: A particular case: correlation Airy transform
                 \\
                 4.3: Other kinds of transformations \\
                 4.3.1: Laplace transform of Airy functions \\
                 4.3.2: Mellin transform of Airy functions \\
                 4.3.3: Fourier transform of Airy functions \\
                 4.3.4: Hankel transform and the Airy kernel \\
                 4.4: Expansion into Fourier--Airy series \\
                 5: The Uniform Approximation / 101 \\
                 5.1: Oscillating integrals \\
                 5.1.1: The method of stationary phase \\
                 5.1.2: The uniform approximation of oscillating
                 integrals \\
                 5.1.3: The Airy uniform approximation \\
                 5.2: Differential equations of the second order \\
                 5.2.1: The JWKB method \\
                 5.2.2: The Langer generalisation \\
                 5.3: Inhomogeneous differential equations \\
                 6: Generalisation of Airy Functions / 111 \\
                 6.1: Generalisation of the Airy integral \\
                 6.1.1: The generalisation of Watson \\
                 6.1.2: Oscillating integrals and catastrophes \\
                 6.2: Third order differential equations \\
                 6.2.1: The linear third order differential equation \\
                 6.2.2: Asymptotic solutions \\
                 6.2.3: The comparison equation \\
                 6.3: A differential equation of the fourth order \\
                 7: Applications to Classical Physics / 127 \\
                 7.1: Optics and electromagnetism \\
                 7.2: Fluid mechanics \\
                 7.2.1: The Tricomi equation \\
                 7.2.2: The Orr--Sommerfeld equation \\
                 7.3: Elasticity \\
                 7.4: The heat equation \\
                 7.5: Nonlinear physics \\
                 7.5.1: Korteweg--de Vries equation \\
                 7.5.2: The Second Painlev{\'e} equation \\
                 8: Applications to Quantum Physics / 147 \\
                 8.1: The Schr{\"o}dinger equation \\
                 8.1.1: Particle in a Uniform field \\
                 8.1.2: The 8.1.3: Uniform approximation of the
                 Schr{\"o}dinger equation \\
                 8.2: Evaluation of the Franck--Condon factors \\
                 8.2.1: The Franck--Condon principle \\
                 8.2.2: The JWKB approximation \\
                 8.2.3: The uniform approximation \\
                 8.3: The semiclassical Wigner distribution \\
                 8.3.1: The Weyl--Wigner formalism \\
                 8.3.2: The one-dimensional Wigner distribution \\
                 8.3.3: The two-dimensional Wigner distribution \\
                 8.3.4: Configuration of the Wigner distribution \\
                 8.4: Airy transform of the Schr{\"o}dinger equation \\
                 Appendix A: Numerical Computation of the Airy Functions
                 / 185 \\
                 A.1: Homogeneous functions \\
                 A.2: Inhomogeneous functions \\
                 Bibliography / 191 \\
                 Index / 201",
}

@Article{Weniger:2010:SDP,
  author =       "E. J. Weniger",
  title =        "Summation of divergent power series by means of
                 factorial series",
  journal =      j-APPL-NUM-MATH,
  volume =       "60",
  number =       "12",
  pages =        "1429--1441",
  month =        "????",
  year =         "2010",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Thu Dec 01 10:37:55 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Presented at Approximation and Extrapolation of
                 Convergent and Divergent Sequences and Series (CIRM,
                 Luminy --- France, 2009).",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
}

@Article{Wozny:2010:EAS,
  author =       "Pawe{\l} Wo{\'z}ny",
  title =        "Efficient algorithm for summation of some slowly
                 convergent series",
  journal =      j-APPL-NUM-MATH,
  volume =       "60",
  number =       "12",
  pages =        "1442--1453",
  month =        "????",
  year =         "2010",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Thu Dec 01 09:26:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Presented at Approximation and Extrapolation of
                 Convergent and Divergent Sequences and Series (CIRM,
                 Luminy - France, 2009).",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}

@Article{Zhu:2010:JTI,
  author =       "Ling Zhu",
  title =        "{Jordan} type inequalities involving the {Bessel} and
                 modified {Bessel} functions",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "59",
  number =       "2",
  pages =        "724--736",
  month =        jan,
  year =         "2010",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:50:34 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122109007196",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Ali:2011:NGJ,
  author =       "Ahmad T. Ali",
  title =        "New generalized {Jacobi} elliptic function rational
                 expansion method",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "235",
  number =       "14",
  pages =        "4117--4127",
  day =          "15",
  month =        may,
  year =         "2011",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/j.cam.2011.03.002",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:24:28 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042711001257",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Borwein:2011:SVG,
  author =       "Jonathan M. Borwein and Armin Straub",
  title =        "Special values of generalized log-sine integrals",
  crossref =     "Schost:2011:IPI",
  pages =        "43--50",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1993886.1993899",
  bibdate =      "Fri Mar 14 12:20:08 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/issac.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  abstract =     "We study generalized log-sine integrals at special
                 values. At $ \pi $ and multiples thereof explicit
                 evaluations are obtained in terms of Nielsen
                 polylogarithms at $ \pm 1 $. For general arguments we
                 present algorithmic evaluations involving Nielsen
                 polylogarithms at related arguments. In particular, we
                 consider log-sine integrals at $ \pi / 3 $ which
                 evaluate in terms of polylogarithms at the sixth root
                 of unity. An implementation of our results for the
                 computer algebra systems Mathematica and SAGE is
                 provided.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brisebarre:2011:APS,
  author =       "Nicolas Brisebarre and Mioara Joldes and Peter
                 Kornerup and {\'E}rik Martin-Dorel and Jean-Michel
                 Muller",
  title =        "Augmented Precision Square Roots and {$2$-D} Norms,
                 and Discussion on Correctly Rounding $ \sqrt {x^2 +
                 y^2} $",
  crossref =     "Schwarz:2011:PIS",
  pages =        "23--30",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.13",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992105",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20; hypotenuse",
}

@InProceedings{Butts:2011:RDR,
  author =       "J. Adam Butts and Ping Tak Peter Tang and Ron O. Dror
                 and David E. Shaw",
  title =        "Radix-8 Digit-by-Rounding: Achieving High-Performance
                 Reciprocals, Square Roots, and Reciprocal Square
                 Roots",
  crossref =     "Schwarz:2011:PIS",
  pages =        "149--158",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.28",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992120",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@Article{Cai:2011:CSB,
  author =       "Liang-Wu Cai",
  title =        "On the computation of spherical {Bessel} functions of
                 complex arguments",
  journal =      j-COMP-PHYS-COMM,
  volume =       "182",
  number =       "3",
  pages =        "663--668",
  month =        mar,
  year =         "2011",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2010.11.019",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 11 10:10:56 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465510004650",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Cardoso:2011:IFP,
  author =       "Jo{\~a}o Ribeiro Cardoso and Ana F. Loureiro",
  title =        "Iteration functions for $p$ th roots of complex
                 numbers",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "57",
  number =       "3",
  pages =        "329--356",
  month =        jul,
  year =         "2011",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Fri Jul 22 09:48:58 MDT 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=57&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=57&issue=3&spage=329",
  abstract =     "A novel way of generating higher-order iteration
                 functions for the computation of pth roots of complex
                 numbers is the main contribution of the present work.
                 The behavior of some of these iteration functions will
                 be analyzed and the conditions on the starting values
                 that guarantee the convergence will be stated. The
                 illustration of the basins of attractions of the pth
                 roots will be carried out by some computer generated
                 plots. In order to compare the performance of the
                 iterations some numerical examples will be
                 considered.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Chang:2011:CTB,
  author =       "Seok-Ho Chang and Pamela C. Cosman and Laurence B.
                 Milstein",
  title =        "{Chernoff}-Type Bounds for the {Gaussian} Error
                 Function",
  journal =      j-IEEE-TRANS-COMM,
  volume =       "59",
  number =       "11",
  pages =        "2939--2944",
  month =        nov,
  year =         "2011",
  CODEN =        "IECMBT",
  DOI =          "https://doi.org/10.1109/tcomm.2011.072011.100049",
  ISSN =         "0090-6778 (print), 1558-0857 (electronic)",
  ISSN-L =       "0090-6778",
  bibdate =      "Fri Jul 22 09:48:58 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Communications",
}

@Article{Chen:2011:SPF,
  author =       "Chao-Ping Chen",
  title =        "Some properties of functions related to the gamma, psi
                 and tetragamma functions",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "62",
  number =       "9",
  pages =        "3389--3395",
  month =        nov,
  year =         "2011",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:51:02 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122111007267",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@InProceedings{Chen:2011:TSA,
  author =       "Jianxun Chen and Yongzhong Huang and Shaozhong Guo and
                 Shimiao Chen and Wei Wang",
  booktitle =    "{2011 Third International Conference on Measuring
                 Technology and Mechatronics Automation (ICMTMA)}",
  title =        "Test Standardization and Analyse Model of Mathematical
                 Functions for Precision",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "652--655",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ICMTMA.2011.734",
  ISBN =         "0-7695-4296-4",
  ISBN-13 =      "978-0-7695-4296-6",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5721571",
  abstract =     "This article describes problems of meet the
                 requirements to implementations of mathematical
                 functions working with floating-point numbers, and so
                 facilitate the comprehensive testing of mathematical
                 functions. Inconsistency and incompleteness of
                 available standards in the domain is demonstrated.
                 Correct rounding requirement is suggested to guarantee
                 preservation of all important properties of functions
                 and to support high level of interoperability between
                 different mathematical libraries and software using
                 them. The article also concerns precision analyse of
                 mathematical functions. Conformance test construction
                 method is proposed based on different sources of test
                 data.",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5720445",
  remark =       "This paper contains unattributed plagiaristic copying
                 of material from
                 \url{https://www.math.utah.edu/~beebe/software/ieee/index.html}.",
}

@Article{Chlebus:2011:RSI,
  author =       "Edward Chlebus",
  title =        "A Recursive Scheme for Improving the Original Rate of
                 Convergence to the {Euler--Mascheroni} Constant",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "118",
  number =       "3",
  pages =        "268--274",
  month =        mar,
  year =         "2011",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.118.03.268",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jan 30 08:58:19 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00029890.html;
                 http://www.jstor.org/stable/10.4169/amermathmont.118.issue-3;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.118.03.268.pdf",
  abstract =     "We have used Euler--Maclaurin summation to develop a
                 recursive scheme for modifying the original
                 approximation for the Euler--Mascheroni constant $
                 \gamma $. Convergence to $ \gamma $ resulting from
                 successively employing the proposed scheme has been
                 significantly accelerated while the form of the
                 approximation originally introduced by Euler is still
                 preserved.",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  remark =       "The author derives relations between $ \gamma $ and
                 the $n$-th partial sum of the harmonic series that have
                 an error $ O(n^{-2 k}) $ for increasing $k$. He also
                 references prior work from 2009 that computes $ \gamma
                 $ to 29,844,489,545 decimal digits.",
}

@Article{Choi:2011:AFT,
  author =       "Junesang Choi and H. M. Srivastava",
  title =        "Asymptotic formulas for the triple {Gamma} function {$
                 \Gamma_3 $} by means of its integral representation",
  journal =      j-APPL-MATH-COMP,
  volume =       "218",
  number =       "6",
  pages =        "2631--2640",
  day =          "15",
  month =        nov,
  year =         "2011",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2011.08.002",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Oct 25 09:03:08 MDT 2011",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300311010289",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Colman:2011:VCC,
  author =       "Michel Colman and Annie Cuyt and Joris {Van Deun}",
  title =        "Validated computation of certain hypergeometric
                 functions",
  journal =      j-TOMS,
  volume =       "38",
  number =       "2",
  pages =        "11:1--11:20",
  month =        dec,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049673.2049675",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 30 17:43:07 MST 2011",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present an efficient algorithm for the validated
                 high-precision computation of real continued fractions,
                 accurate to the last digit. The algorithm proceeds in
                 two stages. In the first stage, computations are done
                 in double precision. A forward error analysis and some
                 heuristics are used to obtain an a priori error
                 estimate. This estimate is used in the second stage to
                 compute the fraction to the requested accuracy in high
                 precision (adaptively incrementing the precision for
                 reasons of efficiency). A running error analysis and
                 techniques from interval arithmetic are used to
                 validate the result.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{deDinechin:2011:CFP,
  author =       "Florent de Dinechin and Christoph Lauter and Guillaume
                 Melquiond",
  title =        "Certifying the Floating-Point Implementation of an
                 Elementary Function Using {Gappa}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "242--253",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.128",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "High confidence in floating-point programs requires
                 proving numerical properties of final and intermediate
                 values. One may need to guarantee that a value stays
                 within some range, or that the error relative to some
                 ideal value is well bounded. This certification may
                 require a time-consuming proof for each line of code,
                 and it is usually broken by the smallest change to the
                 code, e.g., for maintenance or optimization purpose.
                 Certifying floating-point programs by hand is,
                 therefore, very tedious and error-prone. The Gappa
                 proof assistant is designed to make this task both
                 easier and more secure, due to the following novel
                 features: It automates the evaluation and propagation
                 of rounding errors using interval arithmetic. Its input
                 format is very close to the actual code to validate. It
                 can be used incrementally to prove complex mathematical
                 properties pertaining to the code. It generates a
                 formal proof of the results, which can be checked
                 independently by a lower level proof assistant like
                 Coq. Yet it does not require any specific knowledge
                 about automatic theorem proving, and thus, is
                 accessible to a wide community. This paper demonstrates
                 the practical use of this tool for a widely used class
                 of floating-point programs: implementations of
                 elementary functions in a mathematical library.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Fu:2011:ETB,
  author =       "Hua Fu and Pooi-Yuen Kam",
  booktitle =    "2011 {IEEE} Global Telecommunications Conference ---
                 {GLOBECOM 2011}",
  title =        "Exponential-Type Bounds on the First-Order {Marcum}
                 Q-Function",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  month =        dec,
  year =         "2011",
  DOI =          "https://doi.org/10.1109/glocom.2011.6133801",
  bibdate =      "Sat Dec 16 16:28:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/6133801/",
  acknowledgement = ack-nhfb,
}

@Article{Fukushima:2011:PFC,
  author =       "Toshio Fukushima",
  title =        "Precise and fast computation of the general complete
                 elliptic integral of the second kind",
  journal =      j-MATH-COMPUT,
  volume =       "80",
  number =       "275",
  pages =        "1725--1743",
  month =        jul,
  year =         "2011",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon Apr 18 06:32:30 MDT 2011",
  bibsource =    "http://www.ams.org/mcom/2011-80-275;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02455-5/home.html;
                 http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02455-5/S0025-5718-2011-02455-5.pdf",
  abstract =     "We developed an efficient procedure to evaluate two
                 auxiliary complete elliptic integrals of the second
                 kind $ B(m) $ and $ D(m) $ by using their Taylor series
                 expansions, the definition of Jacobi's nome, and
                 Legendre's relation. The developed procedure is more
                 precise than the existing ones in the sense that the
                 maximum relative errors are 1--3 machine epsilons, and
                 it runs drastically faster; around 5 times faster than
                 Bulirsch's cel2 and 16 times faster than Carlson's $
                 R_F $ and $ R_D $.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Gautschi:2011:LWF,
  author =       "Walter Gautschi",
  title =        "The {Lambert} {$W$}-functions and some of their
                 integrals: a case study of high-precision computation",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "57",
  number =       "1",
  pages =        "27--34",
  month =        may,
  year =         "2011",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-010-9409-6",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Apr 27 08:44:14 MDT 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=57&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=57&issue=1&spage=27",
  abstract =     "The real-valued Lambert W-functions considered here
                 are $ w_0 (y) $ and $ w_{-1}(y) $, solutions of $ w e^w
                 = y $, $ - 1 / e < y < 0 $, with values respectively in
                 $ ( - 1, 0) $ and $ ( - \infty, - 1) $. A study is made
                 of the numerical evaluation to high precision of these
                 functions and of the integrals, $ \alpha > 0 $, $ \beta
                 \in \mathbb {R} $, and $ \alpha > - 1 $, $ \beta < 1 $.
                 For the latter we use known integral representations
                 and their evaluation by nonstandard Gaussian
                 quadrature, if $ \alpha \neq \beta $, and explicit
                 formulae involving the trigamma function, if $ \alpha =
                 \beta $.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Integrals of Lambert W-functions; Lambert W-functions;
                 Nonstandard Gaussian quadrature; Variable-precision
                 computation",
}

@Article{Gil:2011:APC,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 914}: {Parabolic} cylinder function {$ W(a,
                 x) $} and its derivative",
  journal =      j-TOMS,
  volume =       "38",
  number =       "1",
  pages =        "6:1--6:5",
  month =        nov,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049662.2049668",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 15 08:59:34 MST 2011",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A Fortran 90 program for the computation of the real
                 parabolic cylinder functions $ W(a, \pm x) $, $ x \geq
                 0 $ and their derivatives is presented. The code also
                 computes scaled functions for $ a > 50 $. The functions
                 $ W(a, \pm x) $ are a numerically satisfactory pair of
                 solutions of the parabolic cylinder equation $ y^\prime
                 + (x^2 / 4 - a)y = 0 $, $ x \geq 0 $. Using Wronskian
                 tests, we claim a relative accuracy better than $ 5
                 \times 10^{-13} $ in the computable range of unscaled
                 functions, while for scaled functions the aimed
                 relative accuracy is better than $ 5 \times 10^{-14} $.
                 This code, together with the algorithm and related
                 software described in Gil et al.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gil:2011:FAC,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Fast and accurate computation of the {Weber} parabolic
                 cylinder function {$ W(a, x) $}",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "31",
  number =       "3",
  pages =        "1194--1216",
  month =        jul,
  year =         "2011",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/drq012",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  bibdate =      "Fri Jul 15 12:37:42 MDT 2011",
  bibsource =    "http://imanum.oxfordjournals.org/content/31/3.toc;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://imajna.oxfordjournals.org/content/31/3/1194.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  onlinedate =   "July 7, 2010",
}

@Article{Jaime:2011:HSA,
  author =       "F. J. Jaime and M. A. S{\'a}nchez and J. Hormigo and
                 J. Villalba and E. L. Zapata",
  title =        "High-Speed Algorithms and Architectures for Range
                 Reduction Computation",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "19",
  number =       "3",
  pages =        "512--516",
  month =        "????",
  year =         "2011",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2009.2033932",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5308221",
  abstract =     "Range reduction is a crucial step for accuracy in
                 trigonometric functions evaluation. This paper shows
                 and compares a set of algorithms for additive range
                 reduction computation and their corresponding
                 application-specific integrated circuit implementations
                 (ensuring an accuracy of one unit in the last place). A
                 word-serial architecture implementation has been used
                 as a reference for clearer comparisons. Besides, a new
                 table-based pipelined architecture for range reduction
                 has also been proposed.",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=92",
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
}

@Article{Jang:2011:CTS,
  author =       "Won Mee Jang",
  title =        "Corrections to {``A Simple Upper Bound of the Gaussian
                 $Q$-Function with Closed-form Error Bound''}",
  journal =      j-IEEE-COMMUN-LET,
  volume =       "15",
  number =       "12",
  pages =        "1274--1274",
  month =        dec,
  year =         "2011",
  CODEN =        "ICLEF6",
  DOI =          "https://doi.org/10.1109/lcomm.2011.101911.111996",
  ISSN =         "1089-7798 (print), 1558-2558 (electronic)",
  ISSN-L =       "1089-7798",
  bibdate =      "Sat Dec 16 16:46:05 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/6065242/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Communications Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}

@Article{Jang:2011:SUB,
  author =       "Won Mee Jang",
  title =        "A Simple Upper Bound of the {Gaussian} {$Q$}-Function
                 with Closed-Form Error Bound",
  journal =      j-IEEE-COMMUN-LET,
  volume =       "15",
  number =       "2",
  pages =        "157--159",
  month =        feb,
  year =         "2011",
  CODEN =        "ICLEF6",
  DOI =          "https://doi.org/10.1109/lcomm.2011.011011.102207",
  ISSN =         "1089-7798 (print), 1558-2558 (electronic)",
  ISSN-L =       "1089-7798",
  bibdate =      "Sat Dec 16 16:47:28 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/5692888/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Communications Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}

@Article{Jeannerod:2011:CFP,
  author =       "Claude-Pierre Jeannerod and Herv{\'e} Knochel and
                 Christophe Monat and Guillaume Revy",
  title =        "Computing Floating-Point Square Roots via Bivariate
                 Polynomial Evaluation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "214--227",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.152",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  abstract =     "In this paper, we show how to reduce the computation
                 of correctly rounded square roots of binary
                 floating-point data to the fixed-point evaluation of
                 some particular integer polynomials in two variables.
                 By designing parallel and accurate evaluation schemes
                 for such bivariate polynomials, we show further that
                 this approach allows for high instruction-level
                 parallelism (ILP) exposure, and thus, potentially
                 low-latency implementations. Then, as an illustration,
                 we detail a C implementation of our method in the case
                 of IEEE 754-2008 binary32 floating-point data (formerly
                 called single precision in the 1985 version of the IEEE
                 754 standard). This software implementation, which
                 assumes 32-bit unsigned integer arithmetic only, is
                 almost complete in the sense that it supports special
                 operands, subnormal numbers, and all rounding-direction
                 attributes, but not exception handling (that is, status
                 flags are not set). Finally, we have carried out
                 experiments with this implementation on the ST231, an
                 integer processor from the STMicroelectronics' ST200
                 family, using the ST200 family VLIW compiler. The
                 results obtained demonstrate the practical interest of
                 our approach in that context: for all
                 rounding-direction attributes, the generated assembly
                 code is optimally scheduled and has indeed low latency
                 (23 cycles).",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Johansson:2011:CRE,
  author =       "Bo G{\"o}ran Johansson",
  title =        "Cube root extraction in medieval mathematics",
  journal =      j-HIST-MATH,
  volume =       "38",
  number =       "3",
  pages =        "338--367",
  month =        aug,
  year =         "2011",
  CODEN =        "HIMADS",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Jun 26 06:21:13 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0315086010000546",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
}

@Article{Knessl:2011:EAF,
  author =       "Charles Knessl and Mark W. Coffey",
  title =        "An effective asymptotic formula for the {Stieltjes}
                 constants",
  journal =      j-MATH-COMPUT,
  volume =       "80",
  number =       "273",
  pages =        "379--386",
  month =        jan,
  year =         "2011",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-2010-02390-7",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Wed Oct 13 16:46:42 MDT 2010",
  bibsource =    "http://www.ams.org/mcom/2011-80-273;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/journals/mcom/2011-80-273/S0025-5718-2010-02390-7/home.html;
                 http://www.ams.org/journals/mcom/2011-80-273/S0025-5718-2010-02390-7/S0025-5718-2010-02390-7.pdf",
  abstract =     "The Stieltjes constants $ \gamma_k $ appear in the
                 coefficients in the regular part of the Laurent
                 expansion of the Riemann zeta function $ \zeta (s) $
                 about its only pole at $ s = 1 $. We present an
                 asymptotic expression for $ \gamma_k $ for $ k \gg 1 $.
                 This form encapsulates both the leading rate of growth
                 and the oscillations with $k$. Furthermore, our result
                 is effective for computation, consistently in close
                 agreement (for both magnitude and sign) for even
                 moderate values of $k$. Comparison to some earlier work
                 is made.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Kodama:2011:AMC,
  author =       "Masao Kodama",
  title =        "{Algorithm 912}: a Module for Calculating Cylindrical
                 Functions of Complex Order and Complex Argument",
  journal =      j-TOMS,
  volume =       "37",
  number =       "4",
  pages =        "47:1--47:25",
  month =        feb,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1916461.1916471",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 16:05:18 MST 2011",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The present algorithm provides a module for
                 calculating the cylindrical functions $ J_\nu (z) $, $
                 Y_\nu (z) $, $ H_{\nu (1)}(z) $, and $ H_{\nu (2)}(z)
                 $, where the order $ \nu $ is complex and the complex
                 argument $z$ satisfies $ - \pi < \arg z \leq \pi $. The
                 algorithm is written in Fortran 90 and calculates the
                 functions using real and complex numbers of any
                 intrinsic data type whose kind type parameter the
                 user's Fortran system accepts. The methods of
                 calculating the functions are based on two kinds of
                 series expansions and numerical integration. Wronskian
                 tests examine the functional values computed by this
                 algorithm with double precision at 4,100,625
                 pseudorandom test points in the region $ | \Re \nu |
                 \leq 60 $, $ | \Im \nu | \leq 60 $, $ | \Re z| \leq 300
                 $, $ | \Im z| \leq 300 $.",
  acknowledgement = ack-nhfb,
  articleno =    "47",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kormanyos:2011:APC,
  author =       "Christopher Kormanyos",
  title =        "{Algorithm 910}: a Portable {C++} Multiple-Precision
                 System for Special-Function Calculations",
  journal =      j-TOMS,
  volume =       "37",
  number =       "4",
  pages =        "45:1--45:27",
  month =        feb,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1916461.1916469",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 16:05:18 MST 2011",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article presents a portable C++ system for
                 multiple precision calculations of special functions
                 called {\tt e\_float}. It has an extendable
                 architecture with a uniform C++ layer which can be used
                 with any suitably prepared MP type. The system
                 implements many high-precision special functions and
                 extends some of these to very large parameter ranges.
                 It supports calculations with 30 \ldots{} 300 decimal
                 digits of precision. Interoperabilities with
                 Microsoft's CLR, Python, and Mathematica{\reg} are
                 supported. The {\tt e\_float} system and its usage are
                 described in detail. Implementation notes, testing
                 results, and performance measurements are provided.",
  acknowledgement = ack-nhfb,
  articleno =    "45",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lopez-Benitez:2011:VAA,
  author =       "Miguel L{\"o}pez-Benitez and Fernando Casadevall",
  title =        "Versatile, Accurate, and Analytically Tractable
                 Approximation for the {Gaussian} {$Q$}-Function",
  journal =      j-IEEE-TRANS-COMM,
  volume =       "59",
  number =       "4",
  pages =        "917--922",
  month =        apr,
  year =         "2011",
  CODEN =        "IECMBT",
  DOI =          "https://doi.org/10.1109/tcomm.2011.012711.100105",
  ISSN =         "0090-6778 (print), 1558-0857 (electronic)",
  ISSN-L =       "0090-6778",
  bibdate =      "Sat Dec 16 17:01:00 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/5706433/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Communications",
}

@Article{Mortici:2011:IAF,
  author =       "Cristinel Mortici",
  title =        "Improved asymptotic formulas for the gamma function",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "61",
  number =       "11",
  pages =        "3364--3369",
  month =        jun,
  year =         "2011",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/j.camwa.2011.04.036",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:50:47 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122111003373",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@InProceedings{Nannarelli:2011:RCD,
  author =       "Alberto Nannarelli",
  title =        "Radix-16 Combined Division and Square Root Unit",
  crossref =     "Schwarz:2011:PIS",
  pages =        "169--176",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.30",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992122",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20; sqrt(x); square root",
}

@Article{Paszkowski:2011:UMC,
  author =       "Stefan Paszkowski",
  title =        "Untypical methods of convergence acceleration",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "56",
  number =       "2",
  pages =        "185--209",
  month =        "????",
  year =         "2011",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65B10 (33C20 33E05 41Axx)",
  MRnumber =     "MR2755669",
  bibdate =      "Thu Dec 01 09:27:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "convergence acceleration",
}

@Article{Pawellek:2011:GJE,
  author =       "Michael Pawellek",
  title =        "On a generalization of {Jacobi}'s elliptic functions
                 and the double {sine--Gordon} kink chain",
  journal =      j-J-MATH-PHYS,
  volume =       "52",
  number =       "11",
  pages =        "113701",
  month =        nov,
  year =         "2011",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.3656873",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Wed Jan 4 08:04:23 MST 2012",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2010.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v52/i11/p113701_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  onlinedate =   "4 November 2011",
  pagecount =    "18",
}

@Article{Pegoraro:2011:ECV,
  author =       "Vincent Pegoraro and Philipp Slusallek",
  title =        "On the Evaluation of the Complex-Valued Exponential
                 Integral",
  journal =      j-J-GRAPHICS-GPU-GAME-TOOLS,
  volume =       "15",
  number =       "3",
  pages =        "183--198",
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/2151237X.2011.617177",
  ISSN =         "2151-237X",
  bibdate =      "Wed Dec 14 10:31:39 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jgraphtools.bib",
  abstract =     "Although its applications span a broad scope of
                 scientific fields ranging from applied physics to
                 computer graphics, the exponential integral is a
                 nonelementary special function available in specialized
                 software packages but not in standard libraries,
                 consequently requiring custom implementations on most
                 platforms. In this paper, we provide a concise and
                 comprehensive description of how to evaluate the
                 complex-valued exponential integral. We first introduce
                 some theoretical background on the main characteristics
                 of the function, and outline available third-party
                 proprietary implementations. We then provide an
                 analysis of the various known representations of the
                 function and present an effective algorithm allowing
                 the computation of results within a desired accuracy,
                 together with the corresponding pseudocode in order to
                 facilitate portability onto various systems. An
                 application to the calculation of the closed-form
                 solution to single light scattering in homogeneous
                 participating media illustrates the practical benefits
                 of the provided implementation with the hope that, in
                 the long term, the latter will contribute to
                 standardizing the availability of the complex-valued
                 exponential integral on graphics platforms.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.tandfonline.com/loi/ujgt20",
  onlinedate =   "21 Oct 2011",
}

@Article{Shi:2011:AEA,
  author =       "Qinghua Shi and Y. Karasawa",
  title =        "An Accurate and Efficient Approximation to the
                 {Gaussian} {$Q$}-Function and its Applications in
                 Performance Analysis in {Nakagami}-$m$ Fading",
  journal =      j-IEEE-COMMUN-LET,
  volume =       "15",
  number =       "5",
  pages =        "479--481",
  month =        may,
  year =         "2011",
  CODEN =        "ICLEF6",
  DOI =          "https://doi.org/10.1109/lcomm.2011.032111.102440",
  ISSN =         "1089-7798 (print), 1558-2558 (electronic)",
  ISSN-L =       "1089-7798",
  bibdate =      "Sat Dec 16 17:32:51 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/5740503/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Communications Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
}

@Article{Smith:2011:AMP,
  author =       "David M. Smith",
  title =        "{Algorithm 911}: Multiple-Precision Exponential
                 Integral and Related Functions",
  journal =      j-TOMS,
  volume =       "37",
  number =       "4",
  pages =        "46:1--46:16",
  month =        feb,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1916461.1916470",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 16:05:18 MST 2011",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article describes a collection of Fortran-95
                 routines for evaluating the exponential integral
                 function, error function, sine and cosine integrals,
                 Fresnel integrals, Bessel functions, and related
                 mathematical special functions using the FM
                 multiple-precision arithmetic package.",
  acknowledgement = ack-nhfb,
  articleno =    "46",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Srivastava:2011:ADZ,
  author =       "H. M. Srivastava and Jian-Rong Zhou and Zhi-Gang
                 Wang",
  title =        "Asymptotic distributions of the zeros of certain
                 classes of hypergeometric functions and polynomials",
  journal =      j-MATH-COMPUT,
  volume =       "80",
  number =       "275",
  pages =        "1769--1784",
  month =        jul,
  year =         "2011",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon Apr 18 06:32:30 MDT 2011",
  bibsource =    "http://www.ams.org/mcom/2011-80-275;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02409-9/home.html;
                 http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-02409-9/S0025-5718-2011-02409-9.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Strollo:2011:EFH,
  author =       "Antonio Giuseppe Maria Strollo and Davide {De Caro}
                 and Nicola Petra",
  title =        "Elementary Functions Hardware Implementation Using
                 Constrained Piecewise-Polynomial Approximations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  pages =        "418--432",
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.127",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:10:07 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "A novel technique for designing piecewise-polynomial
                 interpolators for hardware implementation of elementary
                 functions is investigated in this paper. In the
                 proposed approach, the interval where the function is
                 approximated is subdivided in equal length segments and
                 two adjacent segments are grouped in a segment pair.
                 Suitable constraints are then imposed between the
                 coefficients of the two interpolating polynomials in
                 each segment pair. This allows reducing the total
                 number of stored coefficients. It is found that the
                 increase in the approximation error due to constraints
                 between polynomial coefficients can easily be overcome
                 by increasing the fractional bits of the coefficients.
                 Overall, compared with standard unconstrained
                 piecewise-polynomial approximation having the same
                 accuracy, the proposed method results in a considerable
                 advantage in terms of the size of the lookup table
                 needed to store polynomial coefficients. The calculus
                 of the coefficients of constrained polynomials and the
                 optimization of coefficients bit width is also
                 investigated in this paper. Results for several
                 elementary functions and target precision ranging from
                 12 to 42 bits are presented. The paper also presents
                 VLSI implementation results, targeting a 90 nm CMOS
                 technology, and using both direct and Horner
                 architectures for constrained degree-1, degree-2, and
                 degree-3 approximations.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "computer arithmetic; elementary functions; min-max
                 approximation; polynomial approximation; VLSI
                 systems.",
}

@InProceedings{Tang:2011:TCT,
  author =       "Ping Tak Peter Tang and J. Adam Butts and Ron O. Dror
                 and David E. Shaw",
  title =        "Tight Certification Techniques for Digit-by-Rounding
                 Algorithms with Application to a New $ 1 / \sqrt {x} $
                 Design",
  crossref =     "Schwarz:2011:PIS",
  pages =        "159--168",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.29",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992121",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20; reciprocal square root; rsqrt(x)",
}

@Article{Trudgian:2011:ITM,
  author =       "Timothy Trudgian",
  title =        "Improvements to {Turing}'s method",
  journal =      j-MATH-COMPUT,
  volume =       "80",
  number =       "276",
  pages =        "2259--2279",
  month =        oct,
  year =         "2011",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon Oct 24 10:33:34 MDT 2011",
  bibsource =    "http://www.ams.org/mcom/2011-80-276;
                 https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  note =         "See \cite{Turing:1953:SCR,Lehman:1970:DZR}.",
  URL =          "http://www.ams.org/journals/mcom/2011-80-276/S0025-5718-2011-02470-1/home.html;
                 http://www.ams.org/journals/mcom/2011-80-276/S0025-5718-2011-02470-1/S0025-5718-2011-02470-1.pdf;
                 http://www.ams.org/mathscinet-getitem?mr=2813359",
  abstract =     "This article improves the estimate of the size of the
                 definite integral of {$ S(t) $}, the argument of the
                 Riemann zeta-function. The primary application of this
                 improvement is Turing's Method for the Riemann
                 zeta-function. Analogous improvements are given for the
                 arguments of Dirichlet {$L$}-functions and of Dedekind
                 zeta-functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{VanDeun:2011:RIC,
  author =       "Joris {Van Deun} and Lloyd N. Trefethen",
  title =        "A robust implementation of the
                 {Carath{\'e}odory-Fej{\'e}r} method for rational
                 approximation",
  journal =      j-BIT-NUM-MATH,
  volume =       "51",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2011",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-011-0331-7",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Thu Sep 29 07:17:26 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/content/ag2514840142707r/",
  abstract =     "Best rational approximations are notoriously difficult
                 to compute. However, the difference between the best
                 rational approximation to a function and its
                 Carath{\'e}odory-Fej{\'e}r (CF) approximation is often
                 so small as to be negligible in practice, while CF
                 approximations are far easier to compute. We present a
                 robust and fast implementation of this method in the
                 Chebfun software system and illustrate its use with
                 several examples. Our implementation handles both
                 polynomial and rational approximation and substantially
                 improves upon earlier published software.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "Carath{\'e}odory-Fej{\'e}r approximation; Chebfun;
                 Near-best rational approximation",
  onlinedate =   "04 May 2011",
}

@Article{Veling:2011:GIG,
  author =       "E. J. M. Veling",
  title =        "The Generalized Incomplete Gamma Function as sum over
                 Modified {Bessel} Functions of the First Kind",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "235",
  number =       "14",
  pages =        "4107--4116",
  day =          "15",
  month =        may,
  year =         "2011",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:24:28 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042711001245",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Wu:2011:NEL,
  author =       "Mingwei Wu and Xuzheng Lin and Pooi-Yuen Kam",
  booktitle =    "{2011 IEEE 73rd Vehicular Technology Conference (VTC
                 Spring)}",
  title =        "New Exponential Lower Bounds on the {Gaussian}
                 {$Q$}-Function via {Jensen}'s Inequality",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1109/vetecs.2011.5956392",
  bibdate =      "Sat Dec 16 16:53:49 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/5956392/",
  acknowledgement = ack-nhfb,
}

@Article{Yerukala:2011:ACS,
  author =       "R. Yerukala and N. K. Boiroju and M. K. Reddy",
  title =        "An Approximation to the {CDF} of Standard Normal
                 Distribution",
  journal =      "International Journal of Mathematical Archive",
  volume =       "2",
  number =       "7",
  pages =        "1077--1079",
  month =        "????",
  year =         "2011",
  ISSN =         "2229-5046",
  ISSN-L =       "2229-5046",
  bibdate =      "Sat Dec 16 18:03:12 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ijma.info/index.php/ijma/article/view/393",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Math. Arch.",
}

@Article{Zaghloul:2011:ACF,
  author =       "Mofreh R. Zaghloul and Ahmed N. Ali",
  title =        "{Algorithm 916}: Computing the {Faddeyeva} and {Voigt}
                 functions",
  journal =      j-TOMS,
  volume =       "38",
  number =       "2",
  pages =        "15:1--15:22",
  month =        dec,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049673.2049679",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 30 17:43:07 MST 2011",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Zaghloul:2016:RAC}.",
  abstract =     "We present a MATLAB function for the numerical
                 evaluation of the Faddeyeva function $ w(z) $. The
                 function is based on a newly developed accurate
                 algorithm. In addition to its higher accuracy, the
                 software provides a flexible accuracy vs efficiency
                 trade-off through a controlling parameter that may be
                 used to reduce accuracy and computational time and vice
                 versa. Verification of the flexibility, reliability,
                 and superior accuracy of the algorithm is provided
                 through comparison with standard algorithms available
                 in other libraries and software packages.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Zhou:2011:ADZ,
  author =       "Jian-Rong Zhou and Yu-Qiu Zhao",
  title =        "Asymptotic distributions of the zeros of certain
                 classes of {Gauss} hypergeometric polynomials",
  journal =      j-APPL-MATH-COMP,
  volume =       "218",
  number =       "3",
  pages =        "1153--1159",
  day =          "1",
  month =        oct,
  year =         "2011",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2011.05.106",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Oct 25 09:02:50 MDT 2011",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Special Issue in Honour of Hari M. Srivastava on his
                 70th birth anniversary.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300311007892",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Adlaj:2012:EFP,
  author =       "Semjon Adlaj",
  title =        "An Eloquent Formula for the Perimeter of an Ellipse",
  journal =      j-NAMS,
  volume =       "59",
  number =       "8",
  pages =        "1094--1099",
  month =        sep,
  year =         "2012",
  CODEN =        "AMNOAN",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  bibdate =      "Wed Sep 05 09:12:25 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/notices/201208/rtx120801094p.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
  keywords =     "complete elliptic integral; pendulum; perimeter of
                 ellipse",
  remark =       "This paper introduces several arithmetic-geometric
                 mean (AGM) algorithms for fast and practical
                 computation of complete elliptic integrals.",
}

@Article{Al-Mohy:2012:MAB,
  author =       "Awad H. Al-Mohy",
  title =        "A more accurate {Briggs} method for the logarithm",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "59",
  number =       "3",
  pages =        "393--402",
  month =        mar,
  year =         "2012",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-011-9496-z",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Fri Oct 26 08:07:24 MDT 2012",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=59&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://www.springerlink.com/content/4110609h521kg66m/;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=59&issue=3&spage=393",
  abstract =     "A new approach for computing an expression of the form
                 $ a^{1 / 2^k} - 1 $ is presented that avoids the danger
                 of subtractive cancellation in floating point
                 arithmetic, where $a$ is a complex number not belonging
                 to the closed negative real axis and $k$ is a
                 nonnegative integer. We also derive a condition number
                 for the problem. The algorithm therefore allows highly
                 accurate numerical calculation of $ \log (a) $ using
                 Briggs' method.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Briggs' method; Briggs' tables; Inverse scaling and
                 squaring method; Logarithm function",
}

@Misc{Anonymous:2012:FIS,
  author =       "Anonymous",
  title =        "Fast inverse square root",
  howpublished = "Wikipedia article.",
  day =          "20",
  month =        mar,
  year =         "2012",
  bibdate =      "Mon Apr 02 17:03:18 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This article describes an algorithm for the inverse
                 square root. The only novel feature is use of two
                 IEEE-754 specific magic constants for 32-bit and 64-bit
                 binary arithmetic that allow obtaining fast starting
                 estimates for Newton--Raphson iterations by
                 manipulating the floating-point representations as
                 integers. The code fails to handle signed zero,
                 Infinity, and NaN arguments, uses too few iterations,
                 and does not adjust for rounding errors to obtain
                 correctly-rounded results. See \cite{Blinn:1997:JBC}.",
  URL =          "http://en.wikipedia.org/wiki/Fast_inverse_square_root",
  acknowledgement = ack-nhfb,
}

@Article{Bailey:2012:AIS,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Ancient {Indian} Square Roots: An Exercise in Forensic
                 Paleo-Mathematics",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "119",
  number =       "8",
  pages =        "646--657",
  month =        oct,
  year =         "2012",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.119.08.646",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Thu Nov 8 07:34:21 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00029890.html;
                 http://www.jstor.org/stable/10.4169/amermathmont.119.issue-8;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.119.08.646.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@InProceedings{Brisebarre:2012:MPK,
  author =       "Nicolas Brisebarre and Milo D. Ercegovac and
                 Jean-Michel Muller",
  editor =       "{IEEE}",
  booktitle =    "{2012 IEEE 23rd International Conference on
                 Application-Specific Systems, Architectures and
                 Processors, 9--11 July 2012. Delft, The Netherlands}",
  title =        "{$ (M, p, k) $}-Friendly Points: a Table-Based Method
                 for Trigonometric Function Evaluation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "46--52",
  year =         "2012",
  DOI =          "https://doi.org/10.1109/ASAP.2012.17",
  ISBN =         "0-7695-4768-0",
  ISBN-13 =      "978-0-7695-4768-8",
  ISSN =         "1063-6862",
  ISSN-L =       "1063-6862",
  bibdate =      "Fri Sep 29 10:49:22 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Chen:2012:SIM,
  author =       "Chao-Ping Chen and Necdet Batir",
  title =        "Some inequalities and monotonicity properties
                 associated with the gamma and psi functions",
  journal =      j-APPL-MATH-COMP,
  volume =       "218",
  number =       "17",
  pages =        "8217--8225",
  day =          "1",
  month =        may,
  year =         "2012",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2012.02.007",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Thu Apr 5 06:00:26 MDT 2012",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300312001257",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  remark =       "New bounds on the gamma function in terms of the psi
                 function, and a new estimate for the error in
                 Stirling's formula, $ \Gamma (x + 1) \approx x^x e^{-x}
                 \sqrt {2 \pi x} $.",
}

@Article{Cohl:2012:TEF,
  author =       "Howard S. Cohl",
  title =        "Table Errata to {``Formulas and theorems for the
                 special functions of mathematical physics'' by W.
                 Magnus, F. Oberhettinger \& R. P. Soni (1966)}",
  journal =      j-MATH-COMPUT,
  volume =       "81",
  number =       "280",
  pages =        "2251--2251",
  month =        oct,
  year =         "2012",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Nov 6 09:52:53 MST 2012",
  bibsource =    "http://www.ams.org/mcom/2012-81-280;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  note =         "See \cite{Magnus:1966:FTS}.",
  URL =          "http://www.ams.org/journals/mcom/2012-81-280/S0025-5718-2012-02612-3;
                 http://www.ams.org/journals/mcom/2012-81-280/S0025-5718-2012-02612-3/S0025-5718-2012-02612-3.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Report of sign error in a sum of two Gauss
                 hypergeometric functions for Ferrers function of the
                 second kind.",
}

@Article{Cote:2012:CTL,
  author =       "F. D. C{\^o}t{\'e} and I. N. Psaromiligkos and W. J.
                 Gross",
  title =        "A {Chernoff}-type lower bound for the {Gaussian}
                 {$Q$}-function",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  year =         "2012",
  bibdate =      "Sat Dec 16 16:04:00 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://arxiv.org/abs/1202.6483",
  acknowledgement = ack-nhfb,
  pagecount =    "3",
}

@Book{Crandall:2012:ARS,
  author =       "Richard E. Crandall",
  title =        "Algorithmic Reflections: Selected Works",
  publisher =    "PSI Press",
  address =      "Portland, OR, USA",
  edition =      "First Perfectly Scientific Press paperback",
  pages =        "410",
  year =         "2012",
  ISBN =         "1-935638-19-X",
  ISBN-13 =      "978-1-935638-19-3",
  LCCN =         "QA958 .C736 2012",
  bibdate =      "Fri Jun 30 11:14:26 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1947--2012",
  subject =      "Algorithms; Algorithmes",
  tableofcontents = "Part I: Number theory \\
                 On the $ 3 x + 1$ problem \\
                 On a conjecture of Crandall concerning the $ q n + 1$
                 problem \\
                 A search for Wieferich and Wilson primes \\
                 Parallelization of Pollard-rho factorization \\
                 Three new factors of Fermat numbers \\
                 Random generators and normal numbers \\
                 The googol-th bit of the Erd{\H{o}}s--Borwein constant
                 \\
                 Part II: Analytical algorithms \\
                 Fast evaluation of multiple zeta sums \\
                 On the Khintchine Constant \\
                 On the dynamics of certain recurrence relations \\
                 Effective Laguerre asymptotics \\
                 Theory of ROOF walks \\
                 Unified algorithms for polylogarithm, $L$-series, and
                 zeta variants \\
                 Part III: Physics, biology, epidemics, and physiology
                 \\
                 The potential within a crystal lattice \\
                 The fractal character of space-time epidemics \\
                 Mathematical signatures as tools for visual dysfunction
                 \\
                 NLA system for medical-data classification \\
                 On the fractal distribution of brain synapses",
}

@Misc{Crandall:2012:UAP,
  author =       "R. E. Crandall",
  title =        "Unified algorithms for polylogarithm, {$L$}-series,
                 and zeta variants",
  type =         "Preprint",
  pages =        "53",
  year =         "2012",
  bibdate =      "Tue Sep 09 11:50:04 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Published in \cite{Crandall:2012:ARS}.",
  URL =          "http://www.perfscipress.com/papers/universalTOC25.pdf;
                 https://web.archive.org/web/20130430193005/http://www.perfscipress.com/papers/universalTOC25.pdf",
  abstract =     "We describe a general computational scheme for
                 evaluation of a wide class of number-theoretical
                 functions. We avoid asymptotic expansions in favor of
                 manifestly convergent series that lend themselves
                 naturally to rigorous error bounds. By employing three
                 fundamental series algorithms we achieve a unified
                 strategy to compute the various functions via parameter
                 selection. This work amounts to a compendium of methods
                 to establish extreme-precision results as typify modern
                 experimental mathematics. A fortuitous byproduct of
                 this unified approach is automatic analytic
                 continuation over complex parameters. Another byproduct
                 is a host of converging series for various fundamental
                 constants.",
  acknowledgement = ack-nhfb,
  remark-1 =     "In memory of gentle colleague Jerry Keiper
                 (1953--1995).",
  remark-2 =     "Host in URL field no longer exists; cited in
                 \cite{Coffey:2014:SRR}.",
}

@Article{DeSchrijver:2012:DPRa,
  author =       "Steven K. {De Schrijver} and El-Houssaine Aghezzaf and
                 Hendrik Vanmaele",
  title =        "Double precision rational approximation algorithm for
                 the inverse standard normal first order loss function",
  journal =      j-APPL-MATH-COMP,
  volume =       "219",
  number =       "3",
  pages =        "1375--1382",
  day =          "15",
  month =        oct,
  year =         "2012",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2012.07.011",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Thu Oct 25 09:05:16 MDT 2012",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300312007114",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{DeSchrijver:2012:DPRb,
  author =       "Steven K. {De Schrijver} and El-Houssaine Aghezzaf and
                 Hendrik Vanmaele",
  title =        "Double precision rational approximation algorithms for
                 the standard normal first and second order loss
                 functions",
  journal =      j-APPL-MATH-COMP,
  volume =       "219",
  number =       "4",
  pages =        "2320--2330",
  day =          "1",
  month =        nov,
  year =         "2012",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2012.08.012",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Thu Oct 25 09:05:21 MDT 2012",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300312008041",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Develi:2012:NAB,
  author =       "I. Develi",
  title =        "A new approximation based on the differential
                 evolution algorithm for the {Gaussian} {$Q$}-function",
  journal =      "Int. J. Innov. Comput. Inf. Control",
  volume =       "8",
  number =       "10(B)",
  pages =        "7095--7102",
  month =        "????",
  year =         "2012",
  bibdate =      "Sat Dec 16 16:14:27 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/s10957-012-0217-0.pdf;
                 http://www.ijicic.org/ijicic-11-08039.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Fukushima:2012:SES,
  author =       "Toshio Fukushima",
  title =        "Series expansions of symmetric elliptic integrals",
  journal =      j-MATH-COMPUT,
  volume =       "81",
  number =       "278",
  pages =        "957--990",
  month =        "",
  year =         "2012",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Sat Feb 4 09:28:39 MST 2012",
  bibsource =    "http://www.ams.org/mcom/2012-81-278;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2012-81-278/S0025-5718-2011-02531-7;
                 http://www.ams.org/journals/mcom/2012-81-278/S0025-5718-2011-02531-7/S0025-5718-2011-02531-7.pdf",
  abstract =     "Based on general discussion of series expansions of
                 Carlson's symmetric elliptic integrals, we developed
                 fifteen kinds of them including eleven new ones by
                 utilizing the symmetric nature of the integrals. Thanks
                 to the special addition formulas of the integrals, we
                 also obtained their complementary series expansions. By
                 considering the balance between the speed of
                 convergence and the amount of computational labor, we
                 chose four of them as the best series expansions.
                 Practical evaluation of the integrals is conducted by
                 the most suitable one among these four series
                 expansions. Its selection rule was analytically
                 specified in terms of the numerical values of given
                 parameters. As a by-product, we obtained an efficient
                 asymptotic expansion of the integrals around their
                 logarithmic singularities. Numerical experiments
                 confirmed the effectiveness of these new series
                 expansions.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Gaudreau:2012:CTP,
  author =       "Philippe Gaudreau and Richard M. Slevinsky and Hassan
                 Safouhi",
  title =        "Computation of Tail Probabilities via Extrapolation
                 Methods and Connection with Rational and {Pad{\'e}}
                 Approximants",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "34",
  number =       "1",
  pages =        "B65--B85",
  month =        jan,
  year =         "2012",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/100803778",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Sat Dec 16 16:33:00 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  URL =          "http://epubs.siam.org/doi/abs/10.1137/100803778",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@Article{Gil:2012:CRZ,
  author =       "Amparo Gil and Javier Segura",
  title =        "Computing the real zeros of cylinder functions and the
                 roots of the equation {$ x C^\prime_\nu (x) + \gamma
                 C_\nu (x) = 0 $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "64",
  number =       "1",
  pages =        "11--21",
  month =        jul,
  year =         "2012",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/j.camwa.2012.02.032",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:51:09 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122112001460",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  remark =       "From the abstract: ``Fast methods to compute the zeros
                 of general cylinder functions $ C_\nu (x) = \cos \alpha
                 J_\nu (x) - \sin \alpha Y_\nu (x) C_\nu (x) = \cos
                 \alpha J_\nu (x) - \sin \alpha Y_\nu (x) $ in real
                 intervals can be obtained from an approximate
                 integration of the second order ODE satisfied by these
                 functions, leading to fourth order methods with global
                 convergence.''",
}

@Article{Gil:2012:EAA,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Efficient and Accurate Algorithms for the Computation
                 and Inversion of the Incomplete Gamma Function Ratios",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "34",
  number =       "6",
  pages =        "A2965--A2981",
  month =        "????",
  year =         "2012",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/120872553",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Fri Jul 19 07:43:33 MDT 2013",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/34/6;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2012",
}

@Article{Gil:2012:IAF,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "An improved algorithm and a {Fortran 90} module for
                 computing the conical function $ p^m_{1 / 2 + i \tau
                 }(x) $",
  journal =      j-COMP-PHYS-COMM,
  volume =       "183",
  number =       "3",
  pages =        "794--799",
  month =        mar,
  year =         "2012",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2011.11.025",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 11 10:11:02 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465511003936",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Jablonski:2012:EAC,
  author =       "A. Jablonski",
  title =        "An effective algorithm for calculating the
                 {Chandrasekhar} function",
  journal =      j-COMP-PHYS-COMM,
  volume =       "183",
  number =       "8",
  pages =        "1773--1782",
  month =        aug,
  year =         "2012",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2012.02.022",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Tue Apr 24 06:33:31 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465512000847",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@InCollection{Jargstorff:2012:AEF,
  author =       "Frank Jargstorff",
  title =        "Approximating the {{\tt erfinv}} Function",
  crossref =     "Hwu:2012:GCG",
  chapter =      "10",
  pages =        "??--??",
  year =         "2012",
  bibdate =      "Sat Feb 08 19:05:23 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Jentschura:2012:NCB,
  author =       "U. D. Jentschura and E. L{\"o}tstedt",
  title =        "Numerical calculation of {Bessel}, {Hankel} and {Airy}
                 functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "183",
  number =       "3",
  pages =        "506--519",
  month =        mar,
  year =         "2012",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2011.11.010",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 11 10:11:02 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465511003729",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Misc{Johnson:2012:FPF,
  author =       "Steven G. Johnson",
  title =        "{Faddeeva} package, a free\slash open-source {C++}
                 Software to compute the various error functions of
                 arbitrary complex arguments",
  howpublished = "Web site",
  year =         "2012",
  bibdate =      "Sat Feb 17 14:11:45 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ab-initio.mit.edu/wiki/index.php/Faddeeva_Package",
  acknowledgement = ack-nhfb,
  keywords =     "$\erf(x) (the error function); $\erfc() (complementary
                 error function = $1 - \erf(z)$); $\erfcx() (scaled
                 complementary error function $e^{z^2} \erfc(z) = w(i
                 z)$); $\erfi(z) (imaginary error function = $-i \erf(i
                 z)$); Dawson ($((\sqrt \pi)/2) e^{-z^2} \erfi(z)$); w
                 (Faddeeva function $w(z) = e^{-z^2} \erfc(-i z)$)",
}

@InProceedings{Phong:2012:EAG,
  author =       "Dao Ngoc Phong and Nguyen Quang Uy and Nguyen Xuan
                 Hoai and R. I. (Bob) McKay",
  editor =       "????",
  booktitle =    "Proceedings of the 2012 {IEEE} Congress on
                 Evolutionary Computation, June 10--15, 2012 ---
                 Brisbane, {QLD}, Australia",
  title =        "Evolving approximations for the {Gaussian}
                 {$Q$}-function by genetic programming with semantic
                 based crossover",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2012",
  DOI =          "https://doi.org/10.1109/CEC.2012.6256588",
  bibdate =      "Sat Dec 16 16:08:39 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/6256588/",
  acknowledgement = ack-nhfb,
}

@Article{Poelke:2012:DCC,
  author =       "Konstantin Poelke and Konrad Polthier",
  title =        "Domain Coloring of Complex Functions: An
                 Implementation-Oriented Introduction",
  journal =      j-IEEE-CGA,
  volume =       "32",
  number =       "5",
  pages =        "90--97",
  month =        sep # "\slash " # oct,
  year =         "2012",
  CODEN =        "ICGADZ",
  DOI =          "https://doi.org/10.1109/MCG.2012.100",
  ISSN =         "0272-1716 (print), 1558-1756 (electronic)",
  ISSN-L =       "0272-1716",
  bibdate =      "Mon Oct 22 06:56:23 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeecga.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Computer Graphics and Applications",
  journal-URL =  "http://www.computer.org/portal/web/csdl/magazines/cga",
}

@Article{Rzadkowski:2012:SEE,
  author =       "Grzegorz Rz{\k{a}}dkowski",
  title =        "On some expansions for the {Euler} Gamma function and
                 the {Riemann} Zeta function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "236",
  number =       "15",
  pages =        "3710--3719",
  month =        sep,
  year =         "2012",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:24:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042711004663",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Book{Srivastava:2012:ZZF,
  author =       "H. M. Srivastava and Choi Junesang",
  title =        "Zeta and $q$-Zeta functions and associated series and
                 integrals",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "xvi + 657",
  year =         "2012",
  ISBN =         "0-12-385218-8",
  ISBN-13 =      "978-0-12-385218-2",
  LCCN =         "QA351 .S745 2012",
  bibdate =      "Wed Jun 10 16:19:46 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Elsevier Insights",
  URL =          "http://www.sciencedirect.com/science/book/9780123852182",
  acknowledgement = ack-nhfb,
  remark =       "Revised, enlarged, and updated version of
                 \cite{Srivastava:2001:SAZ}.",
  subject =      "Functions, Zeta",
  tableofcontents = "1. Introduction and preliminaries \\
                 2. The zeta and related functions \\
                 3. Series involving zeta functions \\
                 4. Evaluations and series representations \\
                 5. Determinants of the laplacians \\
                 6. q-Extensions of some special functions and
                 polynomials \\
                 7. Miscellaneous results",
}

@Article{Vazquez-Leal:2012:HAS,
  author =       "Hector Vazquez-Leal and Roberto Castaneda-Sheissa and
                 Uriel Filobello-Nino and Arturo Sarmiento-Reyes and
                 Jesus Sanchez Orea",
  title =        "High Accurate Simple Approximation of Normal
                 Distribution Integral",
  journal =      "Mathematical Problems in Engineering",
  volume =       "2012",
  pages =        "1--22",
  year =         "2012",
  DOI =          "https://doi.org/10.1155/2012/124029",
  ISSN =         "1024-123X (print), 1563-5147 (electronic)",
  bibdate =      "Sat Dec 16 17:54:09 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.hindawi.com/journals/mpe/2012/124029/",
  acknowledgement = ack-nhfb,
}

@Article{Veberic:2012:LFA,
  author =       "Darko Veberi{\v{c}}",
  title =        "{Lambert} {$W$} function for applications in physics",
  journal =      j-COMP-PHYS-COMM,
  volume =       "183",
  number =       "12",
  pages =        "2622--2628",
  month =        dec,
  year =         "2012",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2012.07.008",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Tue Aug 28 17:36:53 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465512002366",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Willis:2012:AGH,
  author =       "Joshua L. Willis",
  title =        "Acceleration of generalized hypergeometric functions
                 through precise remainder asymptotics",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "59",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2012",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-011-9499-9",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Nov 30 06:42:07 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arxiv.org/abs/1102.3003;
                 http://www.springerlink.com/content/k413064448600815/",
  abstract =     "We express the asymptotics of the remainders of the
                 partial sums $ \{ s_n \} $ of the generalized
                 hypergeometric function through an inverse power series
                 $ z^n n^\lambda \sum c_k / n_k $, where the exponent $
                 \lambda $ and the asymptotic coefficients $ \{ c_k \} $
                 may be recursively computed to any desired order from
                 the hypergeometric parameters and argument. From this
                 we derive a new series acceleration technique that can
                 be applied to any such function, even with complex
                 parameters and at the branch point $ z = 1 $. For
                 moderate parameters (up to approximately ten) a C
                 implementation at fixed precision is very effective at
                 computing these functions; for larger parameters an
                 implementation in higher than machine precision would
                 be needed. Even for larger parameters, however, our C
                 implementation is able to correctly determine whether
                 or not it has converged; and when it converges, its
                 estimate of its error is accurate.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Generalized hypergeometric functions; Recurrence
                 asymptotics; Series acceleration",
}

@InCollection{Arfken:2013:BF,
  author =       "George B. (George Brown) Arfken and Hans-J{\"u}rgen
                 Weber and Frank E. Harris",
  title =        "{Bessel} Functions",
  crossref =     "Arfken:2013:MMP",
  chapter =      "14",
  pages =        "643--713",
  year =         "2013",
  bibdate =      "Thu Dec 5 05:54:14 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/B9780123846549000141",
  acknowledgement = ack-nhfb,
}

@InCollection{Arfken:2013:GFb,
  author =       "George B. (George Brown) Arfken and Hans-J{\"u}rgen
                 Weber and Frank E. Harris",
  title =        "{Gamma} Function",
  crossref =     "Arfken:2013:MMP",
  chapter =      "13",
  pages =        "599--641",
  year =         "2013",
  bibdate =      "Thu Dec 5 05:54:14 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/B978012384654900013X",
  acknowledgement = ack-nhfb,
}

@Article{Babusci:2013:SME,
  author =       "D. Babusci and G. Dattoli and K. G{\'o}rska and K. A.
                 Penson",
  title =        "Symbolic methods for the evaluation of sum rules of
                 {Bessel} functions",
  journal =      j-J-MATH-PHYS,
  volume =       "54",
  number =       "7",
  pages =        "073501",
  month =        jul,
  year =         "2013",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.4812325",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Wed Feb 12 12:24:18 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
}

@Article{Booker:2013:BAB,
  author =       "Andrew R. Booker and Andreas Str{\"o}mbergsson and
                 Holger Then",
  title =        "Bounds and algorithms for the {$K$-Bessel} function of
                 imaginary order",
  journal =      j-LMS-J-COMPUT-MATH,
  volume =       "16",
  pages =        "78--108",
  year =         "2013",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1112/S1461157013000028",
  ISSN =         "1461-1570",
  ISSN-L =       "1461-1570",
  MRclass =      "26D07; 33C10; 33F05; 34D05; 41A58 (primary); 41A80;
                 65D05; 40H05; 26B99 (secondary)",
  bibdate =      "Sat Jun 22 11:29:28 MDT 2013",
  bibsource =    "http://journals.cambridge.org/action/displayJournal?jid=JCM;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lms-j-comput-math.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "LMS J. Comput. Math.",
  fjournal =     "LMS Journal of Computation and Mathematics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=JCM",
  onlinedate =   "10 April 2013",
}

@Article{Chen:2013:CFE,
  author =       "Chao-Ping Chen",
  title =        "Continued fraction estimates for the psi function",
  journal =      j-APPL-MATH-COMP,
  volume =       "219",
  number =       "19",
  pages =        "9865--9871",
  day =          "1",
  month =        jun,
  year =         "2013",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2013.03.134",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon May 20 19:05:31 MDT 2013",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300313003962",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Chen:2013:LIA,
  author =       "Chao-Ping Chen and Cristinel Mortici",
  title =        "Limits and inequalities associated with the
                 {Euler--Mascheroni} constant",
  journal =      j-APPL-MATH-COMP,
  volume =       "219",
  number =       "18",
  pages =        "9755--9761",
  day =          "15",
  month =        may,
  year =         "2013",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2013.03.089",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon May 20 19:05:27 MDT 2013",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300313003500",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "asymptotic expansion; Euler-Mascheroni constant;
                 harmonic numbers; inequality; polygamma functions; psi
                 function",
}

@Article{Chen:2013:UTS,
  author =       "Chao-Ping Chen",
  title =        "Unified treatment of several asymptotic formulas for
                 the gamma function",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "64",
  number =       "2",
  pages =        "311--319",
  month =        oct,
  year =         "2013",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-012-9667-6",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Dec 2 18:18:08 MST 2013",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=64&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://link.springer.com/article/10.1007/s11075-012-9667-6",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@InProceedings{Chevillard:2013:MPE,
  author =       "Sylvain Chevillard and Marc Mezzarobba",
  title =        "Multiple-Precision Evaluation of the {Airy} {Ai}
                 Function with Reduced Cancellation",
  crossref =     "IEEE:2013:PIS",
  pages =        "175--182",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.33",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Airy Ai function; algorithm; Algorithm
                 design and analysis; Approximation algorithms;
                 Approximation methods; arbitrary precision; ARITH-21;
                 asymptotics; cancellation reduction; classical Miller
                 algorithm; correct rounding; differential equations;
                 Equations; error bounds; ill-conditioned three-term
                 recurrence; linear ordinary differential equation;
                 Miller method; multiple-precision evaluation;
                 nonnegative Taylor expansions; numerical evaluation;
                 series (mathematics); series expansion; Shape; Special
                 functions; Taylor coefficients; Taylor series",
}

@Article{deDinechin:2013:FPT,
  author =       "Florent de Dinechin and Matei Istoan and Guillaume
                 Sergent",
  title =        "Fixed-point trigonometric functions on {FPGAs}",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "41",
  number =       "5",
  pages =        "83--88",
  month =        dec,
  year =         "2013",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/2641361.2641375",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Mon Aug 18 17:12:43 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  abstract =     "Three approaches for computing sines and cosines on
                 FPGAs are studied in this paper, with a focus of
                 high-throughput pipelined architecture, and
                 state-of-the-art implementation techniques. The first
                 approach is the classical CORDIC iteration, for which
                 we suggest a reduced iteration technique and fine
                 optimizations in datapath width and latency. The second
                 is an ad-hoc architecture specifically designed around
                 trigonometric identities. The third uses a generic
                 table- and DSP-based polynomial approximator. These
                 three architectures are implemented and compared in the
                 FloPoCo framework.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J89",
}

@Article{Develi:2013:HAA,
  author =       "I. Develi and A. Basturk",
  title =        "Highly Accurate Analytic Approximation to the
                 {Gaussian} {$Q$}-function Based on the Use of Nonlinear
                 Least Squares Optimization Algorithm",
  journal =      j-J-OPT-THEORY-APPL,
  volume =       "159",
  number =       "1",
  pages =        "183--191",
  day =          "01",
  month =        oct,
  year =         "2013",
  CODEN =        "JOTABN",
  DOI =          "https://doi.org/10.1007/s10957-012-0217-0",
  ISSN =         "1573-2878",
  ISSN-L =       "0022-3239",
  bibdate =      "Sat Dec 16 16:18:18 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://link.springer.com/article/10.1007/s10957-012-0217-0",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Optim. Theory Appl.",
  fjournal =     "Journal of Optimization Theory and Applications",
  journal-URL =  "http://link.springer.com/journal/volumesAndIssues/10957",
}

@Article{Erricolo:2013:AFS,
  author =       "Danilo Erricolo and Giuseppe Carluccio",
  title =        "{Algorithm 934}: {Fortran 90} subroutines to compute
                 {Mathieu} functions for complex values of the
                 parameter",
  journal =      j-TOMS,
  volume =       "40",
  number =       "1",
  pages =        "8:1--8:19",
  month =        sep,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2513109.2513117",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 30 16:05:58 MDT 2013",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Software to compute angular and radial Mathieu
                 functions is provided in the case that the parameter q
                 is a complex variable and the independent variable x is
                 real. After an introduction on the notation and the
                 definitions of Mathieu functions and their related
                 properties, Fortran 90 subroutines to compute them are
                 described and validated with some comparisons. A sample
                 application is also provided.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Feng:2013:TFA,
  author =       "Lei Feng and Weiping Wang",
  title =        "Two families of approximations for the gamma
                 function",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "64",
  number =       "3",
  pages =        "403--416",
  month =        nov,
  year =         "2013",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-012-9671-x",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Dec 2 18:18:12 MST 2013",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=64&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://link.springer.com/article/10.1007/s11075-012-9671-x",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Fukushima:2013:PFC,
  author =       "Toshio Fukushima",
  title =        "Precise and fast computation of {Jacobian} elliptic
                 functions by conditional duplication",
  journal =      j-NUM-MATH,
  volume =       "123",
  number =       "4",
  pages =        "585--605",
  month =        apr,
  year =         "2013",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s00211-012-0498-0",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sat Apr 27 13:30:29 MDT 2013",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=123&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath2010.bib",
  URL =          "http://link.springer.com/article/10.1007/s00211-012-0498-0",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Fukushima:2013:RCD,
  author =       "Toshio Fukushima",
  title =        "Recursive computation of derivatives of elliptic
                 functions and of incomplete elliptic integrals",
  journal =      j-APPL-MATH-COMP,
  volume =       "221",
  number =       "??",
  pages =        "21--31",
  day =          "15",
  month =        sep,
  year =         "2013",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon Dec 2 12:34:28 MST 2013",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300313006152",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Gonzalez-Morales:2013:NII,
  author =       "M. J. Gonz{\'a}lez-Morales and R. Mahillo-Isla and C.
                 Dehesa-Mart{\'\i}nez",
  title =        "A new integral identity involving the elliptic
                 integral {$ E(m) $}",
  journal =      j-APPL-MATH-COMP,
  volume =       "221",
  number =       "??",
  pages =        "568--570",
  day =          "15",
  month =        sep,
  year =         "2013",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon Dec 2 12:34:28 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300313007303",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Hale:2013:FAC,
  author =       "Nicholas Hale and Alex Townsend",
  title =        "Fast and Accurate Computation of {Gauss--Legendre} and
                 {Gauss--Jacobi} Quadrature Nodes and Weights",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "35",
  number =       "2",
  pages =        "A652--A674",
  month =        "????",
  year =         "2013",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/120889873",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Fri Jul 19 07:43:46 MDT 2013",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/35/2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2013",
}

@Article{Huang:2013:NNE,
  author =       "Zhi-Wei Huang and Jueping Liu",
  title =        "{NumExp}: Numerical epsilon expansion of
                 hypergeometric functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "184",
  number =       "8",
  pages =        "1973--1980",
  month =        aug,
  year =         "2013",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2013.03.016",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Wed May 15 07:02:08 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465513001136",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Jablonski:2013:IAC,
  author =       "A. Jablonski",
  title =        "Improved algorithm for calculating the {Chandrasekhar}
                 function",
  journal =      j-COMP-PHYS-COMM,
  volume =       "184",
  number =       "2",
  pages =        "440--442",
  month =        feb,
  year =         "2013",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2012.08.020",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Nov 2 11:55:56 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S001046551200286X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@InProceedings{Jiang:2013:AFE,
  author =       "Hao Jiang and Stef Graillat and Roberto Barrio",
  title =        "Accurate and Fast Evaluation of Elementary Symmetric
                 Functions",
  crossref =     "IEEE:2013:PIS",
  pages =        "183--190",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.18",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; accurate algorithm; Algorithm design and
                 analysis; ARITH-21; compensated algorithm;
                 double-double library; elementary symmetric functions;
                 error-free transformation; error-free transformations;
                 floating point arithmetic; floating-point arithmetic;
                 forward roundoff error bound; Libraries; mathematics
                 computing; MATLAB poly function; Polynomials;
                 psychological measurement; Rasch model; roundoff error;
                 Roundoff errors; running error bound; shaper bound;
                 summation algorithm; Vectors",
}

@Article{Lopez:2013:NSE,
  author =       "Jos{\'e} L. L{\'o}pez and Nico M. Temme",
  title =        "New series expansions of the {Gauss} hypergeometric
                 function",
  journal =      j-ADV-COMPUT-MATH,
  volume =       "39",
  number =       "2",
  pages =        "349--365",
  month =        aug,
  year =         "2013",
  CODEN =        "ACMHEX",
  DOI =          "https://doi.org/10.1007/s10444-012-9283-y",
  ISSN =         "1019-7168 (print), 1572-9044 (electronic)",
  ISSN-L =       "1019-7168",
  MRclass =      "33C05 (33F05 41A58 65D20)",
  MRnumber =     "3082518",
  MRreviewer =   "Jochen Denzler",
  bibdate =      "Sat Feb 3 18:23:06 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/s10444-012-9283-y",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in Computational Mathematics",
  journal-URL =  "http://link.springer.com/journal/10444",
  keywords =     "Gauss hypergeometric function $_2F_1(a,b,c; z)$",
  remark =       "Improvement on
                 \cite{Buhring:1987:ACH,Buhring:1987:BUA} and \cite[\S
                 2.3]{Gil:2007:NMS} by removal of points excluded from
                 the domain of convergence.",
}

@Article{Low:2013:MET,
  author =       "Joshua Yung Lih Low and Ching Chuen Jong",
  title =        "A Memory-Efficient Tables-and-Additions Method for
                 Accurate Computation of Elementary Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "62",
  number =       "5",
  pages =        "858--872",
  month =        may,
  year =         "2013",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2012.43",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Apr 30 12:26:22 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Mastin:2013:LQB,
  author =       "Andrew Mastin and Patrick Jaillet",
  title =        "Log-quadratic bounds for the {Gaussian}
                 {$Q$}-function",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "9",
  month =        apr,
  year =         "2013",
  bibdate =      "Sat Dec 16 17:09:03 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arxiv.org/abs/1304.2488",
  acknowledgement = ack-nhfb,
}

@Article{Neta:2013:FHL,
  author =       "Beny Neta and Melvin Scott",
  title =        "On a family of {Halley}-like methods to find simple
                 roots of nonlinear equations",
  journal =      j-APPL-MATH-COMP,
  volume =       "219",
  number =       "15",
  pages =        "7940--7944",
  day =          "1",
  month =        apr,
  year =         "2013",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2013.02.035",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon May 6 18:04:12 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300313001574",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
  keywords =     "basin of attraction; Euler--Chebyshev method; Halley
                 method; nonlinear equations; simple roots",
}

@Book{Osipov:2013:PSW,
  author =       "Andrei Osipov",
  title =        "Prolate Spheroidal Wave Functions of Order Zero:
                 Mathematical Tools for Bandlimited Approximation",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "????",
  year =         "2013",
  ISBN =         "1-4614-8258-5",
  ISBN-13 =      "978-1-4614-8258-1",
  LCCN =         "????",
  bibdate =      "Sat Apr 1 14:32:29 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy1315/2013945079-b.html;
                 http://www.loc.gov/catdir/enhancements/fy1315/2013945079-d.html;
                 http://www.loc.gov/catdir/enhancements/fy1315/2013945079-t.html",
  acknowledgement = ack-nhfb,
  tableofcontents = "Introduction \\
                 Mathematical and Numerical Preliminaries \\
                 Overview \\
                 Analysis of the Differential Operator \\
                 Analysis of the Integral Operator \\
                 Rational Approximations of PSWFs \\
                 Miscellaneous Properties of PSWFs \\
                 Asymptotic Analysis of PSWFs \\
                 Quadrature Rules and Interpolation via PSWFs \\
                 Numerical Algorithms",
}

@Article{Russinoff:2013:CFV,
  author =       "David M. Russinoff",
  title =        "Computation and Formal Verification of {SRT} Quotient
                 and Square Root Digit Selection Tables",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "62",
  number =       "5",
  pages =        "900--913",
  month =        may,
  year =         "2013",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2012.40",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Apr 30 12:26:22 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Szmytkowski:2013:EBT,
  author =       "Rados{\l}aw Szmytkowski",
  title =        "Erratum to {{\booktitle{Formulas and Theorems for the
                 Special Functions of Mathematical Physics}} by W.
                 Magnus, F. Oberhettinger, R. P. Soni}",
  journal =      j-MATH-COMPUT,
  volume =       "82",
  number =       "283",
  pages =        "1709--1710",
  month =        "????",
  year =         "2013",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Apr 30 16:18:02 MDT 2013",
  bibsource =    "http://www.ams.org/mcom/2013-82-283;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2013-82-283/S0025-5718-2013-02671-3;
                 http://www.ams.org/journals/mcom/2013-82-283/S0025-5718-2013-02671-3/S0025-5718-2013-02671-3.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Thompson:2013:AIG,
  author =       "Ian Thompson",
  title =        "{Algorithm 926}: Incomplete {Gamma} Functions with
                 Negative Arguments",
  journal =      j-TOMS,
  volume =       "39",
  number =       "2",
  pages =        "14:1--14:9",
  month =        feb,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2427023.2427031",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 20 16:46:13 MST 2013",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "An algorithm for accurately computing the lower
                 incomplete gamma function $ \gamma (a, t) $ in the case
                 where $ a = n + 1 / 2 $, $ n \in Z $ and $ t < 0 $ is
                 described. Series expansions and analytic continuation
                 are employed to compute the function for certain
                 critical values of $n$, and these results are used to
                 initiate stable recurrence. The algorithm has been
                 implemented in Fortran 2003, with precomputations
                 carried out in Maple.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Zhong:2013:AKF,
  author =       "Min Zhong and R. J. Loy and R. S. Anderssen",
  title =        "Approximating the {Kohlrausch} function by sums of
                 exponentials",
  journal =      j-ANZIAM-J,
  volume =       "54",
  number =       "4",
  pages =        "306--323",
  month =        apr,
  year =         "2013",
  CODEN =        "AJNOA2",
  DOI =          "https://doi.org/10.1017/S1446181113000229",
  ISSN =         "1446-1811 (print), 1446-8735 (electronic)",
  ISSN-L =       "1446-1811",
  bibdate =      "Fri Apr 26 16:14:05 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/anziamj.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.cambridge.org/core/journals/anziam-journal/article/approximating-the-kohlrausch-function-by-sums-of-exponentials/1F2BD299466198D202D9D2355E34116F",
  acknowledgement = ack-nhfb,
  ajournal =     "ANZIAM J.",
  fjournal =     "The ANZIAM Journal. The Australian \& New Zealand
                 Industrial and Applied Mathematics Journal",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
  keywords =     "Kohlrausch function $\exp(-t^\beta)$, with $\beta \in
                 (0,1)$",
  onlinedate =   "04 September 2013",
}

@Article{Adj:2014:SRC,
  author =       "G. Adj and F. Rodriguez-Henriquez",
  title =        "Square Root Computation over Even Extension Fields",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "63",
  number =       "11",
  pages =        "2829--2841",
  month =        nov,
  year =         "2014",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2013.145",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 06 07:39:04 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Algorithm design and analysis; Complexity theory;
                 Computational efficiency; Computer science; Elliptic
                 curve cryptography; Elliptic curves; even extension
                 fields; finite extension fields; finite field
                 arithmetic; Modular square root; number theoretical
                 problem; number theory; square root computation;
                 Taxonomy",
}

@Misc{Anonymous:2014:CLL,
  author =       "Anonymous",
  title =        "{CR-Libm} --- a library of correctly rounded
                 elementary functions in double-precision",
  howpublished = "Web site",
  year =         "2014",
  bibdate =      "Sat Oct 31 07:21:21 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://lipforge.ens-lyon.fr/www/crlibm/",
  abstract =     "CRlibm is a free mathematical library (libm) that
                 provides: (1) implementations of the double-precision
                 C99 standard elementary functions; (2) correctly
                 rounded in the four IEEE-754 rounding modes; (3) with a
                 comprehensive proof of both the algorithms used and
                 their implementation; (4) sufficiently efficient in
                 average time, worst-case time, and memory consumption
                 to replace existing libms transparently.",
  acknowledgement = ack-nhfb,
  keywords =     "CR-Libm; scslib (software carry save library)",
}

@Article{Babusci:2014:SBS,
  author =       "D. Babusci and G. Dattoli and K. G{\'o}rska and K. A.
                 Penson",
  title =        "The spherical {Bessel} and {Struve} functions and
                 operational methods",
  journal =      j-APPL-MATH-COMP,
  volume =       "238",
  number =       "??",
  pages =        "1--6",
  day =          "1",
  month =        jul,
  year =         "2014",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri May 23 10:53:19 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300314005086",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Backeljauw:2014:VES,
  author =       "Franky Backeljauw and Stefan Becuwe and Annie Cuyt and
                 Joris {Van Deun} and Daniel W. Lozier",
  title =        "Validated evaluation of special mathematical
                 functions",
  journal =      j-SCI-COMPUT-PROGRAM,
  volume =       "90 (part A)",
  number =       "??",
  pages =        "2--20",
  day =          "15",
  month =        sep,
  year =         "2014",
  CODEN =        "SCPGD4",
  DOI =          "https://doi.org/10.1016/j.scico.2013.05.006",
  ISSN =         "0167-6423 (print), 1872-7964 (electronic)",
  ISSN-L =       "0167-6423",
  bibdate =      "Thu May 22 07:49:47 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/scicomputprogram.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167642313001263",
  acknowledgement = ack-nhfb,
  fjournal =     "Science of Computer Programming",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676423/",
}

@Book{Bartsch:2014:TMF,
  author =       "Hans-Jochen Bartsch",
  title =        "{Taschenbuch mathematischer Formeln f{\"u}r Ingenieure
                 und Naturwissenschaftler: [F{\"u}r Studium und Beruf]}.
                 ({German}) [{Pocketbook} of mathematical formulas for
                 engineers and natural sciences: [For study and job]]",
  publisher =    "Fachbuchverlag Leipzig im Hanser-Verlag",
  address =      "M{\"u}nchen, Germany",
  edition =      "Twenty-third",
  pages =        "832",
  year =         "2014",
  ISBN =         "3-446-43800-9",
  ISBN-13 =      "978-3-446-43800-2",
  LCCN =         "????",
  bibdate =      "Wed Mar 1 17:30:07 MST 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://d-nb.info/1045240478/04",
  acknowledgement = ack-nhfb,
  language =     "German",
  tableofcontents = "1 Logik, Mengen, Zahlensysteme / 21 \\
                 2 Arithmetik / 46 \\
                 3 Gleichungen und Ungleichungen / 91 \\
                 4 Elementare Geometrie / 124 \\
                 5 Lineare Algebra / 168 \\
                 6 Vektoren, Analytische Geometrie / 244 \\
                 7 Funktionen und Kurven / 335 \\
                 8 Differenzialrechnung / 421 \\
                 9 Integralrechnung / 467 \\
                 10 Vektoranalysis / 512 \\
                 11 Differenzialgleichungen / 536 \\
                 12 Reihen, F- und L-/ Transformation \\
                 13 Statistik, Stochastik / 643 \\
                 14 Integraltabellen / 719",
}

@Book{Boyd:2014:STE,
  author =       "John P. (John Philip) Boyd",
  title =        "Solving transcendental equations: the {Chebyshev}
                 polynomial proxy and other numerical rootfinders,
                 perturbation series, and oracles",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xviii + 460",
  year =         "2014",
  ISBN =         "1-61197-351-1 (paperback)",
  ISBN-13 =      "978-1-61197-351-8 (paperback)",
  LCCN =         "QA353.T7 B69 2014",
  bibdate =      "Wed Sep 23 17:10:53 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy1503/2014017078-b.html;
                 http://www.loc.gov/catdir/enhancements/fy1503/2014017078-d.html;
                 http://www.loc.gov/catdir/enhancements/fy1503/2014017078-t.html",
  acknowledgement = ack-nhfb,
  author-dates = "1951--",
  subject =      "Transcendental functions; Chebyshev polynomials;
                 Transcendental numbers",
  tableofcontents = "I: Introduction and overview \\
                 Introduction: Key themes in rootfinding \\
                 II: the Chebyshev-Proxy rootfinder and its
                 generalizations \\
                 The Chebyshev-Proxy/Companion matrix rootfinder \\
                 Adaptive Chebyshev interpolation \\
                 Adaptive Fourier interpolation and rootfinding \\
                 Complex zeros: Interpolation on a disk, the
                 Delves--Lyness algorithm, and contour integrals \\
                 III: Fundamentals: Iterations, bifurcation, and
                 continuation \\
                 Newton iteration and its kin \\
                 Bifurcation theory \\
                 Continuation in a parameter \\
                 IV: Polynomials \\
                 Polynomial equations and the irony of Galois Theory \\
                 The Quadratic Equation \\
                 Roots of a cubic polynomial \\
                 Roots of a quartic polynomial \\
                 V: Analytical methods \\
                 Methods for explicit solutions \\
                 Regular perturbation methods for roots \\
                 Singular perturbation methods: fractional powers,
                 logarithms, and exponential asymptotics \\
                 VI: Classics, special functions, inverses, and oracles
                 \\
                 Classical methods for solving one equation in one
                 unknown \\
                 Special algorithms for special functions \\
                 Inverse functions of one unknown \\
                 Oracles: Theorems and algorithms for determining the
                 existence, nonexistence, and number of zeros \\
                 VII: Bivariate systems \\
                 Two equations in two unknowns \\
                 VIII: Challenges \\
                 Past and future \\
                 A: Companion matrices \\
                 B: Chebyshev interpolation and quadrature \\
                 Marching triangles \\
                 D: Imbricate-Fourier series and the Poisson Summation
                 Theorem",
}

@Article{Buehler:2014:CCH,
  author =       "Stephan Buehler and Claude Duhr",
  title =        "{CHAPLIN-Complex Harmonic Polylogarithms} in
                 {Fortran}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "185",
  number =       "10",
  pages =        "2703--2713",
  month =        oct,
  year =         "2014",
  CODEN =        "CPHCBZ",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Aug 16 08:37:41 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465514001969",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655/",
}

@Article{Choudhury:2014:SAA,
  author =       "Amit Choudhury",
  title =        "A simple approximation to the area under standard
                 normal curve",
  journal =      "Mathematics and Statistics",
  volume =       "2",
  number =       "3",
  pages =        "147--149",
  month =        "????",
  year =         "2014",
  DOI =          "https://doi.org/10.13189/ms.2014.020307",
  ISSN =         "2332-2071 (print), 2332-2144 (electronic)",
  ISSN-L =       "2332-2071",
  bibdate =      "Sat Dec 16 15:57:04 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.hrpub.org/journals/article_info.php?aid=1470;
                 https://www.hrpub.org/download/20140305/MS7-13401470.pdf",
  acknowledgement = ack-nhfb,
}

@Book{Dunkl:2014:OPS,
  author =       "Charles F. Dunkl and Yuan Xu",
  title =        "Orthogonal Polynomials of Several Variables",
  volume =       "155",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Second",
  pages =        "xvii + 420",
  year =         "2014",
  ISBN =         "1-107-07189-5, 1-316-05717-8 (e-book)",
  ISBN-13 =      "978-1-107-07189-6, 978-1-316-05717-9 (e-book)",
  LCCN =         "QA404.5 .D86 2014",
  bibdate =      "Sat Nov 11 06:43:34 MST 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Encyclopedia of mathematics and its applications",
  URL =          "http://catdir.loc.gov/catdir/enhancements/fy1408/2014001846-b.html;
                 http://catdir.loc.gov/catdir/enhancements/fy1408/2014001846-d.html;
                 http://catdir.loc.gov/catdir/enhancements/fy1408/2014001846-t.html;
                 http://digitale-objekte.hbz-nrw.de/storage2/2014/11/17/file_11/5877666.pdf",
  acknowledgement = ack-nhfb,
  remark =       "See also first edition \cite{Dunkl:2001:OPS}",
  shorttableofcontents = "Preface to the Second Edition / xiii \\
                 Preface to the First Edition / xv \\
                 1 Background / 1 \\
                 2 Orthogonal Polynomials in Two Variables / 28 \\
                 3 General Properties of Orthogonal Polynomials in
                 Several Variables / 57 \\
                 4 Orthogonal Polynomials on the Unit Sphere / 114 \\
                 5 Examples of Orthogonal Polynomials in Several
                 Variables / 137 \\
                 6 Root Systems and Coxeter Groups / 174 \\
                 7 Spherical Harmonics Associated with Reflection Groups
                 / 208 \\
                 8 Generalized Classical Orthogonal Polynomials / 258
                 \\
                 9 Summability of Orthogonal Expansions / 289 \\
                 10 Orthogonal Polynomials Associated with Symmetric
                 Groups / 318 \\
                 11 Orthogonal Polynomials Associated with Octahedral
                 Groups and Applications / 364 \\
                 References / 396 \\
                 Author Index / 413 \\
                 Symbol Index / 416 \\
                 Subject Index / 418",
  subject =      "Orthogonal polynomials; Functions of several real
                 variables; Polyn{\^o}mes orthogonaux; Fonctions de
                 plusieurs variables r{\'e}elles; Functions of several
                 real variables; Orthogonal polynomials; Orthogonale
                 reeksen; Ortogonalpolynom",
  tableofcontents = "Preface to the Second Edition / xiii \\
                 Preface to the First Edition / xv \\
                 \\
                 1 Background / 1 \\
                 1.1 The Gamma and Beta Functions / 1 \\
                 1.2 Hypergeometric Series / 3 \\
                 1.2.1 Lauricella series / 5 \\
                 1.3 Orthogonal Polynomials of One Variable / 6 \\
                 1.3.1 General properties / 6 \\
                 1.3.2 Three-term recurrence / 9 \\
                 1.4 Classical Orthogonal Polynomials / 13 \\
                 1.4.1 Hermite polynomials / 13 \\
                 1.4.2 Laguerre polynomials / 14 \\
                 1.4.3 Gegenbauer polynomials / 16 \\
                 1.4.4 Jacobi polynomials / 20 \\
                 1.5 Modified Classical Polynomials / 22 \\
                 1.5.1 Generalized Hermite polynomials / 24 \\
                 1.5.2 Generalized Gegenbauer polynomials / 25 \\
                 1.5.3 A limiting relation / 27 \\
                 1.6 Notes / 27 \\
                 \\
                 2 Orthogonal Polynomials in Two Variables / 28 \\
                 2.1 Introduction / 28 \\
                 2.2 Product Orthogonal Polynomials / 29 \\
                 2.3 Orthogonal Polynomials on the Unit Disk / 30 \\
                 2.4 Orthogonal Polynomials on the Triangle / 35 \\
                 2.5 Orthogonal Polynomials and Differential Equations /
                 37 \\
                 2.6 Generating Orthogonal Polynomials of Two Variables
                 / 38 \\
                 2.6.1 A method for generating orthogonal polynomials /
                 38 \\
                 2.6.2 Orthogonal polynomials for a radial weight / 40
                 \\
                 2.6.3 Orthogonal polynomials in complex variables / 41
                 \\
                 2.7 First Family of Koornwinder Polynomials / 45 \\
                 2.8 A Related Family of Orthogonal Polynomials / 43 \\
                 2.9 Second Family of Koornwinder Polynomials / 50 \\
                 2.10 Notes / 54 \\
                 \\
                 3 General Properties of Orthogonal Polynomials in
                 Several Variables / 57 \\
                 3.1 Notation and Preliminaries / 58 \\
                 3.2 Moment Functionals and Orthogonal Polynomials in
                 Several Variables / 60 \\
                 3.2.1 Definition of orthogonal polynomials / 60 \\
                 3.2.2 Orthogonal polynomials and moment matrices / 64
                 \\
                 3.2.3 The moment problem / 67 \\
                 3.3 The Three-Term Relation / 70 \\
                 3.3.1 Definition and basic properties / 70 \\
                 3.3.2 Favard's theorem / 73 \\
                 3.3.3 Centrally symmetric integrals / 76 \\
                 3.3.4 Examples / 79 \\
                 3.4 Jacobi Matrices and Commuting Operators / 82 \\
                 3.5 Further Properties of the Three-Term Relation / 87
                 \\
                 3.5.1 Recurrence formula / 87 \\
                 3.5.2 General solutions of the three-term relation / 94
                 \\
                 3.6 Reproducing Kernels and Fourier Orthogonal Series /
                 96 \\
                 3.6.1 Reproducing kernels / 97 \\
                 3.6.2 Fourier orthogonal series / 101 \\
                 3.7 Common Zeros of Orthogonal Polynomials in Several
                 Variables / 103 \\
                 3.8 Gaussian Cubature Formulae / 107 \\
                 3.9 Notes / 112 \\
                 \\
                 4 Orthogonal Polynomials on the Unit Sphere / 114 \\
                 4.1 Spherical Harmonics / 114 \\
                 4.2 Orthogonal Structures on $S^d$ and on $B^d$ / 119
                 \\
                 4.3 Orthogonal Structures on $B^d$ and on $S^{d + m -
                 1}$ / 125 \\
                 4.4 Orthogonal Structures on the Simplex / 129 \\
                 4.5 Van der Corput--Schaake Inequality / 133 \\
                 4.6 Notes / 136 \\
                 \\
                 5 Examples of Orthogonal Polynomials in Several
                 Variables / 137 \\
                 5.1 Orthogonal Polynomials for Simple Weight Functions
                 / 137 \\
                 5.1.1 Product weight functions / 138 \\
                 5.1.2 Rotation-invariant weight functions / 138 \\
                 5.1.3 Multiple Hermite polynomials on $\mathbb{R}^d$ /
                 139 \\
                 5.1.4 Multiple Laguerre polynomials on $\mathbb{R}^d__$
                 / 141 \\
                 5.2 Classical Orthogonal Polynomials on the Unit Ball /
                 141 \\
                 5.2.1 Orthonormal bases / 142 \\
                 5.2.2 Appell's monic orthogonal and biorthogonal
                 polynomials / 143 \\
                 5.2.3 Reproducing kernel with respect to $W_\mu^B$ on
                 $B^d$ / 148 \\
                 53.3 Classical Orthogonal Polynomials on the Simplex /
                 150 \\
                 5.4 Orthogonal Polynomials via Symmetric Functions /
                 154 \\
                 5.4.1 Two general families of orthogonal polynomials /
                 154 \\
                 5.4.2 Common zeros and Gaussian cubature formulae / 156
                 \\
                 5.5 Chebyshev Polynomials of Type ${\cal A}_d$ / 165
                 \\
                 5.6 Sobolev Orthogonal Polynomials on the Unit Ball /
                 165 \\
                 5.6.1 Sobolev orthogonal polynomials defined via the
                 gradient operator / 165 \\
                 5.6.2 Sobolev orthogonal polynomials defined via the
                 Laplacian operator / 168 \\
                 5.7 Notes / 171 \\
                 \\
                 6 Root Systems and Coxeter Groups / 174 \\
                 6.1 Introduction and Overview / 174 \\
                 6.2 Root Systems / 176 \\
                 6.2.1 Type $A_{d - 1}$ / 179 \\
                 6.2.2 Type $B_d$ / 179 \\
                 6.2.3 Type $I_2(m)$ / 180 \\
                 6.2.4 Type $D_d$ / 181 \\
                 6.2.5 Type $H_3$ / 181 \\
                 6.2.6 Type $F_4$ / 182 \\
                 6.2.7 Other types / 182 \\
                 6.2.8 Miscellaneous results / 182 \\
                 6.3 Invariant Polynomials / 183 \\
                 6.3.1 Type $A_{d - 1}$ invariants / 183 \\
                 6.3.2 Type $B_d$ invariants / 186 \\
                 6.3.3 Type $D_d$ invariants / 186 \\
                 6.3.4 Type $I_2(m)$ invariants / 186 \\
                 6.3.5 Type $H_3$ invariants / 186 \\
                 6.3.6 Type $F_4$ invariants / 187 \\
                 6.4 Differential--Difference Operators / 187 \\
                 6.5 The Intertwining Operator / 192 \\
                 6.6 The $\kappa$-Analogue of the Exponential / 200 \\
                 6.7 Invariant Differential Operators / 202 \\
                 6.8 Notes / 207 \\
                 \\
                 7 Spherical Harmonics Associated with Reflection Groups
                 / 208 \\
                 7.1 $h$-Harmonic Polynomials / 208 \\
                 7.2 Inner Products on Polynomials / 217 \\
                 7.3 Reproducing Kernels and the Poisson Kernel / 221
                 \\
                 7.4 Integration of the Intertwining Operator / 224 \\
                 7.5 Example: Abelian Group ${\cal Z}_2^d$ / 228 \\
                 7.5.1 Orthogonal basis for $h$-harmonics / 228 \\
                 7.5.2 Intertwining and projection operators / 232 \\
                 7.5.3 Monic orthogonal basis / 235 \\
                 7.6 Example: Dihedral Groups / 240 \\
                 7.6.1 An orthonormal basis of ${\cal H}_(h^2_{\alpha,
                 \beta})$ / 241 \\
                 7.6.2 Cauchy and Poisson kernels / 248 \\
                 7.7 The Dunkl Transform / 250 \\
                 7.8 Notes / 256 \\
                 \\
                 8 Generalized Classical Orthogonal Polynomials / 258
                 \\
                 8.1 Generalized Classical Orthogonal Polynomials on the
                 Ball / 258 \\
                 8.1.1 Definition and differential-difference equations
                 / 258 \\
                 8.1.2 Orthogonal basis and reproducing kernel / 263 \\
                 8.1.3 Orthogonal polynomials for ${\cal
                 Z}_2^d$-invariant weight functions / 266 \\
                 8.1.4 Reproducing kernel for ${\cal Z}_2^d$-invariant
                 weight functions / 268 \\
                 8.2 Generalized Classical Orthogonal Polynomials on the
                 Simplex / 271 \\
                 8.2.1 Weight function and differential-difference
                 equation / 271 \\
                 8.2.2 Orthogonal basis and reproducing kernel / 273 \\
                 8.2.3 Monic orthogonal polynomials / 287 \\
                 8.3 Generalized Hermite Polynomials / 278 \\
                 8.4 Generalized Laguerre Polynomials / 283 \\
                 8.5 Notes / 287 \\
                 \\
                 9 Summability of Orthogonal Expansions / 289 \\
                 9.1 General Results on Orthogonal Expansions / 289 \\
                 9.1.1 Uniform convergence of partial sums / 289 \\
                 9.1.2 Ces{\`a}ro means of the orthogonal expansion /
                 293 \\
                 9.2 Orthogonal Expansion on the Sphere / 296 \\
                 9.3 Orthogonal Expansion on the Ball / 299 \\
                 9.4 Orthogonal Expansion on the Simplex / 304 \\
                 9.5 Orthogonal Expansion of Laguerre and Hermite
                 Polynomials / 306 \\
                 9.6 Multiple Jacobi Expansion / 311 \\
                 9.7 Notes / 315 \\
                 \\
                 10 Orthogonal Polynomials Associated with Symmetric
                 Groups / 318 \\
                 10.1 Partitions, Compositions and Orderings / 318 \\
                 10.2 Commuting Self-Adjoint Operators / 320 \\
                 10.3 The Dual Polynomial Basis / 322 \\
                 10.4 $S_d$-Invariant Subspaces / 329 \\
                 10.5 Degree-Changing Recurrences / 334 \\
                 10.6 Norm Formulae / 337 \\
                 10.6.1 Hook-length products and the pairing norm / 337
                 \\
                 10.6.2 The biorthogonal-type norm / 341 \\
                 10.6.3 The torus inner product / 343 \\
                 10.6.4 Monic polynomials / 346 \\
                 10.6.5 Normalizing constants / 346 \\
                 10.7 Symmetric Functions and Jack Polynomials / 350 \\
                 10.8 Miscellaneous Topics / 357 \\
                 10.9 Notes / 362 \\
                 \\
                 11 Orthogonal Polynomials Associated with Octahedral
                 Groups and Applications / 364 \\
                 11.1 Introduction / 364 \\
                 11.2 Operators of Type $B$ / 365 \\
                 11.3 Polynomial Eigenfunctions of Type $B$ / 368 \\
                 11.4 Generalized Binomial Coefficients / 376 \\
                 11.5 Hermite Polynomials of Type $B$ / 373 \\
                 11.6 Calogero--Sutherland Systems / 385 \\
                 11.6.1 The simple harmonic oscillator / 386 \\
                 11.6.2 Root systems and the Laplacian / 387 \\
                 11.6.3 Type $A$ models on the line / 387 \\
                 11.6.4 Type $A$ models on the circle / 389 \\
                 11.6.5 Type $B$ models on the line / 392 \\
                 11.7 Notes / 394 \\
                 \\
                 References / 396 \\
                 Author Index / 413 \\
                 Symbol Index / 416 \\
                 Subject Index / 418",
}

@Article{Fukushima:2014:ACG,
  author =       "Toshio Fukushima",
  title =        "Analytical computation of generalized {Fermi--Dirac}
                 integrals by truncated {Sommerfeld} expansions",
  journal =      j-APPL-MATH-COMP,
  volume =       "234",
  number =       "??",
  pages =        "417--433",
  day =          "15",
  month =        may,
  year =         "2014",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon Apr 21 18:04:13 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300314002926",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Fukushima:2014:CGI,
  author =       "Toshio Fukushima",
  title =        "Computation of a general integral of {Fermi--Dirac}
                 distribution by {McDougall--Stoner} method",
  journal =      j-APPL-MATH-COMP,
  volume =       "238",
  number =       "??",
  pages =        "485--510",
  day =          "1",
  month =        jul,
  year =         "2014",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri May 23 10:53:19 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S009630031400561X",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Gil:2014:ACM,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 939}: Computation of the {Marcum}
                 {$Q$}-Function",
  journal =      j-TOMS,
  volume =       "40",
  number =       "3",
  pages =        "20:1--20:21",
  month =        apr,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2591004",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Apr 21 17:42:14 MDT 2014",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Methods and an algorithm for computing the generalized
                 Marcum $Q$-function $ (Q_\mu (x, y))$ and the
                 complementary function $ (P_\mu (x, y))$ are described.
                 These functions appear in problems of different
                 technical and scientific areas such as, for example,
                 radar detection and communications, statistics, and
                 probability theory, where they are called the
                 noncentral chi-square or the noncentral gamma
                 cumulative distribution functions. The algorithm for
                 computing the Marcum functions combines different
                 methods of evaluation in different regions: series
                 expansions, integral representations, asymptotic
                 expansions, and use of three-term homogeneous
                 recurrence relations. A relative accuracy close to $
                 10^{-12}$ can be obtained in the parameter region $ (x,
                 y, \mu) \in [0, A] \times [0, A] \times [1, A]$, $ A =
                 200$, while for larger parameters the accuracy
                 decreases (close to $ 10^{-11}$ for $ A = 1000$ and
                 close to $ 5 \times 10^{-11}$ for $ A = 10000$).",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gil:2014:CZA,
  author =       "Amparo Gil and Javier Segura",
  title =        "On the complex zeros of {Airy} and {Bessel} functions
                 and those of their derivatives",
  journal =      j-ANAL-APPL,
  volume =       "12",
  number =       "5",
  pages =        "537--561",
  month =        aug,
  year =         "2014",
  DOI =          "https://doi.org/10.1142/s0219530514500341",
  ISSN =         "0219-5305 (print), 1793-6861 (electronic)",
  ISSN-L =       "0219-5305",
  bibdate =      "Thu Nov 16 07:32:34 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Special Issue: Dedicated to the Memory of Frank Olver
                 (Part II).",
  acknowledgement = ack-nhfb,
  ajournal =     "Anal. Appl. (Singapore)",
  fjournal =     "Analysis and Applications (Singapore)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/aa",
  subject-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
}

@Article{Gil:2014:RSD,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Recent software developments for special functions in
                 the {Santander--Amsterdam} project",
  journal =      j-SCI-COMPUT-PROGRAM,
  volume =       "90 (part A)",
  number =       "??",
  pages =        "42--54",
  day =          "15",
  month =        sep,
  year =         "2014",
  CODEN =        "SCPGD4",
  DOI =          "https://doi.org/10.1016/j.scico.2013.11.004",
  ISSN =         "0167-6423 (print), 1872-7964 (electronic)",
  ISSN-L =       "0167-6423",
  bibdate =      "Thu May 22 07:49:47 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/scicomputprogram.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167642313002888",
  acknowledgement = ack-nhfb,
  fjournal =     "Science of Computer Programming",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676423/",
}

@Article{Goerg:2014:ULW,
  author =       "Georg M. Goerg",
  title =        "Usage of the {Lambert} {$W$} function in statistics",
  journal =      j-ANN-APPL-STAT,
  volume =       "8",
  number =       "4",
  pages =        "2567--2567",
  month =        dec,
  year =         "2014",
  CODEN =        "????",
  ISSN =         "1932-6157 (print), 1941-7330 (electronic)",
  ISSN-L =       "1932-6157",
  bibdate =      "Wed Feb 11 19:26:08 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annapplstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://projecteuclid.org/euclid.aoas/1419001755",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Applied Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoas/;
                 http://www.jstor.org/journals/19326157.html",
}

@InProceedings{Greuel:2014:SIS,
  author =       "Gert-Martin Greuel and Wolfram Sperber",
  title =        "{swMATH} --- an Information Service for Mathematical
                 Software",
  crossref =     "Hong:2014:MSI",
  pages =        "691--701",
  year =         "2014",
  DOI =          "https://doi.org/10.1007/978-3-662-44199-2_103",
  bibdate =      "Tue Sep 26 10:21:48 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Greynat:2014:NAE,
  author =       "David Greynat and Javier Sesma",
  title =        "A new approach to the epsilon expansion of generalized
                 hypergeometric functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "185",
  number =       "2",
  pages =        "472--478",
  month =        feb,
  year =         "2014",
  CODEN =        "CPHCBZ",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Dec 2 12:05:01 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S001046551300324X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Harvey:2014:SAC,
  author =       "David Harvey",
  title =        "A subquadratic algorithm for computing the $n$-th
                 {Bernoulli} number",
  journal =      j-MATH-COMPUT,
  volume =       "83",
  number =       "289",
  pages =        "2471--2477",
  year =         "2014",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Sep 9 11:37:57 MDT 2014",
  bibsource =    "http://www.ams.org/mcom/2014-83-289;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2014-83-289/S0025-5718-2014-02832-9;
                 http://www.ams.org/journals/mcom/2014-83-289/S0025-5718-2014-02832-9/S0025-5718-2014-02832-9.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Johansson:2014:EIE,
  author =       "Fredrik Johansson",
  title =        "Efficient implementation of elementary functions in
                 the medium-precision range",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "27",
  month =        oct,
  year =         "2014",
  bibdate =      "Mon Jun 12 16:12:02 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://arxiv.org/abs/1410.7176",
  abstract =     "We describe a new implementation of the elementary
                 transcendental functions exp, sin, cos, log and atan
                 for variable precision up to approximately 4096 bits.
                 Compared to the MPFR library, we achieve a maximum
                 speedup ranging from a factor 3 for cos to 30 for atan.
                 Our implementation uses table-based argument reduction
                 together with rectangular splitting to evaluate Taylor
                 series. We collect denominators to reduce the number of
                 divisions in the Taylor series, and avoid overhead by
                 doing all multiprecision arithmetic using the mpn layer
                 of the GMP library. Our implementation provides
                 rigorous error bounds.",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Johansson:2014:FRC,
  author =       "Fredrik Johansson",
  title =        "Fast and Rigorous Computation of Special Functions to
                 High Precision",
  type =         "{Ph.D.} thesis",
  school =       "Johannes Kepler University",
  address =      "Linz, Austria",
  pages =        "ix + 109",
  day =          "24",
  month =        mar,
  year =         "2014",
  bibdate =      "Sat Aug 09 09:01:13 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://permalink.obvsg.at/AC10776210",
  abstract =     "The problem of efficiently evaluating special
                 functions to high precision has been considered by
                 numerous authors. Important tools used for this purpose
                 include algorithms for evaluation of linearly recurrent
                 sequences, and algorithms for power series
                 arithmetic.\par

                 In this work, we give new baby-step, giant-step
                 algorithms for evaluation of linearly recurrent
                 sequences involving an expensive parameter (such as a
                 high-precision real number) and for computing
                 compositional inverses of power series. Our algorithms
                 do not have the best asymptotic complexity, but they
                 are faster than previous algorithms in practice over a
                 large input range.\par

                 Using a combination of techniques, we also obtain
                 efficient new algorithms for numerically evaluating the
                 gamma function $ \Gamma (z) $ and the Hurwitz zeta
                 function $ \zeta (s, a) $, or Taylor series expansions
                 of those functions, with rigorous error bounds. Our
                 methods achieve softly optimal complexity when
                 computing a large number of derivatives to
                 proportionally high precision.\par

                 Finally, we show that isolated values of the integer
                 partition function $ p(n) $ can be computed rigorously
                 with softly optimal complexity by means of the
                 Hardy--Ramanujan--Rademacher formula and careful
                 numerical evaluation. We provide open source
                 implementations which run significantly faster than
                 previously published software. The implementations are
                 used for record computations of the partition function,
                 including the tabulation of several billion
                 Ramanujan-type congruences, and of Taylor series
                 associated with the Riemann zeta function.",
  acknowledgement = ack-nhfb,
  remark =       "Reviewed in \booktitle{ACM Communications in Computer
                 Algebra}, {\bf 48}(2) 28--28 (2014).",
}

@Article{Krasikov:2014:ABA,
  author =       "Ilia Krasikov",
  title =        "Approximations for the {Bessel} and {Airy} functions
                 with an explicit error term",
  journal =      j-LMS-J-COMPUT-MATH,
  volume =       "17",
  number =       "1",
  pages =        "209--225",
  year =         "2014",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1112/S1461157013000351",
  ISSN =         "1461-1570",
  bibdate =      "Tue Sep 9 12:34:08 MDT 2014",
  bibsource =    "http://journals.cambridge.org/action/displayJournal?jid=JCM;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lms-j-comput-math.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "LMS J. Comput. Math.",
  fjournal =     "LMS Journal of Computation and Mathematics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=JCM",
  onlinedate =   "19 May 2014",
}

@InProceedings{Kupriianova:2014:MMF,
  author =       "Olga Kupriianova and Christoph Lauter",
  title =        "{Metalibm}: A Mathematical Functions Code Generator",
  crossref =     "Hong:2014:MSI",
  pages =        "713--717",
  year =         "2014",
  DOI =          "https://doi.org/10.1007/978-3-662-44199-2_106",
  bibdate =      "Tue Sep 26 10:21:48 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Li:2014:ICH,
  author =       "Dingfang Li and Ping Liu and Jisheng Kou",
  title =        "An improvement of {Chebyshev--Halley} methods free
                 from second derivative",
  journal =      j-APPL-MATH-COMP,
  volume =       "235",
  number =       "??",
  pages =        "221--225",
  day =          "25",
  month =        may,
  year =         "2014",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon Apr 21 18:04:20 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300314003312",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Lu:2014:GAF,
  author =       "Dawei Lu and Jinghai Feng and Congxu Ma",
  title =        "A general asymptotic formula of the gamma function
                 based on the {Burnside}'s formula",
  journal =      j-J-NUMBER-THEORY,
  volume =       "145",
  number =       "??",
  pages =        "317--328",
  month =        dec,
  year =         "2014",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2014.06.016",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Wed Jul 15 08:49:09 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X14002224",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Lu:2014:GAG,
  author =       "Dawei Lu and Lixin Song and Congxu Ma",
  title =        "A generated approximation of the gamma function
                 related to {Windschitl}'s formula",
  journal =      j-J-NUMBER-THEORY,
  volume =       "140",
  number =       "??",
  pages =        "215--225",
  month =        jul,
  year =         "2014",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2014.01.023",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Wed Jul 15 08:49:07 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X14000687",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Lu:2014:NAE,
  author =       "Dawei Lu and Xiaoguang Wang",
  title =        "A new asymptotic expansion and some inequalities for
                 the gamma function",
  journal =      j-J-NUMBER-THEORY,
  volume =       "140",
  number =       "??",
  pages =        "314--323",
  month =        jul,
  year =         "2014",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2014.01.025",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Wed Jul 15 08:49:07 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X14000705",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Lu:2014:SNI,
  author =       "Dawei Lu",
  title =        "Some new improved classes of convergence towards
                 {Euler}'s constant",
  journal =      j-APPL-MATH-COMP,
  volume =       "243",
  number =       "??",
  pages =        "24--32",
  day =          "15",
  month =        sep,
  year =         "2014",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2014.05.098",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Aug 16 10:10:22 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S009630031400798X",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
  keywords =     "Continued fraction; Euler's constant; Inequalities;
                 Rate of convergence",
}

@Article{Mortici:2014:SBG,
  author =       "Cristinel Mortici",
  title =        "Sharp bounds for gamma function in terms of $ x^{x -
                 1} $",
  journal =      j-APPL-MATH-COMP,
  volume =       "249",
  number =       "??",
  pages =        "278--285",
  day =          "15",
  month =        dec,
  year =         "2014",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Wed Nov 26 10:49:00 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300314013939",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Ogburn:2014:FDC,
  author =       "Daniel X. Ogburn and Colin L. Waters and Murray D.
                 Sciffer and Jeff A. Hogan and Paul C. Abbott",
  title =        "A finite difference construction of the spheroidal
                 wave functions",
  journal =      j-COMP-PHYS-COMM,
  volume =       "185",
  number =       "1",
  pages =        "244--253",
  month =        jan,
  year =         "2014",
  CODEN =        "CPHCBZ",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Dec 2 12:04:56 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465513002610",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Book{Potter:2014:APC,
  author =       "Ronald W. Potter",
  title =        "Arbitrary Precision Calculation of Selected Higher
                 Functions",
  publisher =    "Lulu",
  address =      "????",
  pages =        "????",
  year =         "2014",
  ISBN =         "1-312-59943-X",
  ISBN-13 =      "978-1-312-59943-7",
  LCCN =         "QA76.9.A43 P56 2014",
  bibdate =      "Sat Dec 10 15:39:37 MST 2022",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  subject =      "Computer algorithms; Computational complexity;
                 Functional programming languages; Mathematics;
                 Algorithms; Algorithmes; Complexit{\'e} de calcul
                 (Informatique); Langages de programmation fonctionnels;
                 Math{\'e}matiques; algorithms; mathematics; applied
                 mathematics; Algorithms; Computational complexity;
                 Computer algorithms; Functional programming languages;
                 Mathematics",
  tableofcontents = "Preface / ii \\
                 Introduction / x \\
                 1: Basic Arithmetic / 1-1 \\
                 2: High Precision Computational Techniques / 2-1 \\
                 3: Elementary Functions / 3-1 \\
                 4: Euler's Constant / 4-1 \\
                 5: Gamma and Polygamma Functions / 5-1 \\
                 6: Elliptic Integrals and $ \pi $ / 6-1 \\
                 7: Jacobian Elliptic Functions / 7-1 \\
                 8: Theta Functions / 8-1 \\
                 9: Incomplete Gamma Functions, Chi$^2$ and Inverse
                 Chi$^2$ Distribution / 9-1 \\
                 10: Beta and Incomplete Beta Functions, Student's $t$
                 and $F$-Distributions and Their Inverses / 10-1 \\
                 11: Error Functions, Gaussian Distribution and Inverse
                 / 11-1 \\
                 12: Modified Bessel Functions / 12-1 \\
                 13: Ordinary Bessel Functions / 13-1 \\
                 14: Zeros of Ordinary Bessel Functions / 14-1 \\
                 15: Spherical Bessel Functions / 15-1 \\
                 16: Airy Functions and Zeros / 16-1 \\
                 17: Kelvin Functions / 17-1 \\
                 18: Struve Functions / 18-1 \\
                 19: Fresnel Integrals / 19-1 \\
                 20: Exponential Integrals / 20-1 \\
                 21: Sine\slash Cosine and Sinh\slash Cosh Integrals /
                 21-1 \\
                 22: Orthogonal Polynomials / 22-1 \\
                 23: Polynomial Roots / 23-1 \\
                 24: Matrix Operations / 24-1 \\
                 25: Geometric Operations / 25-1 \\
                 Appendix A: Fast Fourier Transform (FFT) / A-1 \\
                 Appendix B: The AGM Algorithm / B-1 \\
                 Appendix C: Contours of Bessel Function Zeros / C-1 \\
                 Appendix D: A Few Numbers (6071 digits per number) /
                 D-1 \\
                 Appendix E: 315061 Decimal Digits of Euler's Constant /
                 E-1 \\
                 Index / I-1 \\
                 About the Author",
}

@Article{Qi:2014:IRC,
  author =       "Feng Qi",
  title =        "Integral representations and complete monotonicity
                 related to the remainder of {Burnside}'s formula for
                 the gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "268",
  number =       "??",
  pages =        "155--167",
  day =          "1",
  month =        oct,
  year =         "2014",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:34:45 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042714001356",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Rappoport:2014:MSM,
  author =       "Juri Rappoport",
  title =        "Mathematical Software for Modified {Bessel}
                 Functions",
  crossref =     "Hong:2014:MSI",
  pages =        "325--332",
  year =         "2014",
  DOI =          "https://doi.org/10.1007/978-3-662-44199-2_51",
  bibdate =      "Tue Sep 26 10:17:51 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Ratnanather:2014:ATI,
  author =       "J. Tilak Ratnanather and Jung H. Kim and Sirong Zhang
                 and Anthony M. J. Davis and Stephen K. Lucas",
  title =        "{Algorithm 935}: {{\tt IIPBF}}, a {{\tt MATLAB}}
                 toolbox for infinite integral of products of two
                 {Bessel} functions",
  journal =      j-TOMS,
  volume =       "40",
  number =       "2",
  pages =        "14:1--14:12",
  month =        feb,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2508435",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 14 06:30:41 MDT 2014",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A {\tt MATLAB} toolbox, {\tt IIPBF}, for calculating
                 infinite integrals involving a product of two Bessel
                 functions $ J_a(\rho x) J_b(\tau x) $, $ J_a(\rho x)
                 Y_b(\tau x) $, and $ Y_a(\rho x) Y_b(\tau x) $, for
                 non-negative integers $a$, $b$, and a well-behaved
                 function $ f(x) $, is described. Based on the Lucas
                 algorithm previously developed for $ J_a(\rho x)
                 J_b(\tau x) $ only, {\tt IIPBF} recasts each product as
                 the sum of two functions whose oscillatory behavior is
                 exploited in the three-step procedure of adaptive
                 integration, summation, and extrapolation. The toolbox
                 uses customised {\tt QUADPACK} and {\tt IMSL} functions
                 from a {\tt MATLAB} conversion of the {\tt SLATEC}
                 library. In addition, {\tt MATLAB}'s own {\tt quadgk}
                 function for adaptive Gauss--Kronrod quadrature results
                 in a significant speed up compared with the original
                 algorithm. Usage of {\tt IIPBF} is described and
                 eighteen test cases illustrate the robustness of the
                 toolbox; five additional ones are used to compare {\tt
                 IIPBF} with the {\tt BESSELINT} code for rational and
                 exponential forms of $ f(x) $ with $ J_a(\rho x)
                 J_b(\tau x) $. Reliability for a broad range of values
                 of $ \rho $ and $ \tau $ for the three different
                 product types as well as different orders in one case
                 is demonstrated. An electronic appendix provides a
                 novel derivation of formulae for five cases.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Shukla:2014:LLH,
  author =       "R. Shukla and K. C. Ray",
  title =        "Low Latency Hybrid {CORDIC} Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "63",
  number =       "12",
  pages =        "3066--3078",
  month =        dec,
  year =         "2014",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2013.173",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Dec 4 10:36:57 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "adders; Approximation algorithms; communication
                 systems; Computer architecture; coordinate rotational
                 digital computer; CORDIC algorithm; Delays; digital
                 arithmetic; Digital computers; digital computers;
                 double step branching; fast adders; first order
                 hardware architecture; hardware complexity; hybrid
                 CORDIC algorithm; image processing; low latency; low
                 latency hybrid CORDIC algorithm; Mathematical model;
                 radix-4; redundant arithmetic; scale factor
                 calculation; signal processing; Signal processing
                 algorithms",
}

@Article{Soranzo:2014:VSE,
  author =       "Alessandro Soranzo and Emanuela Epure",
  title =        "Very simply explicitly invertible approximations of
                 normal cumulative and normal quantile function",
  journal =      j-APPL-MATH-SCI-RUSE,
  volume =       "8",
  pages =        "4323--4341",
  year =         "2014",
  DOI =          "https://doi.org/10.12988/ams.2014.45338",
  ISSN =         "1312-885X (print), 1314-7552 (electronic)",
  ISSN-L =       "1312-885X",
  bibdate =      "Sat Dec 16 17:41:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://m-hikari.com/ams/ams-2014/ams-85-88-2014/epureAMS85-88-2014.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematical Sciences (Ruse)",
  journal-URL =  "http://www.m-hikari.com/ams/",
}

@Article{Wang:2014:CFA,
  author =       "Dong Wang and Milo{\v{s}} D. Ercegovac and Yang Xiao",
  title =        "Complex Function Approximation Using Two-Dimensional
                 Interpolation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "63",
  number =       "12",
  pages =        "2948--2960",
  month =        dec,
  year =         "2014",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2013.181",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Dec 4 10:36:57 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "2D convolution algorithm; 2D interpolation;
                 Approximation error; ASIC; bipartite schemes; bivariate
                 functions; coefficient table; complex exponential;
                 complex function approximation; complex function
                 evaluation; complex reciprocal; Complex reciprocal;
                 Computational complexity; cubic interpolation;
                 exponential functions; field programmable gate arrays;
                 FPGA; Function approximation; generic hardware
                 architecture; interpolation; interpolation degree;
                 interpolation kernels; Lagrange interpolation;
                 Lagrangian functions; linear interpolation; lookup
                 tables; memory requirements; multipartite schemes;
                 quadratic interpolation; Quadratic programming; table
                 lookup; tabulated function; two-dimensional
                 interpolation",
}

@Article{Wang:2014:FPT,
  author =       "Dong Wang and Jean-Michel Muller and Nicolas
                 Brisebarre and Milo D. Ercegovac",
  title =        "{$ (M, p, k)$-Friendly} Points: a Table-Based Method
                 to Evaluate Trigonometric Function",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "61",
  number =       "9",
  pages =        "711--715",
  year =         "2014",
  DOI =          "https://doi.org/10.1109/TCSII.2014.2331094",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Fri Sep 29 10:46:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}

@Article{Xu:2014:SII,
  author =       "Ai-Min Xu and Zhong-Di Cen",
  title =        "Some identities involving exponential functions and
                 {Stirling} numbers and applications",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "260",
  number =       "??",
  pages =        "201--207",
  month =        apr,
  year =         "2014",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:34:42 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042713005323",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Yun:2014:AHA,
  author =       "Beong In Yun",
  title =        "An ad hoc approximation to the {Gauss} error function
                 and a correction method",
  journal =      j-APPL-MATH-SCI-RUSE,
  volume =       "8",
  pages =        "4261--4273",
  year =         "2014",
  DOI =          "https://doi.org/10.12988/ams.2014.45345",
  ISSN =         "1312-885X (print), 1314-7552 (electronic)",
  bibdate =      "Sat Dec 16 18:06:18 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.m-hikari.com/ams/ams-2014/ams-85-88-2014/yunAMS85-88-2014.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematical Sciences (Ruse)",
  journal-URL =  "http://www.m-hikari.com/ams/",
}

@InProceedings{Zafar:2014:HAD,
  author =       "Saad Zafar and Raviteja Adapa",
  booktitle =    "2014 International Conference on Advances in
                 Electrical Engineering {(ICAEE)}",
  title =        "Hardware architecture design and mapping of ``{Fast
                 Inverse Square Root}'' algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  month =        jan,
  year =         "2014",
  DOI =          "https://doi.org/10.1109/icaee.2014.6838433",
  bibdate =      "Wed Dec 20 07:29:37 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Fast Inverse Square Root algorithm has been used
                 in 3D games of past for lighting and reflection
                 calculations, because it offers up to four times
                 performance gains. This paper presents a hardware
                 implementation of the algorithm on an FPGA board by
                 designing the complete architecture and successfully
                 mapping it on Xilinx Spartan 3E after thorough
                 functional verification. The results show that this
                 implementation provides a very efficient
                 single-precision floating point inverse square root
                 calculator with practically accurate results being made
                 available after just 12 short clock cycles. This
                 performance measure is far superior to the software
                 counterpart of the algorithm, and is not processor
                 dependent like rsqrtss of x86 SSE instruction set.
                 Results of this work can aid FPGA based vector
                 processors or graphic processing units with 3D
                 rendering. The hardware design can also form part of a
                 larger floating point arithmetic unit for dedicated
                 reciprocal square root calculations.",
  acknowledgement = ack-nhfb,
}

@Misc{Anonymous:2015:L,
  author =       "Anonymous",
  title =        "libcerf",
  howpublished = "Web site",
  year =         "2015",
  bibdate =      "Mon Jun 12 16:08:24 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://apps.jcns.fz-juelich.de/doku/sc/libcerf",
  abstract =     "This is the home page of libcerf, a self-contained
                 numeric library that provides an efficient and accurate
                 implementation of complex error functions, along with
                 Dawson, Faddeeva, and Voigt functions.",
  acknowledgement = ack-nhfb,
}

@Article{Bailey:2015:CCI,
  author =       "D. H. Bailey and J. M. Borwein",
  title =        "{Crandall}'s computation of the incomplete Gamma
                 function and the {Hurwitz} zeta function, with
                 applications to {Dirichlet} {$L$}-series",
  journal =      j-APPL-MATH-COMP,
  volume =       "268",
  number =       "??",
  pages =        "462--477",
  day =          "1",
  month =        oct,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Wed Sep 16 06:56:32 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315008292",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Beliakov:2015:ARZ,
  author =       "Gleb Beliakov and Yuri Matiyasevich",
  title =        "Approximation of {Riemann}'s Zeta Function by Finite
                 {Dirichlet} Series: A Multiprecision Numerical
                 Approach",
  journal =      j-EXP-MATH,
  volume =       "24",
  number =       "2",
  pages =        "150--161",
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.2014.976801",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  bibdate =      "Mon Jun 8 17:49:44 MDT 2015",
  bibsource =    "http://www.tandfonline.com/toc/uexm20/24/2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/expmath.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
}

@Article{Boyd:2015:FWC,
  author =       "John P. Boyd",
  title =        "Four ways to compute the inverse of the complete
                 elliptic integral of the first kind",
  journal =      j-COMP-PHYS-COMM,
  volume =       "196",
  number =       "??",
  pages =        "13--18",
  month =        nov,
  year =         "2015",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2015.05.006",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Tue Sep 22 13:45:19 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465515001733",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655/",
}

@Article{Brent:2015:BET,
  author =       "Richard P. Brent and Fredrik Johansson",
  title =        "A bound for the error term in the {Brent--McMillan}
                 algorithm",
  journal =      j-MATH-COMPUT,
  volume =       "84",
  number =       "295",
  pages =        "2351--2359",
  month =        "",
  year =         "2015",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Aug 4 08:33:55 MDT 2015",
  bibsource =    "http://www.ams.org/mcom/2015-84-295;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2015-84-295/S0025-5718-2015-02931-7;
                 http://www.ams.org/journals/mcom/2015-84-295/S0025-5718-2015-02931-7/S0025-5718-2015-02931-7.pdf",
  abstract =     "The Brent--McMillan algorithm B3 (1980), when
                 implemented with binary splitting, is the fastest known
                 algorithm for high-precision computation of Euler's
                 constant. However, no rigorous error bound for the
                 algorithm has ever been published. We provide such a
                 bound and justify the empirical observations of Brent
                 and McMillan. We also give bounds on the error in the
                 asymptotic expansions of functions related to the
                 Bessel functions $ I_0 (x) $ and $ K_0 (x) $ for
                 positive real $x$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Euler's constant; multiple-precision arithmetic",
}

@InProceedings{Brunie:2015:CGM,
  author =       "Nicolas Brunie and Florent de Dinechin and Olga
                 Kupriianova and Christoph Lauter",
  title =        "Code Generators for Mathematical Functions",
  crossref =     "Muller:2015:ISC",
  pages =        "66--73",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.22",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-22",
}

@Article{Chen:2015:AEC,
  author =       "Chao-Ping Chen and Neven Elezovi{\'c}",
  title =        "Asymptotic expansions and completely monotonic
                 functions associated with the gamma, psi and polygamma
                 functions",
  journal =      j-APPL-MATH-COMP,
  volume =       "269",
  number =       "??",
  pages =        "232--241",
  day =          "15",
  month =        oct,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Wed Sep 16 06:56:33 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315009637",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Chen:2015:IAEa,
  author =       "Chao-Ping Chen and Richard B. Paris",
  title =        "Inequalities, asymptotic expansions and completely
                 monotonic functions related to the gamma function",
  journal =      j-APPL-MATH-COMP,
  volume =       "250",
  number =       "??",
  pages =        "514--529",
  day =          "1",
  month =        jan,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Wed Jan 7 16:27:08 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S009630031401515X",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Chen:2015:IAEb,
  author =       "Chao-Ping Chen",
  title =        "Inequalities and asymptotic expansions associated with
                 the {Ramanujan} and {Nemes} formulas for the gamma
                 function",
  journal =      j-APPL-MATH-COMP,
  volume =       "261",
  number =       "??",
  pages =        "337--350",
  day =          "15",
  month =        jun,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Wed May 13 09:01:41 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315004610",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Chen:2015:ICM,
  author =       "Chao-Ping Chen",
  title =        "Inequalities and completely monotonic functions
                 associated with the ratios of functions resulting from
                 the gamma function",
  journal =      j-APPL-MATH-COMP,
  volume =       "259",
  number =       "??",
  pages =        "790--799",
  day =          "15",
  month =        may,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Apr 24 18:27:24 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315003148",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@InProceedings{deDinechin:2015:HIF,
  author =       "Florent de Dinechin and Matei Istoan",
  title =        "Hardware Implementations of Fixed-Point {Atan2}",
  crossref =     "Muller:2015:ISC",
  pages =        "34--41",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.23",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-22",
}

@Article{Elezovic:2015:EPF,
  author =       "Neven Elezovi{\'c}",
  title =        "Estimations of psi function and harmonic numbers",
  journal =      j-APPL-MATH-COMP,
  volume =       "258",
  number =       "??",
  pages =        "192--205",
  day =          "1",
  month =        may,
  year =         "2015",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2015.02.008",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Thu Mar 19 09:03:22 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315001617",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Flocke:2015:AAE,
  author =       "N. Flocke",
  title =        "{Algorithm 954}: an Accurate and Efficient Cubic and
                 Quartic Equation Solver for Physical Applications",
  journal =      j-TOMS,
  volume =       "41",
  number =       "4",
  pages =        "30:1--30:24",
  month =        oct,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699468",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 26 17:31:15 MDT 2015",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We report on an accurate and efficient algorithm for
                 obtaining all roots of general real cubic and quartic
                 polynomials. Both the cubic and quartic solvers give
                 highly accurate roots and place no restrictions on the
                 magnitude of the polynomial coefficients. The key to
                 the algorithm is a proper rescaling of both
                 polynomials. This puts upper bounds on the magnitude of
                 the roots and is very useful in stabilizing the root
                 finding process. The cubic solver is based on dividing
                 the cubic polynomial into six classes. By analyzing the
                 root surface for each class, a fast convergent
                 Newton--Raphson starting point for a real root is
                 obtained at a cost no higher than three additions and
                 four multiplications. The quartic solver uses the cubic
                 solver in getting information about stationary points
                 and, when the quartic has real roots, stable
                 Newton--Raphson iterations give one of the extreme real
                 roots. The remaining roots follow by composite
                 deflation to a cubic. If the quartic has only complex
                 roots, the present article shows that a stable
                 Newton--Raphson iteration on a derived symmetric sixth
                 degree polynomial can be formulated for the real parts
                 of the complex roots. The imaginary parts follow by
                 solving suitable quadratics.",
  acknowledgement = ack-nhfb,
  articleno =    "30",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fukushima:2015:PFCa,
  author =       "Toshio Fukushima",
  title =        "Precise and fast computation of inverse {Fermi--Dirac}
                 integral of order $ 1 / 2 $ by minimax rational
                 function approximation",
  journal =      j-APPL-MATH-COMP,
  volume =       "259",
  number =       "??",
  pages =        "698--707",
  day =          "15",
  month =        may,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Apr 24 18:27:24 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315003094",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Fukushima:2015:PFCb,
  author =       "Toshio Fukushima",
  title =        "Precise and fast computation of {Fermi--Dirac}
                 integral of integer and half integer order by piecewise
                 minimax rational approximation",
  journal =      j-APPL-MATH-COMP,
  volume =       "259",
  number =       "??",
  pages =        "708--729",
  day =          "15",
  month =        may,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Apr 24 18:27:24 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315003033",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@InProceedings{Fukushima:2015:PFCc,
  author =       "Toshio Fukushima",
  title =        "Precise and Fast Computation of Elliptic Integrals and
                 Functions",
  crossref =     "Muller:2015:ISC",
  pages =        "50--57",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.15",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-22",
}

@Article{Fukushima:2015:PFCd,
  author =       "Toshio Fukushima",
  title =        "Precise and fast computation of generalized
                 {Fermi--Dirac} integral by parameter polynomial
                 approximation",
  journal =      j-APPL-MATH-COMP,
  volume =       "270",
  number =       "??",
  pages =        "802--807",
  day =          "1",
  month =        nov,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Thu Nov 5 06:24:28 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315011509",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Gil:2015:CKF,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Computing the {Kummer} function {$ U(a, b, z) $} for
                 small values of the arguments",
  journal =      j-APPL-MATH-COMP,
  volume =       "271",
  number =       "??",
  pages =        "532--539",
  day =          "15",
  month =        nov,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Nov 13 08:52:33 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315012837",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Gil:2015:GPI,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{GammaCHI}: a package for the inversion and
                 computation of the gamma and chi-square cumulative
                 distribution functions (central and noncentral)",
  journal =      j-COMP-PHYS-COMM,
  volume =       "191",
  number =       "??",
  pages =        "132--139",
  month =        jun,
  year =         "2015",
  CODEN =        "CPHCBZ",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Apr 24 18:44:55 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465515000107",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655/",
}

@Article{Graillat:2015:ECF,
  author =       "Stef Graillat and Christoph Lauter and Ping Tak Peter
                 Tang and Naoya Yamanaka and Shin'ichi Oishi",
  title =        "Efficient Calculations of Faithfully Rounded $
                 l_2$-Norms of $n$-Vectors",
  journal =      j-TOMS,
  volume =       "41",
  number =       "4",
  pages =        "24:1--24:20",
  month =        oct,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699469",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 26 17:31:15 MDT 2015",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this article, we present an efficient algorithm to
                 compute the faithful rounding of the $ l_2 $-norm of a
                 floating-point vector. This means that the result is
                 accurate to within 1 bit of the underlying
                 floating-point type. This algorithm does not generate
                 overflows or underflows spuriously, but does so when
                 the final result calls for such a numerical exception
                 to be raised. Moreover, the algorithm is well suited
                 for parallel implementation and vectorization. The
                 implementation runs up to 3 times faster than the
                 netlib version on current processors.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Graillat:2015:MRE,
  author =       "Stef Graillat and Vincent Lef{\`e}vre and Jean-Michel
                 Muller",
  title =        "On the maximum relative error when computing integer
                 powers by iterated multiplications in floating-point
                 arithmetic",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "70",
  number =       "3",
  pages =        "653--667",
  month =        nov,
  year =         "2015",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-015-9967-8",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Sun Oct 25 07:27:50 MDT 2015",
  bibsource =    "http://link.springer.com/journal/11075/70/3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://link.springer.com/article/10.1007/s11075-015-9967-8",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  remark =       "The authors show via a complex multipage proof that
                 the iterated product for $ x^n $ in p-bit binary
                 arithmetic with default IEEE 754 rounding (to nearest
                 with ties to even) produces a worst-case relative error
                 in the product that is no larger than $ (n - 1) u $,
                 where $ u = 2^{-p} $ is the rounding unit.",
}

@InProceedings{Johansson:2015:EIE,
  author =       "Fredrik Johansson",
  title =        "Efficient Implementation of Elementary Functions in
                 the Medium-Precision Range",
  crossref =     "Muller:2015:ISC",
  pages =        "83--89",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.16",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-22",
}

@Article{Johansson:2015:RHP,
  author =       "Fredrik Johansson",
  title =        "Rigorous high-precision computation of the {Hurwitz}
                 zeta function and its derivatives",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "69",
  number =       "2",
  pages =        "253--270",
  month =        jun,
  year =         "2015",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-014-9893-1",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Thu May 28 15:00:06 MDT 2015",
  bibsource =    "http://link.springer.com/journal/11075/69/2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://link.springer.com/article/10.1007/s11075-014-9893-1",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Kuznetsov:2015:CTT,
  author =       "A. Kuznetsov",
  title =        "Computing the truncated theta function via {Mordell}
                 integral",
  journal =      j-MATH-COMPUT,
  volume =       "84",
  number =       "296",
  pages =        "2911--2926",
  month =        "",
  year =         "2015",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 20 16:30:35 MDT 2015",
  bibsource =    "http://www.ams.org/mcom/2015-84-296;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2015-84-296/S0025-5718-2015-02953-6;
                 http://www.ams.org/journals/mcom/2015-84-296/S0025-5718-2015-02953-6/S0025-5718-2015-02953-6.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@InProceedings{Lauter:2015:SAF,
  author =       "Christoph Lauter and Marc Mezzarobba",
  title =        "Semi-Automatic Floating-Point Implementation of
                 Special Functions",
  crossref =     "Muller:2015:ISC",
  pages =        "58--65",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.12",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-22",
}

@Article{Lu:2015:NSC,
  author =       "Dawei Lu and Lixin Song and Yang Yu",
  title =        "New sequences with continued fraction towards
                 {Euler}'s constant",
  journal =      j-APPL-MATH-COMP,
  volume =       "259",
  number =       "??",
  pages =        "12--20",
  day =          "15",
  month =        may,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Apr 24 18:27:24 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315001745",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Lu:2015:SNA,
  author =       "Dawei Lu and Lixin Song and Congxu Ma",
  title =        "Some new asymptotic approximations of the gamma
                 function based on {Nemes}' formula, {Ramanujan}'s
                 formula and {Burnside}'s formula",
  journal =      j-APPL-MATH-COMP,
  volume =       "253",
  number =       "??",
  pages =        "1--7",
  day =          "15",
  month =        feb,
  year =         "2015",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2014.12.077",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Wed Feb 18 09:36:23 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300314017317",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Lu:2015:SNQ,
  author =       "Dawei Lu and Congxu Ma",
  title =        "Some new quicker continued fraction approximations for
                 the gamma function related to the {Nemes}' formula",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "70",
  number =       "4",
  pages =        "825--833",
  month =        dec,
  year =         "2015",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-015-9975-8",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Jan 25 08:55:03 MST 2016",
  bibsource =    "http://link.springer.com/journal/11075/70/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://link.springer.com/article/10.1007/s11075-015-9975-8",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Mortici:2015:PAG,
  author =       "Cristinel Mortici and Hari M. Srivastava",
  title =        "A product approximation of the gamma function",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "69",
  number =       "3",
  pages =        "595--610",
  month =        jul,
  year =         "2015",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-014-9915-z",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Sat Aug 8 13:58:48 MDT 2015",
  bibsource =    "http://link.springer.com/journal/11075/69/3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://link.springer.com/article/10.1007/s11075-014-9915-z",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Nadarajah:2015:CGH,
  author =       "Saralees Nadarajah",
  title =        "On the Computation of {Gauss} Hypergeometric
                 Functions",
  journal =      j-AMER-STAT,
  volume =       "69",
  number =       "2",
  pages =        "146--148",
  year =         "2015",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.1080/00031305.2015.1028595",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Sun Aug 9 16:54:48 MDT 2015",
  bibsource =    "http://www.tandfonline.com/toc/utas20/69/2;
                 https://www.math.utah.edu/pub/tex/bib/amstat2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://amstat.tandfonline.com/loi/utas20",
  onlinedate =   "24 Mar 2015",
}

@Article{Natalini:2015:BPM,
  author =       "Pierpaolo Natalini and Paolo Emilio Ricci",
  title =        "{Bell} polynomials and modified {Bessel} functions of
                 half-integral order",
  journal =      j-APPL-MATH-COMP,
  volume =       "268",
  number =       "??",
  pages =        "270--274",
  day =          "1",
  month =        oct,
  year =         "2015",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2015.06.069",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Wed Sep 16 06:56:32 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315008504",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
  keywords =     "Bell polynomials; Bessel functions; Combinatorial
                 analysis; Hankel functions",
}

@Article{Qi:2015:SIT,
  author =       "Feng Qi and Cristinel Mortici",
  title =        "Some inequalities for the trigamma function in terms
                 of the digamma function",
  journal =      j-APPL-MATH-COMP,
  volume =       "271",
  number =       "??",
  pages =        "502--511",
  day =          "15",
  month =        nov,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Nov 13 08:52:33 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315012758",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Book{Schwalm:2015:EFE,
  author =       "William A. Schwalm",
  title =        "Elliptic Functions and Elliptic Integrals",
  publisher =    "Morgan and Claypool Publishers and IOP Publishing",
  address =      "San Rafael, CA, USA and Bristol, UK",
  pages =        "67",
  year =         "2015",
  DOI =          "https://doi.org/10.1088/978-1-6817-4230-4",
  ISBN =         "1-68174-166-0 (print), 1-68174-230-6 (e-book),
                 1-68174-102-4 (mobi)",
  ISBN-13 =      "978-1-68174-166-6 (print), 978-1-68174-230-4 (e-book),
                 978-1-68174-102-4 (mobi)",
  ISSN =         "2054-7307",
  LCCN =         "QA343 .S355 2015",
  bibdate =      "Tue Mar 14 07:38:46 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "IOP concise physics",
  URL =          "http://iopscience.iop.org/book/978-1-6817-4230-4",
  abstract =     "This volume is a basic introduction to certain aspects
                 of elliptic functions and elliptic integrals.
                 Primarily, the elliptic functions stand out as closed
                 solutions to a class of physical and geometrical
                 problems giving rise to nonlinear differential
                 equations. While these nonlinear equations may not be
                 the types of greatest interest currently, the fact that
                 they are solvable exactly in terms of functions about
                 which much is known makes up for this. The elliptic
                 functions of Jacobi, or equivalently the Weierstrass
                 elliptic functions, inhabit the literature on current
                 problems in condensed matter and statistical physics,
                 on solitons and conformal representations, and all
                 sorts of famous problems in classical mechanics. The
                 lectures on elliptic functions have evolved as part of
                 the first semester of a course on theoretical and
                 mathematical methods given to first- and second-year
                 graduate students in physics and chemistry at the
                 University of North Dakota. They are for graduate
                 students or for researchers who want an elementary
                 introduction to the subject that nevertheless leaves
                 them with enough of the details to address real
                 problems. The style is supposed to be informal. The
                 intention is to introduce the subject as a moderate
                 extension of ordinary trigonometry in which the
                 reference circle is replaced by an ellipse. This entre
                 depends upon fewer tools and has seemed less
                 intimidating that other typical introductions to the
                 subject that depend on some knowledge of complex
                 variables. The first three lectures assume only
                 calculus, including the chain rule and elementary
                 knowledge of differential equations. In the later
                 lectures, the complex analytic properties are
                 introduced naturally so that a more complete study
                 becomes possible",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface \\
                 1. Elliptic functions as trigonometry \\
                 1.1. Definition of Jacobian elliptic functions and
                 trigonometric identities \\
                 1.2. Differential equations \\
                 1.3. Anharmonic oscillator \\
                 2. Differential equations satisfied by the Jacobi
                 elliptic functions: pendula \\
                 2.1. Oscillatory motion of a pendulum at large
                 amplitude \\
                 2.2. Motion traversing the whole circle \\
                 2.3. The sine-Gordon equation: a series of pendula \\
                 2.4. Series of pendula: 'super luminal' case \\
                 3. General reduction of the DE in terms of Jacobi
                 functions \\
                 3.1. Linear fractional transformation and cross ratio
                 \\
                 3.2. Reduction of general quartic case \\
                 3.3. Finding the coefficients of the linear fractional
                 transformation \\
                 4. Elliptic integrals \\
                 4.1. Review of complex variables up through residues
                 \\
                 4.2. Branching and multi-valued functions in complex
                 planes \\
                 4.3. Elliptic integrals and elliptic functions in
                 complex planes \\
                 4.4. Example \\
                 4.5. Reduction of the most general elliptic integral in
                 terms of the three Legendre forms",
}

@Article{Sun:2015:LEG,
  author =       "Qiming Sun",
  title =        "{Libcint}: an efficient general integral library for
                 {Gaussian} basis functions",
  journal =      j-J-COMPUT-CHEM,
  volume =       "36",
  number =       "22",
  pages =        "1664--1671",
  day =          "15",
  month =        aug,
  year =         "2015",
  CODEN =        "JCCHDD",
  DOI =          "https://doi.org/10.1002/jcc.23981",
  ISSN =         "0192-8651 (print), 1096-987X (electronic)",
  ISSN-L =       "0192-8651",
  bibdate =      "Sat Jul 25 20:32:36 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputchem2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0192-8651",
  onlinedate =   "30 Jun 2015",
}

@Book{Temme:2015:AMI,
  author =       "Nico M. Temme",
  title =        "Asymptotic Methods for Integrals",
  volume =       "6",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "xxii + 605",
  year =         "2015",
  ISBN =         "981-4612-15-4 (hardcover), 981-4612-16-2 (e-book)",
  ISBN-13 =      "978-981-4612-15-9 (hardcover), 978-981-4612-16-6
                 (e-book)",
  MRclass =      "41-02 (33Cxx 33E20 65D30)",
  MRnumber =     "3328507",
  MRreviewer =   "Jos{\'e} Luis L{\'o}pez",
  bibdate =      "Tue Feb 06 11:44:21 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
  series =       "Series in Analysis",
  abstract =     "This book gives introductory chapters on the classical
                 basic and standard methods for asymptotic analysis,
                 such as Watson's lemma, Laplace's method, the saddle
                 point and steepest descent methods, stationary phase
                 and Darboux's method. The methods, explained in great
                 detail, will obtain asymptotic approximations of the
                 well-known special functions of mathematical physics
                 and probability theory. After these introductory
                 chapters, the methods of uniform asymptotic analysis
                 are described in which several parameters have
                 influence on typical phenomena: turning points and
                 transition points, coinciding saddle and singularities.
                 In all these examples, the special functions are
                 indicated that describe the peculiar behavior of the
                 integrals. The text extensively covers the classical
                 methods with an emphasis on how to obtain expansions,
                 and how to use the results for numerical methods, in
                 particular for approximating special functions. In this
                 way, we work with a computational mind: how can we use
                 certain expansions in numerical analysis and in
                 computer programs, how can we compute coefficients, and
                 so on.",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Basic methods for integrals \\
                 Basic methods: examples for special functions \\
                 Other methods for integrals \\
                 Uniform methods for integrals \\
                 Uniform methods for Laplace-type integrals \\
                 Uniform examples for special functions \\
                 A class of cumulative distribution factors",
  tableofcontents = "Preface / vii \\
                 Acknowledgments / ix \\
                 Part 1: Basic Methods for Integrals / 1 \\
                 1. Introduction / 3 \\
                 1.1 Symbols used in asymptotic estimates / 3 \\
                 1.2 Asymptotic expansions / 4 \\
                 1.3 A first example: Exponential integral / 5 \\
                 1.4 Generalized asymptotic expansions / 7 \\
                 1.5 Properties of asymptotic power series / 8 \\
                 1.6 Optimal truncation of asymptotic expansions / 10
                 \\
                 2. Expansions of Laplace-type integrals: Watson's lemma
                 / 13 \\
                 2.1 Watson's lemma / 13 \\
                 2.1.1 Watson's lemma for extended sectors / 14 \\
                 2.1.2 More general forms of Watson's lemma / 16 \\
                 2.2 Watson's lemma for loop integrals / 16 \\
                 2.3 More general forms of Laplace-type integrals / 19
                 \\
                 2.3.1 Transformation to the standard form / 19 \\
                 2.4 How to compute the coefficients / 20 \\
                 2.4.1 Inversion method for computing the coefficients /
                 20 \\
                 2.4.2 Integrating by parts / 22 \\
                 2.4.3 Manipulating power series / 23 \\
                 2.4.4 Explicit forms of the coefficients in the
                 expansion / 25 \\
                 2.5 Other kernels / 26 \\
                 2.6 Exponentially improved asymptotic expansions / 27
                 \\
                 2.7 Singularities of the integrand / 29 \\
                 2.7.1 A pole near the endpoint / 29 \\
                 2.7.2 More general cases / 32 \\
                 3. The method of Laplace / 33 \\
                 3.1 A theorem for the general case / 33 \\
                 3.2 Constructing the expansion / 35 \\
                 3.2.1 Inversion method for computing the coefficients /
                 36 \\
                 3.3 Explicit forms of the coefficients in the expansion
                 / 37 \\
                 3.4 The complementary error function / 38 \\
                 4. The saddle point method and paths of steepest
                 descent / 41 \\
                 4.1 The axis of the valley at the saddle point / 43 \\
                 4.2 Examples with simple exponentials / 43 \\
                 4.2.1 A first example / 43 \\
                 4.2.2 A cosine transform / 44 \\
                 4.3 Steepest descent paths not through a saddle point /
                 44 \\
                 4.3.1 A gamma function example / 45 \\
                 4.3.2 An integral related to the error function / 46
                 \\
                 4.4 An example with strong oscillations: A 100-digit
                 challenge / 48 \\
                 4.5 A Laplace inversion formula for $ \erfc z $ / 49
                 \\
                 4.6 A non-oscillatory integral for $ \erfc z $ , $ z
                 \in \mathbb{C} $ / 50 \\
                 4.7 The complex Airy function / 50 \\
                 4.8 A parabolic cylinder function / 53 \\
                 5. The Stokes phenomenon / 57 \\
                 5.1 The Airy function / 57 \\
                 5.2 The recent interest in the Stokes phenomenon / 58
                 \\
                 5.3 Exponentially small terms in the Airy expansions /
                 59 \\
                 5.4 Expansions in connection with the Stokes phenomenon
                 / 60 \\
                 5.4.1 Applications to a Kummer function / 61 \\
                 Part 2: Basic Methods: Examples for Special Functions /
                 63 \\
                 6. The gamma function / 65 \\
                 6.1 $ \Gamma(z) $ by Laplace's method / 66 \\
                 6.1.1 Calculating the coefficients / 67 \\
                 6.1.2 Details on the transformation / 68 \\
                 6.2 $ 1 / \Gamma(z) $ by the saddle point method / 71
                 \\
                 6.2.1 Another integral representation of $ 1 /
                 \Gamma(z) $ / 72 \\
                 6.3 The logarithm of the gamma function / 72 \\
                 6.3.1 Estimations of the remainder / 73 \\
                 6.4 Expansions of $ \Gamma(z + a) $ and $ 1 / \Gamma(z
                 + a) $ / 75 \\
                 6.5 The ratio of two gamma functions / 76 \\
                 6.5.1 A simple expansion / 77 \\
                 6.5.2 A more efficient expansion / 78 \\
                 6.6 A binomial coefficient / 80 \\
                 6.6.1 A uniform expansion of the binomial coefficient /
                 83 \\
                 6.7 Asymptotic expansion of a product of gamma
                 functions / 85 \\
                 6.8 Expansions of ratios of three gamma functions / 88
                 \\
                 7. Incomplete gamma functions / 91 \\
                 7.1 Integral representations / 91 \\
                 7.2 $ \Gamma(a, x) $ : Asymptotic expansion for $ x \gg
                 a $ / 92 \\
                 7.3 $ \gamma(a, x) $ : Asymptotic expansion for $ a > x
                 $ / 93 \\
                 7.3.1 Singularity of the integrand / 94 \\
                 7.3.2 More details on the transformation $ u = \phi(t)
                 $ / 96 \\
                 7.4 $ \Gamma(a, x) $ : Asymptotic expansion for $ x > a
                 $ / 97 \\
                 8. The Airy functions / 101 \\
                 8.1 Expansions of $ \Ai(z) $, $ \Bi(z) $ / 102 \\
                 8.1.1 Transforming the saddle point contour / 102 \\
                 8.2 Expansions of $ \Ai(-z) $, $ \Bi(-z) $ / 105 \\
                 8.3 Two simple ways to obtain the coefficients / 106
                 \\
                 8.4 A generalized form of the Airy function / 107 \\
                 9. Bessel functions: Large argument / 109 \\
                 9.1 The modified Bessel function $ K_\nu(z) $ / 109 \\
                 9.2 The ordinary Bessel functions / 110 \\
                 9.3 The modified Bessel function $ I_\nu(z) $ / 111
                 9.3.1 A compound expansion of $ I_\nu(z) $ / 111 9.4
                 Saddle point method for $ K_\nu(z) $ , $ z \in
                 \mathbb{C} $ / 113 \\
                 9.4.1 Integral representations from saddle point
                 analysis / 115 \\
                 9.4.2 Saddle point method for $ J_\nu(x) $ , $ x < \nu
                 $ / 116 \\
                 9.5 Debye-type expansions of the modified Bessel
                 functions / 117 \\
                 9.6 Modified Bessel functions of purely imaginary order
                 / 119 \\
                 9.6.1 The monotonic case: $ x > \nu > 0 $ / 120 \\
                 9.6.2 The oscillatory case: $ \nu > x > 0 $ / 123 \\
                 9.7 A $ J $ -Bessel integral / 126 \\
                 10. Kummer functions / 129 \\
                 10.1 General properties / 129 \\
                 10.2 Asymptotic expansions for large $ z $ / 131 \\
                 10.3 Expansions for large $ a $ / 132 \\
                 10.3.1 Tricomi's function $ E_\nu(z) $ / 132 \\
                 10.3.2 Expansion of $ U(a, c, z) $ , $ a \to +\infty $
                 / 133 \\
                 10.3.3 Expansion of $ _1F_1(a; c; z) $ , $ a \to
                 +\infty $ / 135 \\
                 10.3.4 Expansion of $ _1F_1(a; c; z) $ , $ a \to
                 -\infty $ / 137 \\
                 10.3.5 Expansion of $ U(a, c, z) $ , $ a \to -\infty $
                 / 138 \\
                 10.3.6 Slater's results for large $ a $ / 140 \\
                 10.4 Expansions for large $ c $ / 142 \\
                 10.4.1 Expansion of $ _1F_1(a; c; z) $ , $ c \to
                 +\infty $ / 142 \\
                 10.4.2 Expansion of $ U(a, c, z) $ , $ c \to +\infty $
                 , $ z < c $ / 143 \\
                 10.4.3 Expansion of $ U(a, c, z) $ , $ c \to +\infty $
                 , $ z > e $ / 144 \\
                 10.4.4 Expansion of $ U(a, c, z) $ , $ c \to -\infty $
                 / 145 \\
                 10.4.5 Expansion of $ _1F_1(a; c; z) $ , $ c \to
                 -\infty $ / 147 \\
                 10.5 Uniform expansions of the Kummer functions / 147
                 \\
                 11. Parabolic cylinder functions: Large argument / 149
                 \\
                 11.1 A few properties of the parabolic cylinder
                 functions / 149 \\
                 11.2 The function $ U(a, z) $ / 150 \\
                 11.3 The function $ U(a, -z) $ / 152 \\
                 11.4 The function $ V(a, z) $ / 153 \\
                 11.5 Expansions of the derivatives / 154 \\
                 12. The Gauss hypergeometric function / 155 \\
                 12.1 Large values of $ c $ / 156 \\
                 12.1.1 Large positive $ c $ ; $ |z| < z_0 $ / 156 \\
                 12.1.2 Large negative $ c $ ; $ |z| < z_0 $ / 157 \\
                 12.1.3 Large positive $ c $ ; $ |z| > z_0 $ / 158 \\
                 12.1.4 Large negative $ c $ ; $ |z| > z_0 $ / 158 \\
                 12.2 Large values of $ b $ / 158 \\
                 12.2.1 Large negative $ b $ ; $ |z| > z_0 $ / 159 \\
                 12.2.2 Large $ b $ , $ |z| < z_0 $ / 159 \\
                 12.3 Other large parameter cases / 160 \\
                 12.3.1 Jacobi polynomials of large degree / 161 \\
                 12.3.2 An example of the case $ _2F_1(a, b - \lambda; c
                 + \lambda; z) $ / 163 \\
                 13. Examples of $ _3F_2 $ -polynomials / 167 \\
                 13.1 A $ _3F_2 $ associated with the
                 Catalan--Larcombe--French sequence / 167 \\
                 13.1.1 Transformations / 169 \\
                 13.1.2 Asymptotic analysis / 170 \\
                 13.1.3 Asymptotic expansion / 172 \\
                 13.1.4 An alternative method / 173 \\
                 13.2 An integral of Laguerre polynomials / 175 \\
                 13.2.1 A first approach / 176 \\
                 13.2.2 A generating function approach / 178 \\
                 Part 3: Other Methods for Integrals / 181 \\
                 14. The method of stationary phase / 183 \\
                 14.1 Critical points / 183 \\
                 14.2 Integrating by parts: No stationary points / 184
                 \\
                 14.3 Three critical points: A formal approach / 185 \\
                 14.4 On the use of neutralizes / 186 \\
                 14.5 How to avoid neutralizes? / 188 \\
                 14.5.1 A few details about the Fresnel integral / 190
                 \\
                 14.6 Algebraic singularities at both endpoints:
                 Erdelyi's example / 191 \\
                 14.6.1 Application: A conical function / 192 \\
                 14.6.2 Avoiding neutralizes in Erdelyi's example / 193
                 \\
                 14.7 Transformation to standard form / 194 \\
                 14.8 General order stationary points / 196 \\
                 14.8.1 Integrating by parts / 196 \\
                 14.9 The method fails: Examples / 197 \\
                 14.9.1 The Airy function / 198 \\
                 14.9.2 A more complicated example / 198 \\
                 15. Coefficients of a power series. Darboux's method /
                 203 \\
                 15.1 A first example: A binomial coefficient / 204 \\
                 15.2 Legendre polynomials of large degree / 205 \\
                 15.2.1 A paradox in asymptotics / 207 \\
                 15.3 Gegenbauer polynomials of large degree / 208 \\
                 15.4 Jacobi polynomials of large degree / 209 \\
                 15.5 Laguerre polynomials of large degree / 209 \\
                 15.6 Generalized Bernoulli polynomials $ B_n^{(\mu)}(z)
                 $ / 210 \\
                 15.6.1 Asymptotic expansions for large degree / 211 \\
                 15.6.2 An alternative expansion / 213 \\
                 15.7 Generalized Euler polynomials $ E_n^{(\mu)}(z) $ /
                 215 \\
                 15.7.1 Asymptotic expansions for large degree / 215 \\
                 15.7.2 An alternative expansion / 216 \\
                 15.8 Coefficients of expansions of the $ _1F_1 $
                 -function / 218 \\
                 15.8.1 Coefficients of Tricomi's expansion / 218 \\
                 15.8.2 Coefficients of Buchholz's expansion / 221 \\
                 16. Mellin--Barnes integrals and Mellin convolution
                 integrals / 225 \\
                 16.1 Mellin--Barnes integrals / 226 \\
                 16.2 Mellin convolution integrals / 228 \\
                 16.3 Error bounds / 230 \\
                 17. Alternative expansions of Laplace-type integrals /
                 231 \\
                 17.1 Hadamard-type expansions / 231 \\
                 17.2 An expansion in terms of Kummer functions / 233
                 \\
                 17.3 An expansion in terms of factorial series / 234
                 \\
                 17.4 The Franklin--Friedman expansion / 237 \\
                 18. Two-point Taylor expansions / 241 \\
                 18.1 The expansions / 242 \\
                 18.2 An alternative form of the expansion / 243 \\
                 18.3 Explicit forms of the coefficients / 244 \\
                 18.4 Manipulations with two-point Taylor expansions /
                 245 \\
                 19. Hermite polynomials as limits of other classical
                 orthogonal polynomials / 249 \\
                 19.1 Limits between orthogonal polynomials / 249 \\
                 19.2 The Askey scheme of orthogonal polynomials / 251
                 \\
                 19.3 Asymptotic representations / 251 \\
                 19.4 Gegenbauer polynomials / 253 \\
                 19.5 Laguerre polynomials / 254 \\
                 19.6 Generalized Bessel polynomials / 255 \\
                 19.7 Meixner--Pollaczek polynomials into Laguerre
                 polynomials / 257 \\
                 Part 4: Uniform Methods for Integrals / 259 \\
                 20. An overview of standard forms / 261 \\
                 20.1 Comments on the table / 263 \\
                 21. A saddle point near a pole / 267 \\
                 21.1 A saddle point near a pole: Van der Waerden's
                 method / 267 \\
                 21.2 An alternative expansion / 269 \\
                 21.3 An example from De Bruijn / 270 \\
                 21.4 A pole near a double saddle point / 271 \\
                 21.5 A singular perturbation problem and $ K $ -Bessel
                 integrals / 272 \\
                 21.5.1 A Bessel $ K_0 $ integral / 272 \\
                 21.5.2 A similar Bessel $ K_1 $ integral / 274 \\
                 21.5.3 A singular perturbation problem / 275 \\
                 21.6 A double integral with poles near saddle points /
                 277 \\
                 21.6.1 Application to a singular perturbation problem /
                 278 \\
                 21.7 The Fermi--Dirac integral / 281 \\
                 22. Saddle point near algebraic singularity / 285 \\
                 22.1 A saddle point near an endpoint of the interval /
                 285 \\
                 22.2 The Bleistein expansion / 286 \\
                 22.3 Extending the role of the parameter /3 / 289 \\
                 22.4 Contour integrals / 291 \\
                 22.5 Kummer functions in terms of parabolic cylinder
                 functions / 292 \\
                 22.5.1 Uniform expansion of $ U(a, c, z) $ , $ c \to
                 +\infty $ / 293 \\
                 22.5.2 Uniform expansion of $ _1F_1(a; c; z) $ , $ c
                 \to +\infty $ / 296 \\
                 23. Two coalescing saddle points: Airy-type expansions
                 / 299 \\
                 23.1 The standard form / 299 \\
                 23.2 An integration by parts method / 300 \\
                 23.3 How to compute the coefficients / 302 \\
                 23.4 An Airy-type expansion of the Hermite polynomial /
                 305 \\
                 23.4.1 The cubic transformation / 306 \\
                 23.4.2 Details on the coefficients / 308 \\
                 23.5 An Airy-type expansion of the Bessel function $
                 J_\nu(z) $ / 309 \\
                 23.6 A semi-infinite interval: Incomplete Scorer
                 function / 313 \\
                 23.6.1 A singular perturbation problem inside a circle
                 / 315 \\
                 24. Hermite-type expansions of integrals / 319 \\
                 24.1 An expansion in terms of Hermite polynomials / 320
                 \\
                 24.1.1 Cauchy-type integrals for the coefficients / 321
                 \\
                 24.2 Gegenbauer polynomials / 323 \\
                 24.2.1 Preliminary steps / 324 \\
                 24.2.2 A first approximation / 325 \\
                 24.2.3 Transformation to the standard form / 326 \\
                 24.2.4 Special cases of the expansion / 331 \\
                 24.2.5 Approximating the zeros / 332 \\
                 24.2.6 The relativistic Hermite polynomials / 333 \\
                 24.3 Tricomi--Carlitz polynomials / 333 \\
                 24.3.1 Contour integral and saddle points / 335 \\
                 24.3.2 A first approximation / 337 \\
                 24.3.3 Transformation to the standard form / 337 \\
                 24.3.4 Approximating the zeros / 339 \\
                 24.4 More examples / 340 \\
                 Part 5: Uniform Methods for Laplace-Type Integrals /
                 341 \\
                 25. The vanishing saddle point / 343 \\
                 25.1 Expanding at the saddle point / 344 \\
                 25.2 An integration by parts method / 346 \\
                 25.2.1 Representing coefficients as a Cauchy-type
                 integral / 347 \\
                 25.3 Expansions for loop integrals / 348 \\
                 25.4 Rummer functions / 350 \\
                 25.5 Generalized zeta function / 350 \\
                 25.6 Transforming to the standard form / 351 \\
                 25.6.1 The ratio of two gamma functions / 352 \\
                 25.6.2 Parabolic cylinder functions / 354 \\
                 26. A moving endpoint: Incomplete Laplace integrals /
                 355 \\
                 26.1 The standard form / 355 \\
                 26.2 Constructing the expansion / 356 \\
                 26.2.1 The complementary function / 357 \\
                 26.3 Application to the incomplete beta function / 358
                 \\
                 26.3.1 Expansions of the coefficients / 361 \\
                 26.4 A corresponding loop integral / 362 \\
                 26.4.1 Application to the incomplete beta function /
                 363 \\
                 27. An essential singularity: Bessel-type expansions /
                 365 \\
                 27.1 Expansions in terms of modified Bessel functions /
                 365 \\
                 27.2 A corresponding loop integral / 368 \\
                 27.3 Expansion at the internal saddle point / 368 \\
                 27.4 Application to Kummer functions / 369 \\
                 27.4.1 Expansion of $ U(a, c, z) $ , $ a \to +\infty $
                 , $ z > 0 $ / 369 \\
                 27.4.2 Auxiliary expansions and further details / 372
                 \\
                 27.4.3 Expansion of $ _1F_1(a: c; z) $ , $ a \to
                 +\infty $ , $ z > 0 $ / 374 \\
                 27.4.4 Expansion of $ _1F_1(a; c: z) $ , $ a \to
                 -\infty $ , $ 0 < z < -4a $ / 375 \\
                 27.4.5 Expansion of $ U(a, c, z) $ , $ a \to -\infty $
                 , $ 0 < z < -4a $ / 377 \\
                 27.5 A second uniformity parameter / 378 \\
                 27.5.1 Expansion of $ U(a, c, z) $ , $ a \to \infty $ ,
                 $ z > 0 $ , $ c < 1 $ / 380 \\
                 27.5.2 Expansion of $ _1F_1(a; c; z), $ a \to \infty $
                 , $ z > 0 $ , $ c > 1 $ / 381 \\
                 28. Expansions in terms of Kummer functions / 383 \\
                 28.1 Approximation in terms of the Kummer J7-function /
                 383 \\
                 28.1.1 Constructing the expansions / 384 \\
                 28.1.2 Expansion for the loop integral / 387 \\
                 28.2 The $ _2F_1 $ function, large $ c $ , in terms of
                 $ U $ / 387 \\
                 28.2.1 Legendre polynomials: Uniform expansions / 388
                 \\
                 28.3 The $ _2F_1 $ -function, large $ b $ : in terms of
                 $ _1F_1 $ / 389 \\
                 28.3.1 Using a real integral / 390 \\
                 28.3.2 Using a loop integral / 394 \\
                 28.4 Jacobi polynomials of large degree: Laguerre-type
                 expansion / 394 \\
                 28.4.1 Laguerre-type expansion for large values of /3 /
                 398 \\
                 28.5 Expansion of a Dirichlet-type integral / 401 \\
                 Part 6: Uniform Examples for Special Functions / 403
                 \\
                 29. Legendre functions / 405 \\
                 29.1 Expansions of $ P_\nu^\mu(z) $ , $ Q_\nu^\mu(z) $
                 ; $ \nu \to \infty $ , $ z \geq 1 $ / 406 \\
                 29.1.1 Expansions for $ z > z_0 > 1 $ / 400 \\
                 29.1.2 Expansion in terms of modified Bessel functions
                 / 407 \\
                 29.1.3 Expansions of $ P_\nu^\mu(z) $ and $
                 Q_\nu^\mu(z) $ in terms of Bessel functions / 411 \\
                 29.2 Expansions of $ P_\nu^\mu(z) $ , $ Q_\nu^\mu(z) $
                 ; $ p \to \infty $ , $ z > 1 $ / 412 \\
                 29.2.1 Expansions for bounded $ z $ / 412 \\
                 29.2.2 Expansions in terms of modified Bessel functions
                 / 412 \\
                 29.2.3 Expansions of $ P_\nu^\mu(z) $ and $
                 Q_\nu^\mu(z) $ / 413 \\
                 29.3 Integrals with nearly coincident branch points /
                 414 \\
                 29.3.1 Ursell's expansions of Legendre functions / 415
                 \\
                 29.3.2 Coefficients of the expansion / 416 \\
                 29.3.3 An alternative expansion of $ P_n^m(\cosh z) $ /
                 417 \\
                 29.3.4 A related integral with nearly coincident branch
                 points / 418 \\
                 29.4 Toroidal harmonics and conical functions / 418 \\
                 30. Parabolic cylinder functions: Large parameter / 419
                 \\
                 30.1 Notation for uniform asymptotic expansions / 419
                 \\
                 30.2 The case $ a < 0 $ / 421 \\
                 30.2.1 The case $ z > 2\sqrt{-a} $ : $ -a + z \to
                 \infty $ / 421 \\
                 30.2.2 The case $ z < -2\sqrt{-a} $ : $ -a - z \to
                 \infty $ / 422 \\
                 30.2.3 The case -2\sqrt{-a} < z < 2\sqrt{-a} / 423 \\
                 30.3 The case $ a > 0 $ / 424 \\
                 30.3.1 The case $ z > 0 $ , $ a + z \to \infty $ / 425
                 \\
                 30.3.2 The case $ z < 0 $ , $ a - z \to \infty $ / 425
                 \\
                 30.4 Expansions from integral representations / 426 \\
                 30.4.1 The case $ a > 0 $ , $ z > 0 $ ; $ a + z \to
                 \infty $ / 426 \\
                 30.4.2 The case $ a > 0 $ , $ z < 0 $ ; $ a - z \to
                 \infty $ / 428 \\
                 30.4.3 The case $ a < 0 $ , $ |z| > 2\sqrt{-a} $ ; $ -a
                 + |z| \to \infty $ / 429 \\
                 30.5 Airy-type expansions / 430 \\
                 31. Coulomb wave functions / 433 \\
                 31.1 Contour integrals for Coulomb functions / 434 \\
                 31.2 Expansions for $ \rho \to \infty $ and bounded $
                 \eta $ / / 435 \\
                 31.3 Expansions for $ \eta \to \infty $ and bounded $
                 \rho $ / 437 \\
                 31.4 Expansions for $ \eta \to -\infty $ and bounded $
                 \rho $ / 439 \\
                 31.5 Expansions for $ \eta \to -\infty and $ \rho \geq
                 \rho_0 > 0 $ / 440 \\
                 31.6 Expansions for $ \eta \to -\infty $ and $ \rho
                 \geq 0 $ / 442 \\
                 31.7 Expansions for $ \eta $ , $ \rho \to \infty $ ;
                 Airy-type expansions / 444 \\
                 32. Laguerre polynomials: Uniform expansions / 449 \\
                 32.1 An expansion for bounded $ z $ and $ a $ / 449 \\
                 32.2 An expansion for bounded $ z $ ; $ a $ depends on
                 $ n $ / 451 \\
                 32.3 Expansions for bounded $ a $ ; $ z $ depends on $
                 n $ / 454 \\
                 32.3.1 An expansion in terms of Airy functions / 455
                 \\
                 32.3.2 An expansion in terms of Bessel functions / 456
                 \\
                 32.4 An expansion in terms of Hermite polynomials;
                 large $ a $ / 458 \\
                 32.4.1 A first approximation / 459 \\
                 32.4.2 Transformation to the standard form / 460 \\
                 32.4.3 Approximating the zeros / 462 \\
                 33. Generalized Bessel polynomials / 465 \\
                 33.1 Relations to Bessel and Kummer functions / 466 \\
                 33.2 An expansion in terms of Laguerre polynomials /
                 467 \\
                 33.3 Expansions in terms of elementary functions / 470
                 \\
                 33.3.1 The case $ |\ph z| < \pi/2 $ / 470 \\
                 33.3.2 The case $ |\ph(-z)| < \pi/2 $ / 471 \\
                 33.3.3 Integral representations / 472 \\
                 33.3.4 Construction of the expansions / 472 \\
                 33.4 Expansions in terms of modified Bessel functions /
                 476 \\
                 33.4.1 Construction of the expansion / 476 \\
                 34. Stirling numbers / 479 \\
                 34.1 Definitions and integral representations / 479 \\
                 34.2 Stirling number of the second kind / 481 \\
                 34.2.1 Higher-order approximations / 483 \\
                 34.2.2 About the positive saddle point / 486 \\
                 34.2.3 About the quantity $ A $ / 487 \\
                 34.3 Stirling numbers of the first kind / 488 \\
                 35. Asymptotics of the integral $ \int_0^1 \cos(b x + a
                 / x) \, dx $ / 491 \\
                 35.1 The case $ b < a $ / 491 \\
                 35.2 The case $ a = b $ / 493 \\
                 35.3 The case $ b > a $ / 494 \\
                 35.3.1 The contribution from $ \mathcal{P}_1 $ / 495
                 \\
                 35.3.2 The contribution from $ \mathcal{P}_2 $ / 496
                 \\
                 35.4 A Fresnel-type expansion / 497 \\
                 Part 7: A Class of Cumulative Distribution Functions /
                 499 \\
                 36. Expansions of a class of cumulative distribution
                 functions / 501 \\
                 36.1 Cumulative distribution functions: A standard form
                 / 501 \\
                 36.2 An incomplete normal distribution function / 505
                 \\
                 36.3 The Sievert integral / 506 \\
                 36.4 The Pearson type IV distribution / 507 \\
                 36.5 The Von Mises distribution / 509 \\
                 36.5.1 An expansion near the lower endpoint of
                 integration / 511 \\
                 37. Incomplete gamma functions: Uniform expansions /
                 513 \\
                 37.1 Using the standard integral representations / 513
                 \\
                 37.2 Representations by contour integrals / 514 \\
                 37.2.1 Constructing the expansions / 516 \\
                 37.2.2 Details on the coefficients / 518 \\
                 37.2.3 Relations to the coefficients of earlier
                 expansions / 520 \\
                 37.3 Incomplete gamma functions, negative parameters /
                 520 \\
                 37.3.1 Expansions near the transition point / 522 \\
                 37.3.2 A real expansion of 7*(-a, -z) / 524 \\
                 38. Incomplete beta function / 525 \\
                 38.1 A power series expansion for large p / 526 \\
                 38.2 A uniform expansion for large p / 526 \\
                 38.3 The nearly symmetric case / 527 \\
                 38.4 The general error function case / 529 \\
                 39. Non-central chi-square, Marcum functions / 531 \\
                 39.1 Properties of the Marcum functions / 532 \\
                 39.2 More integral representations / 533 \\
                 39.3 Asymptotic expansion; $ \mu $ fixed, $ \xi $ large
                 / 535 \\
                 39.4 Asymptotic expansion; $ \xi + \mu $ large / 537
                 \\
                 39.5 An expansion in terms of the incomplete gamma
                 function / 540 \\
                 39.6 Comparison of the expansions numerically / 543 \\
                 40. A weighted sum of exponentials / 545 \\
                 40.1 An integral representation / 546 \\
                 40.2 Saddle point analysis / 547 \\
                 40.3 Details on the coefficients / 548 \\
                 40.4 Auxiliary expansions / 550 \\
                 40.5 Numerical verification / 551 \\
                 41. A generalized incomplete gamma function / 553 \\
                 41.1 An expansion in terms of incomplete gamma
                 functions / 554 \\
                 41.2 An expansion in terms of Laguerre polynomials /
                 554 \\
                 41.3 An expansion in terms of Kummer functions / 555
                 \\
                 41.4 An expansion in terms of the error function / 555
                 \\
                 42. Asymptotic inversion of cumulative distribution
                 functions / 559 \\
                 42.1 The asymptotic inversion method / 559 \\
                 42.2 Asymptotic inversion of the gamma distribution /
                 561 \\
                 42.2.1 Numerical verification / 563 \\
                 42.2.2 Other asymptotic inversion methods / 564 \\
                 42.2.3 Asymptotics of the zeros of $ \Gamma(a, z) $ /
                 565 \\
                 42.3 Asymptotic inversion of the incomplete beta
                 function / 567 \\
                 42.3.1 Inverting by using the error function / 568 \\
                 42.3.2 Inverting by using the incomplete gamma function
                 / 569 \\
                 42.3.3 Numerical verification / 572 \\
                 42.4 The hyperbolic cumulative distribution / 573 \\
                 42.4.1 Numerical verification / 574 \\
                 42.5 The Marcum functions / 575 \\
                 42.5.1 Asymptotic inversion / 576 \\
                 42.5.2 Asymptotic inversion with respect to $ x $ / 576
                 \\
                 42.5.3 Asymptotic inversion with respect to $ y $ / 579
                 \\
                 Bibliography / 583 \\
                 Index / 597",
}

@Article{Weiss:2015:ROS,
  author =       "Alexander K. H. Weiss and Christian Ochsenfeld",
  title =        "A rigorous and optimized strategy for the evaluation
                 of the {Boys} function kernel in molecular electronic
                 structure theory",
  journal =      j-J-COMPUT-CHEM,
  volume =       "36",
  number =       "18",
  pages =        "1390--1398",
  day =          "5",
  month =        jul,
  year =         "2015",
  CODEN =        "JCCHDD",
  DOI =          "https://doi.org/10.1002/jcc.23935",
  ISSN =         "0192-8651 (print), 1096-987X (electronic)",
  ISSN-L =       "0192-8651",
  bibdate =      "Sat Jul 25 20:32:35 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputchem2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0192-8651",
  onlinedate =   "13 May 2015",
}

@Article{Xu:2015:CFC,
  author =       "Ai-Min Xu and Zhong-Di Cen",
  title =        "Closed formulas for computing higher-order derivatives
                 of functions involving exponential functions",
  journal =      j-APPL-MATH-COMP,
  volume =       "270",
  number =       "??",
  pages =        "136--141",
  day =          "1",
  month =        nov,
  year =         "2015",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2015.08.051",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Thu Nov 5 06:24:28 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315011066",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
  keywords =     "closed formula; derivatives of exponential functions;
                 derivatives of trigonometric functions; higher-order
                 derivative; hyperbolic function; tangent number;
                 trigonometric function",
  remark =       "The authors derive closed-form $n$-term sums for the
                 $n$-th order derivatives of exponential and
                 trigonometric functions. The sums involve factorials,
                 powers, and Stirling numbers of the first and second
                 kinds. At the end of their paper, they derive a new
                 computationally-stable formula for the tangent numbers,
                 $ T_{2 n + 1} = \sum_{k = 1}^n \binom {2 n}{2 k - 1}
                 T_{2 k - 1} T_{2(n - k) + 1}$, a sum that involves only
                 positive terms. There is a stable recurrence relation
                 discussed in the MathCW book that is likely faster,
                 because it requires only 2 multiplies and 1 add in each
                 term of the recurrence.",
}

@Article{Yang:2015:AFG,
  author =       "Zhen-Hang Yang and Yu-Ming Chu",
  title =        "Asymptotic formulas for gamma function with
                 applications",
  journal =      j-APPL-MATH-COMP,
  volume =       "270",
  number =       "??",
  pages =        "665--680",
  day =          "1",
  month =        nov,
  year =         "2015",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2015.08.087",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Thu Nov 5 06:24:28 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315011431",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Yang:2015:SBP,
  author =       "Zhen-Hang Yang and Yu-Ming Chu and Xiao-Hui Zhang",
  title =        "Sharp bounds for psi function",
  journal =      j-APPL-MATH-COMP,
  volume =       "268",
  number =       "??",
  pages =        "1055--1063",
  day =          "1",
  month =        oct,
  year =         "2015",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2015.07.012",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Wed Sep 16 06:56:32 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315009248",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
  keywords =     "Gamma function; Monotonicity; Psi function",
}

@Article{Zhang:2015:EAR,
  author =       "Jianfeng Zhang and Paul Chow and Hengzhu Liu",
  title =        "An Enhanced Adaptive Recoding Rotation {CORDIC}",
  journal =      j-TRETS,
  volume =       "9",
  number =       "1",
  pages =        "4:1--4:??",
  month =        nov,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2812813",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Tue Dec 22 16:19:56 MST 2015",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/trets.bib",
  abstract =     "The Conventional Coordinate Rotation Digital Computer
                 (CORDIC) algorithm has been widely used in many
                 applications, particularly in Direct Digital Frequency
                 Synthesizers (DDS) and Fast Fourier Transforms (FFT).
                 However, CORDIC is constrained by the excessive number
                 of iterations, angle data path, and scaling factor
                 compensation. In this article, an enhanced adaptive
                 recoding CORDIC (EARC) is proposed. It uses the
                 enhanced adaptive recoding method to reduce the
                 required iterations and adopts the trigonometric
                 transformation scheme to scale up the rotation angles.
                 Computing sine and cosine is used first to compare the
                 core functionality of EARC with basic CORDIC; then a
                 16-bit DDS and a 1,024-point FFT based on EARC are
                 evaluated to demonstrate the benefits of EARC in larger
                 applications. All the proposed architectures are
                 validated on a Virtex 5 FPGA development platform.
                 Compared with a commercial implementation of CORDIC,
                 EARC requires 33.3\% less hardware resources, provides
                 a twofold speedup, dissipates 70.4\% less power, and
                 improves accuracy in terms of the Bit Error Position
                 (BEP). Compared to the state-of-the-art Hybrid CORDIC,
                 EARC reduces latency by 11.1\% and consumes 17\% less
                 power. Compared with a commercial implementation of
                 DDS, the dissipated power of the proposed DDS is
                 reduced by 27.2\%. The proposed DDS improves
                 Spurious-Free Dynamic Range (SFDR) by nearly 7 dBc and
                 dissipates 21.8\% less power when compared with a
                 recently published DDS circuit. The FFT based on EARC
                 dissipates a factor of 2.05 less power than the
                 commercial FFT even when choosing the 100\% toggle rate
                 for the FFT based on EARC and the 12.5\% toggle rate
                 for the commercial FFT. Compared with a recently
                 published FFT, the FFT based on EARC improves
                 Signal-to-Noise Ratio (SNR) by 8.9 dB and consumes
                 7.78\% less power.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J1151",
}

@Article{Abel:2016:HOA,
  author =       "Ulrich Abel",
  title =        "High order algorithms for calculating roots",
  journal =      j-MATH-GAZ,
  volume =       "100",
  number =       "549",
  pages =        "420--428",
  month =        nov,
  year =         "2016",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.1017/mag.2016.106",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Thu Nov 17 10:32:54 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
  URL =          "https://www.cambridge.org/core/product/2FACD442DB78364B04DA2E64BA06F269",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayIssue?jid=MAG;
                 http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  onlinedate =   "17 October 2016",
}

@Article{Aprahamian:2016:MIT,
  author =       "Mary Aprahamian and Nicholas J. Higham",
  title =        "Matrix Inverse Trigonometric and Inverse Hyperbolic
                 Functions: Theory and Algorithms",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "37",
  number =       "4",
  pages =        "1453--1477",
  month =        "????",
  year =         "2016",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/16M1057577",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Fri Aug 25 09:01:43 MDT 2017",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/37/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2016",
}

@Article{Bailey:2016:CSC,
  author =       "D. H. Bailey and J. M. Borwein",
  title =        "Computation and structure of character polylogarithms
                 with applications to character
                 {Mordell--Tornheim--Witten} sums",
  journal =      j-MATH-COMPUT,
  volume =       "85",
  number =       "297",
  pages =        "295--324",
  month =        "",
  year =         "2016",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/mcom/2974",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon Feb 8 17:02:07 MST 2016",
  bibsource =    "http://www.ams.org/mcom/2016-85-297;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2016-85-297/S0025-5718-2015-02974-3;
                 http://www.ams.org/journals/mcom/2016-85-297/S0025-5718-2015-02974-3/S0025-5718-2015-02974-3.pdf;
                 http://www.ams.org/mathscinet/search/author.html?authorName=Borwein%2C%20J.%20M;
                 http://www.ams.org/mathscinet/search/author.html?mrauthid=29355",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Bao:2016:SAO,
  author =       "Vo Nguyen Quoc Bao and Luu Pham Tuyen and Huynh Huu
                 Tue",
  title =        "A Survey on Approximations of One-Dimensional
                 {Gaussian} {$Q$}-Function",
  journal =      "{REV} Journal on Electronics and Communications",
  volume =       "5",
  number =       "1--2",
  month =        feb,
  year =         "2016",
  DOI =          "https://doi.org/10.21553/rev-jec.92",
  bibdate =      "Sat Dec 16 15:18:22 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.rev-jec.org/index.php/rev-jec/article/view/92",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.rev-jec.org/index.php/rev-jec/",
}

@Article{Bytev:2016:HHF,
  author =       "Vladimir V. Bytev and Bernd A. Kniehl",
  title =        "{HYPERDIRE} --- {HYPERgeometric functions DIfferential
                 REduction}: {Mathematica}-based packages for the
                 differential reduction of generalized hypergeometric
                 functions: {Lauricella} function {$ F_c $} of three
                 variables",
  journal =      j-COMP-PHYS-COMM,
  volume =       "206",
  number =       "??",
  pages =        "78--83",
  month =        sep,
  year =         "2016",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2016.04.016",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Jun 10 18:27:25 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465516301059",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655/",
}

@Article{Chen:2016:AEG,
  author =       "Chao-Ping Chen",
  title =        "On the asymptotic expansions of the gamma function
                 related to the {Nemes}, {Gosper} and {Burnside}
                 formulas",
  journal =      j-APPL-MATH-COMP,
  volume =       "276",
  number =       "??",
  pages =        "417--431",
  day =          "5",
  month =        mar,
  year =         "2016",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Jan 26 17:22:21 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315016057",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Chen:2016:IAEa,
  author =       "Chao-Ping Chen and Long Lin",
  title =        "Inequalities and asymptotic expansions for the gamma
                 function related to {Mortici}'s formula",
  journal =      j-J-NUMBER-THEORY,
  volume =       "162",
  number =       "??",
  pages =        "578--588",
  month =        may,
  year =         "2016",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2015.09.014",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Wed Jul 15 08:49:20 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X15003133",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Chen:2016:IAEb,
  author =       "Chao-Ping Chen",
  title =        "Inequalities and asymptotic expansions for the psi
                 function and the {Euler--Mascheroni} constant",
  journal =      j-J-NUMBER-THEORY,
  volume =       "163",
  number =       "??",
  pages =        "596--607",
  month =        jun,
  year =         "2016",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2015.10.013",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Wed Jul 15 08:49:20 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X15003558",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Chen:2016:IAEc,
  author =       "Chao-Ping Chen",
  title =        "Inequalities and asymptotics for the
                 {Euler--Mascheroni} constant based on {DeTemple's}
                 result",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "73",
  number =       "3",
  pages =        "761--774",
  month =        nov,
  year =         "2016",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-016-0116-9",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Mar 1 09:12:13 MST 2017",
  bibsource =    "http://link.springer.com/journal/11075/73/3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://link.springer.com/article/10.1007/s11075-016-0116-9",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Chen:2016:MAA,
  author =       "Chao-Ping Chen",
  title =        "A more accurate approximation for the gamma function",
  journal =      j-J-NUMBER-THEORY,
  volume =       "164",
  number =       "??",
  pages =        "417--428",
  month =        jul,
  year =         "2016",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2015.11.007",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Wed Jul 15 08:49:21 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X16000068",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Chen:2016:MPI,
  author =       "Chao-Ping Chen",
  title =        "Monotonicity properties, inequalities and asymptotic
                 expansions associated with the gamma function",
  journal =      j-APPL-MATH-COMP,
  volume =       "283",
  number =       "??",
  pages =        "385--396",
  day =          "20",
  month =        jun,
  year =         "2016",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Apr 5 07:51:07 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300316301515",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Chen:2016:SIAa,
  author =       "Chao-Ping Chen and Wei-Wei Tong",
  title =        "Sharp inequalities and asymptotic expansions for the
                 gamma function",
  journal =      j-J-NUMBER-THEORY,
  volume =       "160",
  number =       "??",
  pages =        "418--431",
  month =        mar,
  year =         "2016",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2015.09.021",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Wed Jul 15 08:49:18 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X15003200",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Erascu:2016:RQE,
  author =       "Madalina Erascu and Hoon Hong",
  title =        "Real quantifier elimination for the synthesis of
                 optimal numerical algorithms (Case study: Square root
                 computation)",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "75",
  number =       "??",
  pages =        "110--126",
  month =        jul # "\slash " # aug,
  year =         "2016",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  bibdate =      "Mon Jan 25 06:25:01 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0747717115001091",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171/",
  keywords =     "interval arithmetic; interval square root",
}

@TechReport{Fateman:2016:CUA,
  author =       "Richard J. Fateman",
  title =        "Comments on Unrestricted Algorithms for {Bessel}
                 Functions in Computer Algebra: Arbitrary Precision, The
                 Backwards Recurrence, {Taylor} Series, {Hermite}
                 Interpolation",
  type =         "Report",
  institution =  "University of California, Berkeley",
  address =      "Berkeley, CA 947220-1776, USA",
  day =          "4",
  month =        jun,
  year =         "2016",
  bibdate =      "Fri Feb 24 09:55:02 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://people.eecs.berkeley.edu/~fateman/papers/hermite.pdf",
  abstract =     "We explore various ways of implementing ``unrestricted
                 algorithms'' [3] for approximating Bessel ($J$)
                 functions. An unrestricted algorithm for a function $
                 f(x)$ provides a result to any requested precision in
                 the answer. The emphasis is on higher-than-normal
                 precision with the precision specified as an extra
                 argument to the function. That is, the precision is
                 specified at run-time. We require that the algorithm
                 provide at least the requested number of correct
                 digits, contrary to some existing codes which provide
                 only ``absolute error'' near critical points. We use $
                 J_0 $ of real non-negative argument as an example,
                 although much of the reasoning generalizes to other
                 Bessel functions or related functions.\par

                 Since it is plausible that there will be requests for
                 additional values of $ J_0 $ at the same (high)
                 precision at a collection of nearby arguments, we
                 consider implementations that cache certain re-usable
                 key constants (namely zeros of $ J_0 $ near the
                 argument values).",
  acknowledgement = ack-nhfb,
}

@Article{Gautschi:2016:AER,
  author =       "Walter Gautschi",
  title =        "Algorithm 957: Evaluation of the Repeated Integral of
                 the Coerror Function by Half-Range {Gauss--Hermite}
                 Quadrature",
  journal =      j-TOMS,
  volume =       "42",
  number =       "1",
  pages =        "9:1--9:10",
  month =        feb,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2735626",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 17:07:56 MST 2016",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Nonstandard Gaussian quadrature is applied to evaluate
                 the repeated integral $ i^n \erfc x $ of the coerror
                 function for $ n \in N_0 $, $ x \in R $ in an
                 appropriate domain of the $ (n, x)$-plane. Relevant
                 software in MATLAB is provided: in particular, two
                 routines evaluating the function to an accuracy of 12
                 respective 30-decimal digits.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gil:2016:ACI,
  author =       "Amparo Gil and Diego Ruiz-Antol{\'\i}n and Javier
                 Segura and Nico M. Temme",
  title =        "{Algorithm 969}: Computation of the Incomplete Gamma
                 Function for Negative Values of the Argument",
  journal =      j-TOMS,
  volume =       "43",
  number =       "3",
  pages =        "26:1--26:9",
  month =        nov,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2972951",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2972951",
  abstract =     "An algorithm for computing the incomplete gamma
                 function $ \gamma^(a, z) $ for real values of the
                 parameter $a$ and negative real values of the argument
                 $z$ is presented. The algorithm combines the use of
                 series expansions, Poincar{\'e}-type expansions,
                 uniform asymptotic expansions, and recurrence
                 relations, depending on the parameter region. A
                 relative accuracy $ \approx 10^{-13}$ in the parameter
                 region $ (a, z) \in [500, 500] \times [500, 0)$ can be
                 obtained when computing the function $ \gamma^\ast (a,
                 z)$ with the Fortran 90 module IncgamNEG implementing
                 the algorithm.",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Giles:2016:AAI,
  author =       "Michael B. Giles",
  title =        "Algorithm 955: Approximation of the Inverse {Poisson}
                 Cumulative Distribution Function",
  journal =      j-TOMS,
  volume =       "42",
  number =       "1",
  pages =        "7:1--7:22",
  month =        feb,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699466",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 17:07:56 MST 2016",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "New approximations for the inverse of the incomplete
                 gamma function are derived, which are used to develop
                 efficient evaluations of the inverse Poisson cumulative
                 distribution function. An asymptotic approximation
                 based on the standard Normal approximation is
                 particularly good for CPUs with MIMD cores, while for
                 GPUs and other hardware with vector units, a second
                 asymptotic approximation based on Temme's approximation
                 of the incomplete gamma function is more efficient due
                 to conditional branching within each vector. The
                 accuracy and efficiency of the software implementations
                 is assessed on both CPUs and GPUs.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Jameson:2016:IGF,
  author =       "G. J. O. Jameson",
  title =        "The incomplete gamma functions",
  journal =      j-MATH-GAZ,
  volume =       "100",
  number =       "548",
  pages =        "298--306",
  month =        jul,
  year =         "2016",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.1017/mag.2016.67",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Tue Sep 27 10:11:13 MDT 2016",
  bibsource =    "http://journals.cambridge.org/action/displayIssue?jid=MAG;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
  URL =          "https://www.cambridge.org/core/product/9373A31AD28D793AB5431E35EA5C2AF6",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayIssue?jid=MAG;
                 http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  onlinedate =   "14 June 2016",
  remark =       "This paper exhibits and proves several useful
                 identities for the incomplete gamma functions, but does
                 not discuss their stable numerical computation.",
}

@Article{Johansson:2016:CHF,
  author =       "Fredrik Johansson",
  title =        "Computing hypergeometric functions rigorously",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "2--29",
  day =          "22",
  month =        jun,
  year =         "2016",
  bibdate =      "Thu Jun 23 07:39:32 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://arxiv.org/abs/1606.06977",
  abstract =     "We present an efficient implementation of
                 hypergeometric functions in arbitrary-precision
                 interval arithmetic. The functions 0F1, 1F1, 2F1 and
                 2F0 (or the Kummer U-function) are supported for
                 unrestricted complex parameters and argument, and by
                 extension, we cover exponential and trigonometric
                 integrals, error functions, Fresnel integrals,
                 incomplete gamma and beta functions, Bessel functions,
                 Airy functions, Legendre functions, Jacobi polynomials,
                 complete elliptic integrals, and other special
                 functions. The output can be used directly for interval
                 computations or to generate provably correct
                 floating-point approximations in any format.
                 Performance is competitive with earlier
                 arbitrary-precision software, and sometimes orders of
                 magnitude faster. We also partially cover the
                 generalized hypergeometric function pFq and computation
                 of high-order parameter derivatives.",
  acknowledgement = ack-nhfb,
}

@Article{Johansson:2016:FAE,
  author =       "H. T. Johansson and C. Forss{\'e}n",
  title =        "Fast and Accurate Evaluation of {Wigner} 3$j$, 6$j$,
                 and 9$j$ Symbols Using Prime Factorization and
                 Multiword Integer Arithmetic",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "38",
  number =       "1",
  pages =        "A376--A384",
  month =        "????",
  year =         "2016",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/15M1021908",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Tue Jun 21 08:11:55 MDT 2016",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/38/1;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2016",
}

@Article{Koelink:2016:AST,
  author =       "Erik Koelink",
  title =        "Applications of spectral theory to special functions",
  journal =      "ArXiv e-prints",
  volume =       "??",
  pages =        "1--63",
  month =        dec,
  year =         "2016",
  bibdate =      "Sat Feb 18 09:23:20 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://arxiv.org/abs/1612.07035",
  abstract =     "Many special functions are eigenfunctions to explicit
                 operators, such as difference and differential
                 operators, which is in particular true for the special
                 functions occurring in the Askey-scheme, its
                 $q$-analogue and extensions. The study of the spectral
                 properties of such operators leads to explicit
                 information for the corresponding special functions. We
                 discuss several instances of this application,
                 involving orthogonal polynomials and their
                 matrix-valued analogues.",
  acknowledgement = ack-nhfb,
  eprint =       "1612.07035",
  keywords =     "Mathematics --- Classical Analysis and ODEs;
                 Mathematics --- Functional Analysis",
  primaryclass = "math.CA",
}

@Article{Kutsuna:2016:ARM,
  author =       "Takuro Kutsuna and Yoshinao Ishii",
  title =        "Abstraction and refinement of mathematical functions
                 toward {SMT}-based test-case generation",
  journal =      j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
  volume =       "18",
  number =       "1",
  pages =        "109--120",
  month =        feb,
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s10009-015-0389-7",
  ISSN =         "1433-2779 (print), 1433-2787 (electronic)",
  ISSN-L =       "1433-2779",
  bibdate =      "Mon Jan 25 08:12:53 MST 2016",
  bibsource =    "http://link.springer.com/journal/10009/18/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/multithreading.bib;
                 https://www.math.utah.edu/pub/tex/bib/sttt.bib",
  URL =          "http://link.springer.com/article/10.1007/s10009-015-0389-7",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal on Software Tools for Technology
                 Transfer (STTT)",
  journal-URL =  "http://link.springer.com/journal/10009",
}

@InProceedings{Langhammer:2016:SPN,
  author =       "Martin Langhammer and Bogdan Pasca",
  title =        "Single Precision Natural Logarithm Architecture for
                 Hard Floating-Point and {DSP}-Enabled {FPGAs}",
  crossref =     "Montuschi:2016:ISC",
  pages =        "164--171",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.20",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-23",
}

@InProceedings{LeMaire:2016:CFP,
  author =       "Julien {Le Maire} and Nicolas Brunie and Florent de
                 Dinechin and Jean-Michel Muller",
  title =        "Computing floating-point logarithms with fixed-point
                 operations",
  crossref =     "Montuschi:2016:ISC",
  pages =        "156--163",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.24",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-23",
}

@Article{Lu:2016:QCF,
  author =       "Dawei Lu and Lixin Song and Congxu Ma",
  title =        "A quicker continued fraction approximation of the
                 gamma function related to the {Windschitl}'s formula",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "72",
  number =       "4",
  pages =        "865--874",
  month =        aug,
  year =         "2016",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-015-0070-y",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Tue Sep 20 10:57:47 MDT 2016",
  bibsource =    "http://link.springer.com/journal/11075/72/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://link.springer.com/article/10.1007/s11075-015-0070-y",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  remark =       "The tables at the end of this paper compare six
                 algorithms for approximating $ n! $ for $ n = 50, 100,
                 500, 2500 $. The Burnside, Nemes, and Windschitl
                 formulas are slightly less accurate than the
                 traditional Stirling approximation. The new formula,
                 and the Mortici formula, are slightly better than
                 Stirling's.",
}

@Article{Maignan:2016:FGL,
  author =       "Aude Maignan and Tony C. Scott",
  title =        "Fleshing out the generalized {Lambert} {$W$}
                 function",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "50",
  number =       "2",
  pages =        "45--60",
  month =        jun,
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2992274.2992275",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Thu Aug 25 17:57:39 MDT 2016",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  abstract =     "Herein, we use Hardy's notion of the ``false
                 derivative'' to obtain exact multiple roots in closed
                 form of the transcendental--algebraic equations
                 representing the generalized Lambert $W$ function. In
                 this fashion, we flesh out the generalized Lambert $W$
                 function by complementing previous developments to
                 produce a more complete and integrated body of work.
                 Finally, we demonstrate the usefulness of this special
                 function with some applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Communications in Computer Algebra",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Article{Martin-Dorel:2016:PTB,
  author =       "{\'E}rik Martin-Dorel and Guillaume Melquiond",
  title =        "Proving Tight Bounds on Univariate Expressions with
                 Elementary Functions in {Coq}",
  journal =      j-J-AUTOM-REASON,
  volume =       "57",
  number =       "3",
  pages =        "187--217",
  month =        oct,
  year =         "2016",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1007/s10817-015-9350-4",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  bibdate =      "Fri Sep 2 06:39:36 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "http://link.springer.com/accesspage/article/10.1007/s10817-015-9350-4",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
}

@Article{Mohankumar:2016:VAN,
  author =       "N. Mohankumar and A. Natarajan",
  title =        "On the very accurate numerical evaluation of the
                 {Generalized Fermi--Dirac Integrals}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "207",
  number =       "??",
  pages =        "193--201",
  month =        oct,
  year =         "2016",
  CODEN =        "CPHCBZ",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Tue Aug 30 18:08:51 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465516301667",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655/",
}

@Article{Moroz:2016:FCI,
  author =       "Leonid V. Moroz and Cezary J. Walczyk and Andriy
                 Hrynchyshyn and Vijay Holimath and Jan L.
                 Cie{\'s}li{\'n}ski",
  title =        "Fast calculation of inverse square root with the use
                 of magic constant --- analytical approach",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--23",
  day =          "14",
  month =        mar,
  year =         "2016",
  DOI =          "https://doi.org/10.48550/arXiv.1603.04483",
  bibdate =      "Wed Dec 20 07:34:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/pdf/1603.04483.pdf",
  abstract =     "We present a mathematical analysis of transformations
                 used in fast calculation of inverse square root for
                 single-precision floating-point numbers. Optimal values
                 of the so called magic constants are derived in a
                 systematic way, minimizing either absolute or relative
                 errors at subsequent stages of the discussed
                 algorithm.",
  acknowledgement = ack-nhfb,
}

@Misc{Munshi:2016:OCS,
  author =       "Aaftab Munshi and Lee Howes and Bartosz Sochacki and
                 {Khronos OpenCL Working Group}",
  title =        "The {OpenCL} {C} Specification Version: 2.0 Document
                 Revision: 33",
  howpublished = "Web document.",
  pages =        "205",
  day =          "13",
  month =        apr,
  year =         "2016",
  bibdate =      "Mon Apr 16 14:05:49 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib",
  URL =          "https://www.khronos.org/registry/OpenCL/specs/opencl-2.0-openclc.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Section 6.1.3.2 Math Functions, pages 74ff, defines a
                 function repertoire extended beyond that of ISO C,
                 including {\tt acospi}, {\tt asinpi}, {\tt atanpi},
                 {\tt atan2pi}, {\tt cospi}, {\tt sinpi}, {\tt tanpi},
                 {\tt cospi}, {\tt fract}, {\tt lgamma\_r}, {\tt mad}
                 (approximation to {\tt a * b + c}), {\tt minmag}, {\tt
                 pown}, {\tt rootn}, {\tt sincos}, {\tt sinpi}, and {\tt
                 tanpi}.",
}

@InProceedings{Navas-Palencia:2016:CCH,
  author =       "Guillermo Navas-Palencia and Argimiro Arratia",
  title =        "On the Computation of Confluent Hypergeometric
                 Functions for Large Imaginary Part of Parameters $b$
                 and $z$",
  crossref =     "Greuel:2016:MSI",
  pages =        "241--248",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-42432-3_30",
  bibdate =      "Mon Feb 5 08:27:34 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{OSullivan:2016:ZD,
  author =       "Cormac O'Sullivan",
  title =        "Zeros of the dilogarithm",
  journal =      j-MATH-COMPUT,
  volume =       "85",
  number =       "302",
  pages =        "2967--2993",
  month =        nov,
  year =         "2016",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/mcom/3065",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Sat Nov 5 12:22:19 MDT 2016",
  bibsource =    "http://www.ams.org/mcom/2016-85-302;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2016-85-302/S0025-5718-2016-03065-3;
                 http://www.ams.org/journals/mcom/2016-85-302/S0025-5718-2016-03065-3/S0025-5718-2016-03065-3.pdf;
                 http://www.ams.org/mathscinet/search/author.html?mrauthid=658848",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Ozcag:2016:RPI,
  author =       "Emin {\"O}zc{\d{a}}{\u{g}} and {\.I}nci Ege",
  title =        "Remarks on polygamma and incomplete gamma type
                 functions",
  journal =      j-J-NUMBER-THEORY,
  volume =       "169",
  number =       "??",
  pages =        "369--387",
  month =        dec,
  year =         "2016",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2016.05.021",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Wed Jul 15 08:49:24 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X16301378",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Paris:2016:UAE,
  author =       "R. B. Paris",
  title =        "A uniform asymptotic expansion for the incomplete
                 gamma functions revisited",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--9",
  day =          "2",
  month =        nov,
  year =         "2016",
  bibdate =      "Sat Feb 18 09:13:43 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://arxiv.org/abs/1611.00548",
  abstract =     "A new uniform asymptotic expansion for the incomplete
                 gamma function $ \Gamma (a, z) $ valid for large values
                 of $z$ was given by the author in
                 \cite{Paris:2002:UAE}. This expansion contains a
                 complementary error function of an argument measuring
                 transition across the point $ z = a$, with easily
                 computable coefficients that do not involve a removable
                 singularity in the neighbourhood of this point. In this
                 note we correct a misprint in the listing of certain
                 coefficients in this expansion and discuss in more
                 detail the situation corresponding to $ \Gamma (a,
                 a)$.",
  acknowledgement = ack-nhfb,
  remark =       "Page 9 gives corrections to \cite[Eq.
                 8.12.18--8.12.20]{Olver:2010:NHM}.",
}

@InProceedings{Revy:2016:ADF,
  author =       "Guillaume Revy",
  title =        "Automated Design of Floating-Point Logarithm Functions
                 on Integer Processors",
  crossref =     "Montuschi:2016:ISC",
  pages =        "172--180",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.28",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-23",
}

@Article{Sayed:2016:WCR,
  author =       "Wafaa S. Sayed and Hossam A. H. Fahmy",
  title =        "What are the Correct Results for the Special Values of
                 the Operands of the Power Operation?",
  journal =      j-TOMS,
  volume =       "42",
  number =       "2",
  pages =        "14:1--14:17",
  month =        jun,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2809783",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 3 18:52:21 MDT 2016",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Language standards such as C99 and C11, as well as the
                 IEEE Standard for Floating-Point Arithmetic 754 (IEEE
                 Std 754-2008) specify the expected behavior of binary
                 and decimal floating-point arithmetic in
                 computer-programming environments and the handling of
                 special values and exception conditions. Many
                 researchers focus on verifying the compliance of
                 implementations for binary and decimal floating-point
                 operations with these standards. In this article, we
                 are concerned with the special values of the operands
                 of the power function Z = X$^Y$. We study how the
                 standards define the correct results for this
                 operation, propose a mathematically justified
                 definition for the correct results of the power
                 function on the occurrence of these special values as
                 its operands, test how different software
                 implementations for the power function deal with these
                 special values, and classify the behavior of different
                 programming languages from the viewpoint of how much
                 they conform to the standards and our proposed
                 mathematical definition. We present inconsistencies
                 between the implementations and the standards, and
                 discuss incompatibilities between different versions of
                 the same software.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Schmidt:2016:ZSG,
  author =       "Maxie D. Schmidt",
  title =        "Zeta Series Generating Function Transformations
                 Related to Generalized {Stirling} Numbers and Partial
                 Sums of the {Hurwitz} Zeta Function",
  journal =      "arxiv.org",
  month =        nov,
  year =         "2016",
  bibdate =      "Sat Feb 18 09:26:39 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://adsabs.harvard.edu/abs/2016arXiv161100957S",
  abstract =     "We define a generalized class of modified zeta series
                 transformations generating the partial sums of the
                 Hurwitz zeta function and series expansions of the
                 Lerch transcendent function. The new transformation
                 coefficients we define within the article satisfy
                 expansions by generalized harmonic number sequences, or
                 the partial sums of the Hurwitz zeta function, which
                 are analogous to known properties for the Stirling
                 numbers of the first kind and for the known
                 transformation coefficients employed to enumerate
                 variants of the polylogarithm function series.
                 Applications of the new results we prove in the article
                 include new series expansions of the Dirichlet beta
                 function, the Legendre chi function, BBP-type series
                 identities for special constants, alternating and
                 exotic Euler sum variants, alternating zeta functions
                 with powers of quadratic denominators, and particular
                 series defining special cases of the Riemann zeta
                 function constants at the positive integers $ s \geq 3
                 $.",
  acknowledgement = ack-nhfb,
  eprint =       "1611.00957",
  keywords =     "Mathematics - Combinatorics, Mathematics - Number
                 Theory",
  primaryclass = "math.CO",
}

@Article{Stange:2016:CAM,
  author =       "J. Stange and N. Loginova and T. Dickhaus",
  title =        "Computing and approximating multivariate chi-square
                 probabilities",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "86",
  number =       "6",
  pages =        "1233--1247",
  year =         "2016",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949655.2015.1058798",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Thu Feb 4 07:57:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/00949655.2015.1058798",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
}

@Article{Stefanica:2016:SAA,
  author =       "Dan Stefanica and Rado{\v{s}} Radoi{\v{c}}i{\'c}",
  title =        "A sharp approximation for {ATM}-forward option prices
                 and implied volatilities",
  journal =      "International Journal of Financial Engineering",
  volume =       "3",
  number =       "1",
  pages =        "1650002",
  month =        mar,
  year =         "2016",
  DOI =          "https://doi.org/10.1142/s242478631650002x",
  ISSN =         "2424-7863",
  bibdate =      "Sat Dec 16 17:46:33 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Wang:2016:AFG,
  author =       "Miao-Kun Wang and Yu-Ming Chu and Ying-Qing Song",
  title =        "Asymptotical formulas for {Gaussian} and generalized
                 hypergeometric functions",
  journal =      j-APPL-MATH-COMP,
  volume =       "276",
  number =       "??",
  pages =        "44--60",
  day =          "5",
  month =        mar,
  year =         "2016",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Jan 26 17:22:21 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315015908",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Wang:2016:UAA,
  author =       "Weiping Wang",
  title =        "Unified approaches to the approximations of the gamma
                 function",
  journal =      j-J-NUMBER-THEORY,
  volume =       "163",
  number =       "??",
  pages =        "570--595",
  month =        jun,
  year =         "2016",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2015.12.016",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Wed Jul 15 08:49:20 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X16000470",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Xu:2016:AEG,
  author =       "Aimin Xu and Yongcai Hu and Peipei Tang",
  title =        "Asymptotic expansions for the gamma function",
  journal =      j-J-NUMBER-THEORY,
  volume =       "169",
  number =       "??",
  pages =        "134--143",
  month =        dec,
  year =         "2016",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2016.05.020",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Wed Jul 15 08:49:24 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X16301366",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Zaghloul:2016:RAC,
  author =       "Mofreh R. Zaghloul",
  title =        "Remark on {``Algorithm 916: Computing the Faddeyeva
                 and Voigt Functions''}: Efficiency Improvements and
                 {Fortran} Translation",
  journal =      j-TOMS,
  volume =       "42",
  number =       "3",
  pages =        "26:1--26:9",
  month =        may,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2806884",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 23 16:40:02 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Zaghloul:2011:ACF}.",
  abstract =     "This remark describes efficiency improvements to
                 Algorithm 916 [Zaghloul and Ali 2011]. It is shown that
                 the execution time required by the algorithm, when run
                 at its highest accuracy, may be improved by more than a
                 factor of 2. A better accuracy vs efficiency tradeoff
                 scheme is also implemented; this requires the user to
                 supply the number of significant figures desired in the
                 computed values as an extra input argument to the
                 function. Using this tradeoff, it is shown that the
                 efficiency of the algorithm may be further improved
                 significantly while maintaining reasonably accurate and
                 safe results that are free of the pitfalls and complete
                 loss of accuracy seen in other competitive techniques.
                 The current version of the code is provided in Matlab
                 and Scilab in addition to a Fortran translation
                 prepared to meet the needs of real-world problems where
                 very large numbers of function evaluations would
                 require the use of a compiled language. To fulfill this
                 last requirement, a recently proposed reformed version
                 of Huml{\'\i}cek's w4 routine, shown to maintain the
                 claimed accuracy of the algorithm over a wide and fine
                 grid, is implemented in the present Fortran translation
                 for the case of four significant figures. This latter
                 modification assures the reliability of the code in the
                 solution of practical problems requiring numerous
                 evaluation of the function for applications requiring
                 low-accuracy computations ($ < 10^{-4}$).",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Alonso:2017:EAA,
  author =       "Pedro Alonso and Javier Ib{\'a}{\~n}ez and Jorge
                 Sastre and Jes{\'u}s Peinado and Emilio Defez",
  title =        "Efficient and accurate algorithms for computing matrix
                 trigonometric functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "309",
  number =       "??",
  pages =        "325--332",
  day =          "1",
  month =        jan,
  year =         "2017",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:35:53 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2015.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042716302321",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Baikov:2017:AID,
  author =       "Nikita Baikov",
  title =        "Algorithm and Implementation Details for Complementary
                 Error Function",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "7",
  pages =        "1106--1118",
  month =        jul,
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2016.2641960",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jun 8 10:22:00 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://www.computer.org/csdl/trans/tc/2017/07/07792222-abs.html",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Beebe:2017:MFC,
  author =       "Nelson H. F. Beebe",
  title =        "The Mathematical-Function Computation Handbook:
                 Programming Using the {MathCW} Portable Software
                 Library",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxxvi + 1114",
  year =         "2017",
  DOI =          "https://doi.org/10.1007/978-3-319-64110-2",
  ISBN =         "3-319-64109-3 (hardcover), 3-319-64110-7 (e-book)",
  ISBN-13 =      "978-3-319-64109-6 (hardcover), 978-3-319-64110-2
                 (e-book)",
  LCCN =         "QA75.5-76.95",
  bibdate =      "Sat Jul 15 19:34:43 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
                 https://www.math.utah.edu/pub/tex/bib/axiom.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/mupad.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/redbooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib",
  URL =          "http://www.springer.com/us/book/9783319641096",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Beebe, Nelson H. F./0000-0001-7281-4263",
  tableofcontents = "List of figures / xxv \\
                 List of tables / xxxi \\
                 Quick start / xxxv \\
                 1: Introduction / 1 \\
                 1.1: Programming conventions / 2 \\
                 1.2: Naming conventions / 4 \\
                 1.3: Library contributions and coverage / 5 \\
                 1.4: Summary / 6 \\
                 2: Iterative solutions and other tools / 7 \\
                 2.1: Polynomials and Taylor series / 7 \\
                 2.2: First-order Taylor series approximation / 8 \\
                 2.3: Second-order Taylor series approximation / 9 \\
                 2.4: Another second-order Taylor series approximation /
                 9 \\
                 2.5: Convergence of second-order methods / 10 \\
                 2.6: Taylor series for elementary functions / 10 \\
                 2.7: Continued fractions / 12 \\
                 2.8: Summation of continued fractions / 17 \\
                 2.9: Asymptotic expansions / 19 \\
                 2.10: Series inversion / 20 \\
                 2.11: Summary / 22 \\
                 3: Polynomial approximations / 23 \\
                 3.1: Computation of odd series / 23 \\
                 3.2: Computation of even series / 25 \\
                 3.3: Computation of general series / 25 \\
                 3.4: Limitations of Cody\slash Waite polynomials / 28
                 \\
                 3.5: Polynomial fits with Maple / 32 \\
                 3.6: Polynomial fits with Mathematica / 33 \\
                 3.7: Exact polynomial coefficients / 42 \\
                 3.8: Cody\slash Waite rational polynomials / 43 \\
                 3.9: Chebyshev polynomial economization / 43 \\
                 3.10: Evaluating Chebyshev polynomials / 48 \\
                 3.11: Error compensation in Chebyshev fits / 50 \\
                 3.12: Improving Chebyshev fits / 51 \\
                 3.13: Chebyshev fits in rational form / 52 \\
                 3.14: Chebyshev fits with Mathematica / 56 \\
                 3.15: Chebyshev fits for function representation / 57
                 \\
                 3.16: Extending the library / 57 \\
                 3.17: Summary and further reading / 58 \\
                 4: Implementation issues / 61 \\
                 4.1: Error magnification / 61 \\
                 4.2: Machine representation and machine epsilon / 62
                 \\
                 4.3: IEEE 754 arithmetic / 63 \\
                 4.4: Evaluation order in C / 64 \\
                 4.5: The {\tt volatile} type qualifier / 65 \\
                 4.6: Rounding in floating-point arithmetic / 66 \\
                 4.7: Signed zero / 69 \\
                 4.8: Floating-point zero divide / 70 \\
                 4.9: Floating-point overflow / 71 \\
                 4.10: Integer overflow / 72 \\
                 4.11: Floating-point underflow / 77 \\
                 4.12: Subnormal numbers / 78 \\
                 4.13: Floating-point inexact operation / 79 \\
                 4.14: Floating-point invalid operation / 79 \\
                 4.15: Remarks on NaN tests / 80 \\
                 4.16: Ulps --- units in the last place / 81 \\
                 4.17: Fused multiply-add / 85 \\
                 4.18: Fused multiply-add and polynomials / 88 \\
                 4.19: Significance loss / 89 \\
                 4.20: Error handling and reporting / 89 \\
                 4.21: Interpreting error codes / 93 \\
                 4.22: C99 changes to error reporting / 94 \\
                 4.23: Error reporting with threads / 95 \\
                 4.24: Comments on error reporting / 95 \\
                 4.25: Testing function implementations / 96 \\
                 4.26: Extended data types on Hewlett--Packard HP-UX
                 IA-64 / 100 \\
                 4.27: Extensions for decimal arithmetic / 101 \\
                 4.28: Further reading / 103 \\
                 4.29: Summary / 104 \\
                 5: The floating-point environment / 105 \\
                 5.1: IEEE 754 and programming languages / 105 \\
                 5.2: IEEE 754 and the mathcw library / 106 \\
                 5.3: Exceptions and traps / 106 \\
                 5.4: Access to exception flags and rounding control /
                 107 \\
                 5.5: The environment access pragma / 110 \\
                 5.6: Implementation of exception-flag and
                 rounding-control access / 110 \\
                 5.7: Using exception flags: simple cases / 112 \\
                 5.8: Using rounding control / 115 \\
                 5.9: Additional exception flag access / 116 \\
                 5.10: Using exception flags: complex case / 120 \\
                 5.11: Access to precision control / 123 \\
                 5.12: Using precision control / 126 \\
                 5.13: Summary / 127 \\
                 6: Converting floating-point values to integers / 129
                 \\
                 6.1: Integer conversion in programming languages / 129
                 \\
                 6.2: Programming issues for conversions to integers /
                 130 \\
                 6.3: Hardware out-of-range conversions / 131 \\
                 6.4: Rounding modes and integer conversions / 132 \\
                 6.5: Extracting integral and fractional parts / 132 \\
                 6.6: Truncation functions / 135 \\
                 6.7: Ceiling and floor functions / 136 \\
                 6.8: Floating-point rounding functions with fixed
                 rounding / 137 \\
                 6.9: Floating-point rounding functions: current
                 rounding / 138 \\
                 6.10: Floating-point rounding functions without {\em
                 inexact\/} exception / 139 \\
                 6.11: Integer rounding functions with fixed rounding /
                 140 \\
                 6.12: Integer rounding functions with current rounding
                 / 142 \\
                 6.13: Remainder / 143 \\
                 6.14: Why the remainder functions are hard / 144 \\
                 6.15: Computing {\tt fmod} / 146 \\
                 6.16: Computing {\tt remainder} / 148 \\
                 6.17: Computing {\tt remquo} / 150 \\
                 6.18: Computing one remainder from the other / 152 \\
                 6.19: Computing the remainder in nonbinary bases / 155
                 \\
                 6.20: Summary / 156 \\
                 7: Random numbers / 157 \\
                 7.1: Guidelines for random-number software / 157 \\
                 7.2: Creating generator seeds / 158 \\
                 7.3: Random floating-point values / 160 \\
                 7.4: Random integers from floating-point generator /
                 165 \\
                 7.5: Random integers from an integer generator / 166
                 \\
                 7.6: Random integers in ascending order / 168 \\
                 7.7: How random numbers are generated / 169 \\
                 7.8: Removing generator bias / 178 \\
                 7.9: Improving a poor random number generator / 178 \\
                 7.10: Why long periods matter / 179 \\
                 7.11: Inversive congruential generators / 180 \\
                 7.12: Inversive congruential generators, revisited /
                 189 \\
                 7.13: Distributions of random numbers / 189 \\
                 7.14: Other distributions / 195 \\
                 7.15: Testing random-number generators / 196 \\
                 7.16: Applications of random numbers / 202 \\
                 7.17: The \textsf {mathcw} random number routines / 208
                 \\
                 7.18: Summary, advice, and further reading / 214 \\
                 8: Roots / 215 \\
                 8.1: Square root / 215 \\
                 8.2: Hypotenuse and vector norms / 222 \\
                 8.3: Hypotenuse by iteration / 227 \\
                 8.4: Reciprocal square root / 233 \\
                 8.5: Cube root / 237 \\
                 8.6: Roots in hardware / 240 \\
                 8.7: Summary / 242 \\
                 9: Argument reduction / 243 \\
                 9.1: Simple argument reduction / 243 \\
                 9.2: Exact argument reduction / 250 \\
                 9.3: Implementing exact argument reduction / 253 \\
                 9.4: Testing argument reduction / 265 \\
                 9.5: Retrospective on argument reduction / 265 \\
                 10: Exponential and logarithm / 267 \\
                 10.1: Exponential functions / 267 \\
                 10.2: Exponential near zero / 273 \\
                 10.3: Logarithm functions / 282 \\
                 10.4: Logarithm near one / 290 \\
                 10.5: Exponential and logarithm in hardware / 292 \\
                 10.6: Compound interest and annuities / 294 \\
                 10.7: Summary / 298 \\
                 11: Trigonometric functions / 299 \\
                 11.1: Sine and cosine properties / 299 \\
                 11.2: Tangent properties / 302 \\
                 11.3: Argument conventions and units / 304 \\
                 11.4: Computing the cosine and sine / 306 \\
                 11.5: Computing the tangent / 310 \\
                 11.6: Trigonometric functions in degrees / 313 \\
                 11.7: Trigonometric functions in units of $ \pi $ / 315
                 \\
                 11.8: Computing the cosine and sine together / 320 \\
                 11.9: Inverse sine and cosine / 323 \\
                 11.10: Inverse tangent / 331 \\
                 11.11: Inverse tangent, take two / 336 \\
                 11.12: Trigonometric functions in hardware / 338 \\
                 11.13: Testing trigonometric functions / 339 \\
                 11.14: Retrospective on trigonometric functions / 340
                 \\
                 12: Hyperbolic functions / 341 \\
                 12.1: Hyperbolic functions / 341 \\
                 12.2: Improving the hyperbolic functions / 345 \\
                 12.3: Computing the hyperbolic functions together / 348
                 \\
                 12.4: Inverse hyperbolic functions / 348 \\
                 12.5: Hyperbolic functions in hardware / 350 \\
                 12.6: Summary / 352 \\
                 13: Pair-precision arithmetic / 353 \\
                 13.1: Limitations of pair-precision arithmetic / 354
                 \\
                 13.2: Design of the pair-precision software interface /
                 355 \\
                 13.3: Pair-precision initialization / 356 \\
                 13.4: Pair-precision evaluation / 357 \\
                 13.5: Pair-precision high part / 357 \\
                 13.6: Pair-precision low part / 357 \\
                 13.7: Pair-precision copy / 357 \\
                 13.8: Pair-precision negation / 358 \\
                 13.9: Pair-precision absolute value / 358 \\
                 13.10: Pair-precision sum / 358 \\
                 13.11: Splitting numbers into pair sums / 359 \\
                 13.12: Premature overflow in splitting / 362 \\
                 13.13: Pair-precision addition / 365 \\
                 13.14: Pair-precision subtraction / 367 \\
                 13.15: Pair-precision comparison / 368 \\
                 13.16: Pair-precision multiplication / 368 \\
                 13.17: Pair-precision division / 371 \\
                 13.18: Pair-precision square root / 373 \\
                 13.19: Pair-precision cube root / 377 \\
                 13.20: Accuracy of pair-precision arithmetic / 379 \\
                 13.21: Pair-precision vector sum / 384 \\
                 13.22: Exact vector sums / 385 \\
                 13.23: Pair-precision dot product / 385 \\
                 13.24: Pair-precision product sum / 386 \\
                 13.25: Pair-precision decimal arithmetic / 387 \\
                 13.26: Fused multiply-add with pair precision / 388 \\
                 13.27: Higher intermediate precision and the FMA / 393
                 \\
                 13.28: Fused multiply-add without pair precision / 395
                 \\
                 13.29: Fused multiply-add with multiple precision / 401
                 \\
                 13.30: Fused multiply-add, Boldo/\penalty
                 \exhyphenpenalty Melquiond style / 403 \\
                 13.31: Error correction in fused multiply-add / 406 \\
                 13.32: Retrospective on pair-precision arithmetic / 407
                 \\
                 14: Power function / 411 \\
                 14.1: Why the power function is hard to compute / 411
                 \\
                 14.2: Special cases for the power function / 412 \\
                 14.3: Integer powers / 414 \\
                 14.4: Integer powers, revisited / 420 \\
                 14.5: Outline of the power-function algorithm / 421 \\
                 14.6: Finding $a$ and $p$ / 423 \\
                 14.7: Table searching / 424 \\
                 14.8: Computing $\log_n(g/a)$ / 426 \\
                 14.9: Accuracy required for $\log_n(g/a)$ / 429 \\
                 14.10: Exact products / 430 \\
                 14.11: Computing $w$, $w_1$ and $w_2$ / 433 \\
                 14.12: Computing $n^{w_2}$ / 437 \\
                 14.13: The choice of $q$ / 438 \\
                 14.14: Testing the power function / 438 \\
                 14.15: Retrospective on the power function / 440 \\
                 15: Complex arithmetic primitives / 441 \\
                 15.1: Support macros and type definitions / 442 \\
                 15.2: Complex absolute value / 443 \\
                 15.3: Complex addition / 445 \\
                 15.4: Complex argument / 445 \\
                 15.5: Complex conjugate / 446 \\
                 15.6: Complex conjugation symmetry / 446 \\
                 15.7: Complex conversion / 448 \\
                 15.8: Complex copy / 448 \\
                 15.9: Complex division: C99 style / 449 \\
                 15.10: Complex division: Smith style / 451 \\
                 15.11: Complex division: Stewart style / 452 \\
                 15.12: Complex division: Priest style / 453 \\
                 15.13: Complex division: avoiding subtraction loss /
                 455 \\
                 15.14: Complex imaginary part / 456 \\
                 15.15: Complex multiplication / 456 \\
                 15.16: Complex multiplication: error analysis / 458 \\
                 15.17: Complex negation / 459 \\
                 15.18: Complex projection / 460 \\
                 15.19: Complex real part / 460 \\
                 15.20: Complex subtraction / 461 \\
                 15.21: Complex infinity test / 462 \\
                 15.22: Complex NaN test / 462 \\
                 15.23: Summary / 463 \\
                 16: Quadratic equations / 465 \\
                 16.1: Solving quadratic equations / 465 \\
                 16.2: Root sensitivity / 471 \\
                 16.3: Testing a quadratic-equation solver / 472 \\
                 16.4: Summary / 474 \\
                 17: Elementary functions in complex arithmetic / 475
                 \\
                 17.1: Research on complex elementary functions / 475
                 \\
                 17.2: Principal values / 476 \\
                 17.3: Branch cuts / 476 \\
                 17.4: Software problems with negative zeros / 478 \\
                 17.5: Complex elementary function tree / 479 \\
                 17.6: Series for complex functions / 479 \\
                 17.7: Complex square root / 480 \\
                 17.8: Complex cube root / 485 \\
                 17.9: Complex exponential / 487 \\
                 17.10: Complex exponential near zero / 492 \\
                 17.11: Complex logarithm / 495 \\
                 17.12: Complex logarithm near one / 497 \\
                 17.13: Complex power / 500 \\
                 17.14: Complex trigonometric functions / 502 \\
                 17.15: Complex inverse trigonometric functions / 504
                 \\
                 17.16: Complex hyperbolic functions / 509 \\
                 17.17: Complex inverse hyperbolic functions / 514 \\
                 17.18: Summary / 520 \\
                 18: The Greek functions: gamma, psi, and zeta / 521 \\
                 18.1: Gamma and log-gamma functions / 521 \\
                 18.2: The {\tt psi} and {\tt psiln} functions / 536 \\
                 18.3: Polygamma functions / 547 \\
                 18.4: Incomplete gamma functions / 560 \\
                 18.5: A Swiss diversion: Bernoulli and Euler / 568 \\
                 18.6: An Italian excursion: Fibonacci numbers / 575 \\
                 18.7: A German gem: the Riemann zeta function / 579 \\
                 18.8: Further reading / 590 \\
                 18.9: Summary / 591 \\
                 19: Error and probability functions / 593 \\
                 19.1: Error functions / 593 \\
                 19.2: Scaled complementary error function / 598 \\
                 19.3: Inverse error functions / 600 \\
                 19.4: Normal distribution functions and inverses / 610
                 \\
                 19.5: Summary / 617 \\
                 20: Elliptic integral functions / 619 \\
                 20.1: The arithmetic-geometric mean / 619 \\
                 20.2: Elliptic integral functions of the first kind /
                 624 \\
                 20.3: Elliptic integral functions of the second kind /
                 627 \\
                 20.4: Elliptic integral functions of the third kind /
                 630 \\
                 20.5: Computing $K(m)$ and $K'(m)$ / 631 \\
                 20.6: Computing $E(m)$ and $E'(m)$ / 637 \\
                 20.7: Historical algorithms for elliptic integrals /
                 643 \\
                 20.8: Auxiliary functions for elliptic integrals / 645
                 \\
                 20.9: Computing the elliptic auxiliary functions / 648
                 \\
                 20.10: Historical elliptic functions / 650 \\
                 20.11: Elliptic functions in software / 652 \\
                 20.12: Applications of elliptic auxiliary functions /
                 653 \\
                 20.13: Elementary functions from elliptic auxiliary
                 functions / 654 \\
                 20.14: Computing elementary functions via $R_C(x,y)$ /
                 655 \\
                 20.15: Jacobian elliptic functions / 657 \\
                 20.16: Inverses of Jacobian elliptic functions / 664
                 \\
                 20.17: The modulus and the nome / 668 \\
                 20.18: Jacobian theta functions / 673 \\
                 20.19: Logarithmic derivatives of the Jacobian theta
                 functions / 675 \\
                 20.20: Neville theta functions / 678 \\
                 20.21: Jacobian Eta, Theta, and Zeta functions / 679
                 \\
                 20.22: Weierstrass elliptic functions / 682 \\
                 20.23: Weierstrass functions by duplication / 689 \\
                 20.24: Complete elliptic functions, revisited / 690 \\
                 20.25: Summary / 691 \\
                 21: Bessel functions / 693 \\
                 21.1: Cylindrical Bessel functions / 694 \\
                 21.2: Behavior of $J_n(x)$ and $Y_n(x)$ / 695 \\
                 21.3: Properties of $J_n(z)$ and $Y_n(z)$ / 697 \\
                 21.4: Experiments with recurrences for $J_0(x)$ / 705
                 \\
                 21.5: Computing $J_0(x)$ and $J_1(x)$ / 707 \\
                 21.6: Computing $J_n(x)$ / 710 \\
                 21.7: Computing $Y_0(x)$ and $Y_1(x)$ / 713 \\
                 21.8: Computing $Y_n(x)$ / 715 \\
                 21.9: Improving Bessel code near zeros / 716 \\
                 21.10: Properties of $I_n(z)$ and $K_n(z)$ / 718 \\
                 21.11: Computing $I_0(x)$ and $I_1(x)$ / 724 \\
                 21.12: Computing $K_0(x)$ and $K_1(x)$ / 726 \\
                 21.13: Computing $I_n(x)$ and $K_n(x)$ / 728 \\
                 21.14: Properties of spherical Bessel functions / 731
                 \\
                 21.15: Computing $j_n(x)$ and $y_n(x)$ / 735 \\
                 21.16: Improving $j_1(x)$ and $y_1(x)$ / 740 \\
                 21.17: Modified spherical Bessel functions / 743 \\
                 21.18: Software for Bessel-function sequences / 755 \\
                 21.19: Retrospective on Bessel functions / 761 \\
                 22: Testing the library / 763 \\
                 22.1: Testing {\tt tgamma} and {\tt lgamma} / 765 \\
                 22.2: Testing {\tt psi} and {\tt psiln} / 768 \\
                 22.3: Testing {\tt erf} and {\tt erfc} / 768 \\
                 22.4: Testing cylindrical Bessel functions / 769 \\
                 22.5: Testing exponent/\penalty \exhyphenpenalty
                 significand manipulation / 769 \\
                 22.6: Testing inline assembly code / 769 \\
                 22.7: Testing with Maple / 770 \\
                 22.8: Testing floating-point arithmetic / 773 \\
                 22.9: The Berkeley Elementary Functions Test Suite /
                 774 \\
                 22.10: The AT\&T floating-point test package / 775 \\
                 22.11: The Antwerp test suite / 776 \\
                 22.12: Summary / 776 \\
                 23: Pair-precision elementary functions / 777 \\
                 23.1: Pair-precision integer power / 777 \\
                 23.2: Pair-precision machine epsilon / 779 \\
                 23.3: Pair-precision exponential / 780 \\
                 23.4: Pair-precision logarithm / 787 \\
                 23.5: Pair-precision logarithm near one / 793 \\
                 23.6: Pair-precision exponential near zero / 793 \\
                 23.7: Pair-precision base-$n$ exponentials / 795 \\
                 23.8: Pair-precision trigonometric functions / 796 \\
                 23.9: Pair-precision inverse trigonometric functions /
                 801 \\
                 23.10: Pair-precision hyperbolic functions / 804 \\
                 23.11: Pair-precision inverse hyperbolic functions /
                 808 \\
                 23.12: Summary / 808 \\
                 24: Accuracy of the Cody\slash Waite algorithms / 811
                 \\
                 25: Improving upon the Cody\slash Waite algorithms /
                 823 \\
                 25.1: The Bell Labs libraries / 823 \\
                 25.2: The {Cephes} library / 823 \\
                 25.3: The {Sun} libraries / 824 \\
                 25.4: Mathematical functions on EPIC / 824 \\
                 25.5: The GNU libraries / 825 \\
                 25.6: The French libraries / 825 \\
                 25.7: The NIST effort / 826 \\
                 25.8: Commercial mathematical libraries / 826 \\
                 25.9: Mathematical libraries for decimal arithmetic /
                 826 \\
                 25.10: Mathematical library research publications / 826
                 \\
                 25.11: Books on computing mathematical functions / 827
                 \\
                 25.12: Summary / 828 \\
                 26: Floating-point output / 829 \\
                 26.1: Output character string design issues / 830 \\
                 26.2: Exact output conversion / 831 \\
                 26.3: Hexadecimal floating-point output / 832 \\
                 26.4: Octal floating-point output / 850 \\
                 26.5: Binary floating-point output / 851 \\
                 26.6: Decimal floating-point output / 851 \\
                 26.7: Accuracy of output conversion / 865 \\
                 26.8: Output conversion to a general base / 865 \\
                 26.9: Output conversion of Infinity / 866 \\
                 26.10: Output conversion of NaN / 866 \\
                 26.11: Number-to-string conversion / 867 \\
                 26.12: The {\tt printf} family / 867 \\
                 26.13: Summary / 878 \\
                 27: Floating-point input / 879 \\
                 27.1: Binary floating-point input / 879 \\
                 27.2: Octal floating-point input / 894 \\
                 27.3: Hexadecimal floating-point input / 895 \\
                 27.4: Decimal floating-point input / 895 \\
                 27.5: Based-number input / 899 \\
                 27.6: General floating-point input / 900 \\
                 27.7: The {\tt scanf} family / 901 \\
                 27.8: Summary / 910 \\
                 A: Ada interface / 911 \\
                 A.1: Building the Ada interface / 911 \\
                 A.2: Programming the Ada interface / 912 \\
                 A.3: Using the Ada interface / 915 \\
                 B: C\# interface / 917 \\
                 B.1: C\# on the CLI virtual machine / 917 \\
                 B.2: Building the C\# interface / 918 \\
                 B.3: Programming the C\# interface / 920 \\
                 B.4: Using the C\# interface / 922 \\
                 C: C++ interface / 923 \\
                 C.1: Building the C++ interface / 923 \\
                 C.2: Programming the C++ interface / 924 \\
                 C.3: Using the C++ interface / 925 \\
                 D: Decimal arithmetic / 927 \\
                 D.1: Why we need decimal floating-point arithmetic /
                 927 \\
                 D.2: Decimal floating-point arithmetic design issues /
                 928 \\
                 D.3: How decimal and binary arithmetic differ / 931 \\
                 D.4: Initialization of decimal floating-point storage /
                 935 \\
                 D.5: The {\tt <decfloat.h>} header file / 936 \\
                 D.6: Rounding in decimal arithmetic / 936 \\
                 D.7: Exact scaling in decimal arithmetic / 937 \\
                 E: Errata in the Cody\slash Waite book / 939 \\
                 F: Fortran interface / 941 \\
                 F.1: Building the Fortran interface / 943 \\
                 F.2: Programming the Fortran interface / 944 \\
                 F.3: Using the Fortran interface / 945 \\
                 H: Historical floating-point architectures / 947 \\
                 H.1: CDC family / 949 \\
                 H.2: Cray family / 952 \\
                 H.3: DEC PDP-10 / 953 \\
                 H.4: DEC PDP-11 and VAX / 956 \\
                 H.5: General Electric 600 series / 958 \\
                 H.6: IBM family / 959 \\
                 H.7: Lawrence Livermore S-1 Mark IIA / 965 \\
                 H.8: Unusual floating-point systems / 966 \\
                 H.9: Historical retrospective / 967 \\
                 I: Integer arithmetic / 969 \\
                 I.1: Memory addressing and integers / 971 \\
                 I.2: Representations of signed integers / 971 \\
                 I.3: Parity testing / 975 \\
                 I.4: Sign testing / 975 \\
                 I.5: Arithmetic exceptions / 975 \\
                 I.6: Notations for binary numbers / 977 \\
                 I.7: Summary / 978 \\
                 J: Java interface / 979 \\
                 J.1: Building the Java interface / 979 \\
                 J.2: Programming the Java MathCW class / 980 \\
                 J.3: Programming the Java C interface / 982 \\
                 J.4: Using the Java interface / 985 \\
                 L: Letter notation / 987 \\
                 P: Pascal interface / 989 \\
                 P.1: Building the Pascal interface / 989 \\
                 P.2: Programming the Pascal MathCW module / 990 \\
                 P.3: Using the Pascal module interface / 993 \\
                 P.4: Pascal and numeric programming / 994 \\
                 Bibliography / 995 \\
                 Author/editor index / 1039 \\
                 Function and macro index / 1049 \\
                 Subject index / 1065 \\
                 Colophon / 1115",
}

@TechReport{Brent:2017:JBP,
  author =       "Richard P. Brent",
  title =        "{Jonathan Borwein}, Pi and the {AGM}",
  type =         "Talk slides",
  institution =  "Australian National University and CARMA, University
                 of Newcastle",
  address =      "Canberra, ACT and Newcastle, NSW, Australia",
  pages =        "76",
  day =          "26",
  month =        sep,
  year =         "2017",
  bibdate =      "Fri Sep 04 17:08:54 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://carma.newcastle.edu.au/meetings/jbcc/abstracts/pdf/JBCC-Richard_Brent.pdf",
  abstract =     "We consider some of Jon Borwein s contributions to the
                 high-precision computation of $ \pi $ and the
                 elementary functions, with particular reference to the
                 fascinating book \booktitle{Pi and the AGM}(Wiley,
                 1987) by Jon and his brother Peter Borwein. Here
                 ``AGM'' is the arithmetic-geometric mean, first studied
                 by Euler, Gauss and Legendre. Because the AGM has
                 second-order convergence, it can be combined with fast
                 multiplication algorithms to give fast algorithms for
                 the $n$-bit computation of $ \pi $, and more generally
                 the elementary functions. These algorithms run in
                 ``almost linear' time $ O(M(n) \log n)$, where $ M(n)$
                 is the time for $n$-bit multiplication. The talk will
                 survey some of the results and algorithms, from the
                 time of Archimedes to the present day, that were of
                 interest to Jon. In several cases they were discovered
                 or improved by him",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
}

@Article{Chen:2017:UTS,
  author =       "Chao-Ping Chen and Junesang Choi",
  title =        "Unified treatment of several asymptotic expansions
                 concerning some mathematical constants",
  journal =      j-APPL-MATH-COMP,
  volume =       "305",
  number =       "??",
  pages =        "348--363",
  day =          "15",
  month =        jul,
  year =         "2017",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2017.02.001",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sun Mar 12 13:31:57 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300317300978",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "Asymptotic expansion; Choi--Srivastava constants;
                 constants of Landau and Lebesgue; Euler--Mascheroni
                 constant; Glaisher--Kinkelin constant; psi function
                 (logarithmic derivative of gamma function)",
}

@Article{Gil:2017:ECL,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Efficient computation of {Laguerre} polynomials",
  journal =      j-COMP-PHYS-COMM,
  volume =       "210",
  number =       "??",
  pages =        "124--131",
  month =        jan,
  year =         "2017",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.17632/3jkk659cn8.1",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Dec 1 14:31:09 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465516302727",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655/",
}

@Article{Horsley:2017:BPF,
  author =       "David E. Horsley",
  title =        "{Bessel} phase functions: calculation and
                 application",
  journal =      j-NUM-MATH,
  volume =       "136",
  number =       "3",
  pages =        "679--702",
  month =        jul,
  year =         "2017",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Wed Jun 7 17:52:44 MDT 2017",
  bibsource =    "http://link.springer.com/journal/211/136/3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@InProceedings{Istoan:2017:FFP,
  author =       "M. Istoan and B. Pasca",
  title =        "Flexible Fixed-Point Function Generation for {FPGAs}",
  crossref =     "Burgess:2017:ISC",
  pages =        "123--130",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.31",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Efficient fixed-point function implementation is
                 critical in many FPGA application domains including
                 convolutional neural networks, computer vision, and
                 communication systems. In this work we focus on
                 functions of the form $ x^p $, with $ p \in \{ - 1, - 1
                 / 2, 1 / 2 \} $ as part of a function generator
                 targeting FPGAs. The generator implements architectures
                 based on new but also existing algorithms. In this work
                 we present three distinct methods implemented in this
                 generator that outperform state-of-the-art
                 implementations for certain configurations.
                 Traditionally, fixed-point function implementation
                 requires a normalization stage, compute and
                 denormalization (reconstruction) of the result. The
                 first proposed method implements the function
                 holistically, thus saving the logic and latency
                 required during the normalize and reconstruct stages.
                 The second proposed method is based on a novel second
                 order Taylor implementation. The third method is based
                 on the cubic convergence of Halley's method, which is
                 novel in this context. The proposed methods are
                 compared and contrasted against state-of-the art
                 implementations in the context of FPGA targets.",
  acknowledgement = ack-nhfb,
  keywords =     "arithmetic; communication systems; computer vision;
                 convolutional neural networks; cubic convergence;
                 Digital signal processing; Field programmable gate
                 arrays; field programmable gate arrays; fixed point
                 arithmetic; fixed-point; flexible fixed-point function
                 generation; FPGA; FPGAs; generator; Generators; Halley
                 method; Kernel; Memory management; reciprocal;
                 reciprocal sqrt; second order Taylor implementation;
                 Signal generators; sqrt",
}

@InProceedings{Jeannerod:2017:REC,
  author =       "Claude-Pierre Jeannerod and Jean-Michel Muller",
  editor =       "Michael B. Matthews",
  booktitle =    "{2017 51st Asilomar Conference on Signals, Systems,
                 and Computers. October 29--November 1, 2017. Pacific
                 Grove, California}",
  title =        "On the relative error of computing complex square
                 roots in floating-point arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "737--740",
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ACSSC.2017.8335442",
  ISBN =         "1-5386-1823-0",
  ISBN-13 =      "978-1-5386-1823-3",
  bibdate =      "Fri Sep 29 10:59:32 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We study the accuracy of a classical approach to
                 computing complex square-roots in floating-point
                 arithmetic. Our analyses are done in binary
                 floating-point arithmetic in precision p, and we assume
                 that the (real) arithmetic operations $+$, $-$, $
                 \times $, $ \div $, $ \sqrt {} $ are rounded to
                 nearest, so the unit roundoff is $ u = 2^{-p} $. We
                 show that in the absence of underflow and overflow, the
                 componentwise and normwise relative errors of this
                 approach are at most $ 7 / 2 u $ and $ \sqrt {37} / 2 u
                 $, respectively, and this without having to neglect
                 terms of higher order in $u$. We then provide some
                 input examples showing that these bounds are reasonably
                 sharp for the three basic binary interchange formats
                 (binary32, binary64, and binary128) of the IEEE 754
                 standard for floating-point arithmetic.",
  acknowledgement = ack-nhfb,
}

@Article{Jeffrey:2017:BSI,
  author =       "David J. Jeffrey",
  title =        "Branch Structure and Implementation of {Lambert}
                 {$W$}",
  journal =      j-MATH-COMPUT-SCI,
  volume =       "11",
  number =       "3--4",
  pages =        "341--350",
  month =        dec,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s11786-017-0320-6",
  ISSN =         "1661-8270 (print), 1661-8289 (electronic)",
  ISSN-L =       "1661-8270",
  bibdate =      "Mon Oct 2 10:24:36 MDT 2017",
  bibsource =    "http://link.springer.com/journal/11786/11/3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/math-comput-sci.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics in Computer Science",
  journal-URL =  "http://link.springer.com/journal/11786",
}

@InProceedings{Langhammer:2017:FPT,
  author =       "M. Langhammer and B. Pasca",
  title =        "Floating Point Tangent Implementation for {FPGAs}",
  crossref =     "Burgess:2017:ISC",
  pages =        "64--65",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.25",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents an implementation of the
                 floating-point (FP) tangent function, optimized for an
                 FPGA containing hard floating point (HFP) DSP Blocks.
                 This function inputs values in the interval [- /2, /2],
                 uses the IEEE-754 single-precision (SP) format, and has
                 an accuracy conforming to OpenCL requirements. The
                 presented architecture is based on a combination of
                 mathematical identities and properties of the tangent
                 function in FP. The resultant design outperforms
                 generic polynomial approximation methods targeting the
                 same resource utilization spectrum, and provides better
                 resource trade-offs than classical CORDIC-based
                 implementations. The presented work is widely available
                 as part of the Intel DSP Builder Advanced Blockset.",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation methods; classical CORDIC-based
                 implementations; Digital arithmetic; Digital signal
                 processing; digital signal processing chips; field
                 programmable gate arrays; Field programmable gate
                 arrays; fixed point arithmetic; floating point
                 arithmetic; floating point tangent function; FPGAs;
                 generic polynomial approximation methods; hard floating
                 point DSP blocks; HFP DSP; IEEE-754 single-precision
                 format; Intel DSP Builder Advanced Blockset; OpenCL;
                 reconfigurable architectures; Resource management;
                 resource utilization spectrum; Table lookup",
}

@Article{Langhammer:2017:SPL,
  author =       "Martin Langhammer and Bogdan Pasca",
  title =        "Single Precision Logarithm and Exponential
                 Architectures for Hard Floating-Point Enabled {FPGAs}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "12",
  pages =        "2031--2043",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2703923",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 10 08:32:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "http://ieeexplore.ieee.org/document/7927449/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Matic:2017:PBA,
  author =       "Ivan Mati{\'c} and Rado{\v{s}} Radoi{\v{c}}i{\'c} and
                 Dan Stefanica",
  title =        "{P{\'o}lya}-based approximation for the {ATM}-forward
                 implied volatility",
  journal =      "International Journal of Financial Engineering",
  volume =       "4",
  number =       "2--3",
  pages =        "1--15",
  month =        jun # "\slash " # sep,
  year =         "2017",
  DOI =          "https://doi.org/10.1142/S2424786317500323",
  ISSN =         "2424-7863",
  bibdate =      "Sat Dec 16 17:12:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.worldscientific.com/doi/abs/10.1142/S2424786317500323",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Finan. Eng.",
  journal-URL =  "http://www.worldscientific.com/worldscinet/ijfe",
}

@Article{Pearson:2017:NMC,
  author =       "John W. Pearson and Sheehan Olver and Mason A.
                 Porter",
  title =        "Numerical methods for the computation of the confluent
                 and {Gauss} hypergeometric functions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "74",
  number =       "3",
  pages =        "821--866",
  month =        mar,
  year =         "2017",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-016-0173-0",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Mar 1 09:12:15 MST 2017",
  bibsource =    "http://link.springer.com/journal/11075/74/3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://link.springer.com/article/10.1007/s11075-016-0173-0",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Saint-Genies:2017:ELT,
  author =       "Hugues de Lassus Saint-Geni{\`e}s and David Defour and
                 Guillaume Revy",
  title =        "Exact Lookup Tables for the Evaluation of
                 Trigonometric and Hyperbolic Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "12",
  pages =        "2058--2071",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2703870",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 10 08:32:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "http://ieeexplore.ieee.org/document/7927421/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Staunton:2017:PP,
  author =       "Mike Staunton",
  title =        "Power to {P{\'o}lya}",
  journal =      "Wilmott Magazine",
  volume =       "90",
  pages =        "36--37",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1002/wilm.10605",
  bibdate =      "Sat Dec 16 17:41:48 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/wilm.10605/full",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1541-8286;
                 https://www.wilmott.com/category/magazine/",
  remark =       "No issues online at Wiley before year 2011, or at
                 Wilmott before 2006.",
}

@Article{Tihanyi:2017:CEL,
  author =       "Norbert Tihanyi and Attila Kov{\'a}cs and J{\'o}zsef
                 Kov{\'a}cs",
  title =        "Computing Extremely Large Values of the {Riemann} Zeta
                 Function",
  journal =      j-J-GRID-COMP,
  volume =       "15",
  number =       "4",
  pages =        "527--534",
  month =        dec,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s10723-017-9416-0",
  ISSN =         "1570-7873 (print), 1572-9184 (electronic)",
  ISSN-L =       "1570-7873",
  bibdate =      "Sat Jan 6 08:41:37 MST 2018",
  bibsource =    "http://link.springer.com/journal/10723/15/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jgridcomp.bib",
  URL =          "https://link.springer.com/article/10.1007/s10723-017-9416-0",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Grid Computing",
  journal-URL =  "http://link.springer.com/journal/10723",
}

@Article{Xu:2017:AEP,
  author =       "Aimin Xu and Zhongdi Cen",
  title =        "Asymptotic expansions for the psi function and the
                 {Euler--Mascheroni} constant",
  journal =      j-J-NUMBER-THEORY,
  volume =       "180",
  number =       "??",
  pages =        "360--372",
  month =        nov,
  year =         "2017",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2017.04.014",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Wed Jul 15 08:49:31 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X17302007",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Ye:2017:SDP,
  author =       "Liangjie Ye",
  title =        "A symbolic decision procedure for relations arising
                 among {Taylor} coefficients of classical {Jacobi} theta
                 functions",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "82",
  number =       "??",
  pages =        "134--163",
  month =        sep # "\slash " # oct,
  year =         "2017",
  CODEN =        "JSYCEH",
  DOI =          "https://doi.org/10.1016/j.jsc.2017.01.005",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  bibdate =      "Fri Feb 17 12:14:20 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0747717117300135",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171/",
}

@Article{Zaghloul:2017:ASE,
  author =       "Mofreh R. Zaghloul",
  title =        "Algorithm 985: Simple, Efficient, and Relatively
                 Accurate Approximation for the Evaluation of the
                 {Faddeyeva} Function",
  journal =      j-TOMS,
  volume =       "44",
  number =       "2",
  pages =        "22:1--22:9",
  month =        sep,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3119904",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 17:19:59 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=3119904",
  abstract =     "We present a new simple algorithm for efficient, and
                 relatively accurate computation of the Faddeyeva
                 function $ w(z) $. The algorithm carefully exploits
                 previous approximations by Hui et al. (1978) and
                 Huml{\'\i}cek (1982) along with asymptotic expressions
                 from Laplace continued fractions. Over a wide and fine
                 grid of the complex argument, $ z = x + i y $,
                 numerical results from the present approximation show a
                 maximum relative error less than $ 4.0 \times 10^{-5} $
                 for both real and imaginary parts of $w$ while running
                 in a relatively shorter execution time than other
                 competitive techniques. In addition to the calculation
                 of the Faddeyeva function, $w$, partial derivatives of
                 the real and imaginary parts of the function can easily
                 be calculated and returned as optional output.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Abrarov:2018:RAD,
  author =       "Sanjar M. Abrarov and Brendan M. Quine",
  title =        "A rational approximation of the {Dawson}'s integral
                 for efficient computation of the complex error
                 function",
  journal =      j-APPL-MATH-COMP,
  volume =       "321",
  number =       "??",
  pages =        "526--543",
  day =          "15",
  month =        mar,
  year =         "2018",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Dec 9 07:21:49 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300317307312",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Bober:2018:NCR,
  author =       "Jonathan W. Bober and Ghaith A. Hiary",
  title =        "New Computations of the {Riemann} Zeta Function on the
                 Critical Line",
  journal =      j-EXP-MATH,
  volume =       "27",
  number =       "2",
  pages =        "125--137",
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/10586458.2016.1233083",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  bibdate =      "Thu Sep 27 18:22:33 MDT 2018",
  bibsource =    "http://www.tandfonline.com/toc/uexm20/27/2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/expmath.bib",
  URL =          "http://www.tandfonline.com/doi/full/10.1080/10586458.2016.1233083",
  acknowledgement = ack-nhfb,
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
  onlinedate =   "14 Oct 2016",
}

@Article{Borwein:2018:GFM,
  author =       "Jonathan M. Borwein and Robert M. Corless",
  title =        "Gamma and Factorial in the {{\booktitle{Monthly}}}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "125",
  number =       "5",
  pages =        "400--424",
  month =        may,
  year =         "2018",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2018.1420983",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "33B15",
  MRnumber =     "3785875",
  bibdate =      "Tue Apr 17 09:02:26 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Since its inception in 1894, the Monthly has printed
                 50 articles on the $ \Gamma $ function or Stirling's
                 asymptotic formula, including the magisterial 1959
                 paper by Phillip J. Davis, which won the 1963 Chauvenet
                 prize, and the eye-opening 2000 paper by the Fields
                 medalist Manjul Bhargava. In this article, we look back
                 and comment on what has been said, and why, and try to
                 guess what will be said about the $ \Gamma $ function
                 in future Monthly issues.1 We also identify some gaps,
                 which surprised us: phase plots, Riemann surfaces, and
                 the functional inverse of $ \Gamma $ make their first
                 appearance in the Monthly here. We also give a new
                 elementary treatment of the asymptotics of $ n! $ and
                 the first few terms of a new asymptotic formula for
                 inv$ \Gamma $.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}

@Article{Braumann:2018:RGF,
  author =       "C. A. Braumann and J.-C. Cort{\'e}s and L. J{\'o}dar
                 and L. Villafuerte",
  title =        "On the random gamma function: Theory and computing",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "335",
  number =       "??",
  pages =        "142--155",
  month =        jun,
  year =         "2018",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/j.cam.2017.11.045",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Tue Mar 6 07:50:18 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2015.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042717306064",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Bremer:2018:ANE,
  author =       "James Bremer",
  title =        "An algorithm for the numerical evaluation of the
                 associated {Legendre} functions that runs in time
                 independent of degree and order",
  journal =      j-J-COMPUT-PHYS,
  volume =       "360",
  number =       "??",
  pages =        "15--38",
  day =          "1",
  month =        may,
  year =         "2018",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/j.jcp.2018.01.014",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Thu Mar 15 15:42:48 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys2015.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S002199911830024X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991",
}

@Article{Ceretani:2018:AME,
  author =       "Andrea N. Ceretani and Natalia N. Salva and Domingo A.
                 Tarzia",
  title =        "Approximation of the modified error function",
  journal =      j-APPL-MATH-COMP,
  volume =       "337",
  number =       "??",
  pages =        "591--606",
  day =          "15",
  month =        nov,
  year =         "2018",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2018.05.054",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Sep 14 08:14:13 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300318304715",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Chen:2018:NEH,
  author =       "Ruyun Chen and Gang Yang",
  title =        "Numerical evaluation of highly oscillatory {Bessel}
                 transforms",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "342",
  number =       "??",
  pages =        "16--24",
  month =        nov,
  year =         "2018",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/j.cam.2018.03.026",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Fri Aug 10 18:10:42 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2015.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042718301894",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{DelPunta:2018:LRC,
  author =       "Jessica A. {Del Punta} and Gustavo Gasaneo and Lorenzo
                 U. Ancarani",
  title =        "On the {Laguerre} Representation of {Coulomb}
                 Functions and the Relation to Orthogonal Polynomials",
  chapter =      "4",
  journal =      j-ADV-QUANTUM-CHEM,
  volume =       "76",
  pages =        "79--101",
  year =         "2018",
  CODEN =        "AQCHA9",
  DOI =          "https://doi.org/10.1016/bs.aiq.2017.06.005",
  ISSN =         "0065-3276",
  ISSN-L =       "0065-3276",
  bibdate =      "Thu Feb 1 07:08:30 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advquantumchem.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S0065327617300643",
  acknowledgement = ack-nhfb,
  ajournal =     "Adv. Quantum Chem.",
  fjournal =     "Advances in Quantum Chemistry",
  journal-URL =  "http://www.sciencedirect.com/science/bookseries/00653276/",
  keywords =     "Coulomb functions; Laguerre basis; Orthogonal
                 polynomials",
}

@Article{Dunster:2018:UAE,
  author =       "T. M. Dunster and A. Gil and J. Segura",
  title =        "Uniform asymptotic expansions for {Laguerre}
                 polynomials and related confluent hypergeometric
                 functions",
  journal =      j-ADV-COMPUT-MATH,
  volume =       "??",
  number =       "??",
  pages =        "1--34",
  month =        jan,
  year =         "2018",
  CODEN =        "ACMHEX",
  DOI =          "https://doi.org/10.1007/s10444-018-9589-5",
  ISSN =         "1019-7168 (print), 1572-9044 (electronic)",
  ISSN-L =       "1019-7168",
  bibdate =      "Tue Feb 6 11:33:27 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in Computational Mathematics",
  journal-URL =  "http://link.springer.com/journal/10444",
  xxnote =       "[06-Feb-2018]: online, but not yet assigned
                 volume/number/pages.",
}

@Article{Hanson:2018:RAM,
  author =       "Richard J. Hanson and Tim Hopkins",
  title =        "Remark on {Algorithm 539: A Modern Fortran Reference
                 Implementation for Carefully Computing the Euclidean
                 Norm}",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "24:1--24:23",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3134441",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 22 17:49:32 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3134441",
  abstract =     "We propose a set of new Fortran reference
                 implementations, based on an algorithm proposed by
                 Kahan, for the Level 1 BLAS routines *NRM2 that compute
                 the Euclidean norm of a real or complex input vector.
                 The principal advantage of these routines over the
                 current offerings is that, rather than losing accuracy
                 as the length of the vector increases, they generate
                 results that are accurate to almost machine precision
                 for vectors of length $ N < N_{\rm max} $ where $
                 N_{\rm max} $ depends upon the precision of the
                 floating point arithmetic being used. In addition, we
                 make use of intrinsic modules, introduced in the latest
                 Fortran standards, to detect occurrences of non-finite
                 numbers in the input data and return suitable values as
                 well as setting IEEE floating point status flags as
                 appropriate. A set of C interface routines is also
                 provided to allow simple, portable access to the new
                 routines. To improve execution speed, we advocate a
                 hybrid algorithm; a simple loop is used first and, only
                 if IEEE floating point exception flags signal, do we
                 fall back on Kahan's algorithm. Since most input
                 vectors are ``easy,'' i.e., they do not require the
                 sophistication of Kahan's algorithm, the simple loop
                 improves performance while the use of compensated
                 summation ensures high accuracy. We also report on a
                 comprehensive suite of test problems that has been
                 developed to test both our new implementation and
                 existing codes for both accuracy and the appropriate
                 settings of the IEEE arithmetic status flags.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  xxnote =       "See \cite{Lawson:1979:ABL}.",
}

@Article{Higham:2018:UN,
  author =       "Nicholas J. Higham",
  title =        "The Unwinding Number",
  journal =      j-SIAM-NEWS,
  volume =       "51",
  number =       "8",
  pages =        "??--??",
  month =        oct,
  year =         "2018",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Sat Oct 06 08:46:15 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://sinews.siam.org/Details-Page/the-unwinding-number",
  abstract =     "While Fortran 66 had a complex data type, this was not
                 true of most other early programming languages, such as
                 Algol 60. As a result, programmers had to write their
                 own procedures to implement complex arithmetic and
                 transcendental functions in terms of separately stored
                 real and imaginary parts. They quickly realized that
                 this is not a trivial task; in the early 1960s, it took
                 five published attempts over three years to obtain a
                 correct implementation of the complex logarithm in
                 Algol 60.",
  acknowledgement = ack-nhfb,
}

@Article{Johansson:2018:FRA,
  author =       "Fredrik Johansson and Marc Mezzarobba",
  title =        "Fast and Rigorous Arbitrary-Precision Computation of
                 {Gauss--Legendre} Quadrature Nodes and Weights",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "40",
  number =       "6",
  pages =        "C726--C747",
  month =        "????",
  year =         "2018",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/18M1170133",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Fri Jan 25 18:37:30 MST 2019",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/40/6;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2018",
}

@Misc{Kahan:2018:TD,
  author =       "William Kahan",
  title =        "The tanpi Dilemma",
  howpublished = "Web document.",
  day =          "16",
  month =        apr,
  year =         "2018",
  bibdate =      "Tue Apr 17 06:52:47 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://754r.ucbtest.org/background/tanpi.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The function tanpi(x) satisfies two familiar
                 identities, tanpi(-x) = -tanpi(x), and tanpi(x +
                 integer) = tanpi(x), that cannot both be satisfied {\em
                 everywhere\/} by IEEE 754's arithmetic; the obvious
                 failures occur when tanpi is infinite: does tanpi(-2.5)
                 = -tanpi(2.5) or does tanpi(-2.5) = tanpi(-2.5 + 4) =
                 +tanpi(2.5)? Whoever puts a tanpi subprogram into the
                 Math library has no choice but to disappoint
                 somebody.",
  acknowledgement = ack-nhfb,
}

@Article{Lopez:2018:CEB,
  author =       "Jos{\'e} L. L{\'o}pez",
  title =        "Convergent expansions of the {Bessel} functions in
                 terms of elementary functions",
  journal =      j-ADV-COMPUT-MATH,
  volume =       "44",
  number =       "1",
  pages =        "277--294",
  month =        feb,
  year =         "2018",
  CODEN =        "ACMHEX",
  DOI =          "https://doi.org/10.1007/s10444-017-9543-y",
  ISSN =         "1019-7168 (print), 1572-9044 (electronic)",
  ISSN-L =       "1019-7168",
  MRclass =      "33C10 (41A58)",
  MRnumber =     "3755750",
  bibdate =      "Sat Feb 3 18:23:33 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/s10444-017-9543-y",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in Computational Mathematics",
  journal-URL =  "http://link.springer.com/journal/10444",
}

@Article{Matic:2018:SPB,
  author =       "Ivan Mati{\'c} and Rado{\v{s}} Radoi{\v{c}}i{\'c} and
                 Dan Stefanica",
  title =        "A sharp {P{\'o}lya}-based approximation to the normal
                 cumulative distribution function",
  journal =      j-APPL-MATH-COMP,
  volume =       "322",
  number =       "??",
  pages =        "111--122",
  day =          "1",
  month =        apr,
  year =         "2018",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2017.10.019",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Dec 15 10:03:09 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S009630031730718X",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  remark =       "Although the accuracy of the approximations developed
                 is low (6 to 10 digits), the article shows how it can
                 be increased by taking more series terms. The article
                 is an excellent overview of prior work on computing the
                 normal and inverse normal cumulative distribution
                 function, almost all of which is low accuracy (2 to 4
                 digits). The authors supply 89 references to prior
                 work, all of which are now in this bibliography as of
                 16 December 2017.",
}

@InProceedings{Mikaitis:2018:AFP,
  author =       "Mantas Mikaitis and David R. Lester and Delong Shang
                 and Steve Furber and Gengting Liu and Jim Garside and
                 Stefan Scholze and Sebastian H{\"o}ppner and Andreas
                 Dixius",
  title =        "Approximate Fixed-Point Elementary Function
                 Accelerator for the {SpiNNaker-2} Neuromorphic Chip",
  crossref =     "Tenca:2018:PIS",
  pages =        "37--44",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464785",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Neuromorphic chips are used to model biologically
                 inspired Spiking-Neural-Networks (SNNs) where most
                 models are based on differential equations. Equations
                 for most SNN algorithms usually contain variables with
                 one or more ex components. SpiNNaker is a digital
                 neuromorphic chip that has so far been using
                 pre-calculated look-up tables for exponential function.
                 However this approach is limited because the memory
                 requirements grow as more complex neural models are
                 developed. To save already limited memory resources in
                 the next generation SpiNNaker chip, we are including a
                 fast exponential function in the silicon. In this paper
                 we analyse iterative algorithms for elementary
                 functions and show how to build a single hardware
                 accelerator for exp and natural log, for a neuromorphic
                 chip prototype, to be manufactured in a 22 nm FDSOI
                 process. We present the accelerator that has
                 algorithmic level approximation control, allowing it to
                 trade precision for latency and energy efficiency. As
                 an addition to neuromorphic chip application, we
                 provide analysis of a parameterized elementary function
                 unit that can be tailored for other systems with
                 different power, area, accuracy and latency
                 constraints.",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; algorithmic level approximation control;
                 approximate arithmetic; approximate fixed-point
                 elementary function accelerator; ARITH-25; Biological
                 system modeling; biologically inspired
                 spiking-neural-networks; complex neural models;
                 Computational modeling; Convergence; differential
                 equations; digital neuromorphic chip; energy
                 efficiency; exponential function; fast exponential
                 function; FDSOI process; fixed-point arithmetic;
                 hardware accelerators; iterative algorithms; iterative
                 methods; logarithm function; Mathematical model; memory
                 requirements; memory resources; MPSoC; neural chips;
                 neuromorphic chip prototype; neuromorphic computing;
                 Neuromorphics; next generation SpiNNaker chip;
                 parameterized elementary function unit; pre-calculated
                 look-up tables; single hardware accelerator; size 22.0
                 nm; SNN algorithms; SpiNNaker-2 neuromorphic chip;
                 SpiNNaker2; table lookup; Table lookup",
}

@Article{Moroz:2018:FCI,
  author =       "Leonid V. Moroz and Cezary J. Walczyk and Andriy
                 Hrynchyshyn and Vijay Holimath and Jan L.
                 Cie{\'s}li{\'n}ski",
  title =        "Fast calculation of inverse square root with the use
                 of magic constant --- analytical approach",
  journal =      j-APPL-MATH-COMP,
  volume =       "316",
  number =       "??",
  pages =        "245--255",
  day =          "1",
  month =        jan,
  year =         "2018",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2017.08.025",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Oct 10 15:56:03 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300317305763",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "single-precision 32-bit IEEE 754 binary arithmetic",
}

@Article{Munoz-Coreas:2018:CQO,
  author =       "Edgard Mu{\~n}oz-Coreas and Himanshu Thapliyal",
  title =        "{T}-count and Qubit Optimized Quantum Circuit Design
                 of the Non-Restoring Square Root Algorithm",
  journal =      j-JETC,
  volume =       "14",
  number =       "3",
  pages =        "36:1--36:15",
  month =        oct,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3264816",
  ISSN =         "1550-4832",
  bibdate =      "Thu Nov 1 16:44:41 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jetc.bib",
  abstract =     "Quantum circuits for basic mathematical functions such
                 as the square root are required to implement scientific
                 computing algorithms on quantum computers. Quantum
                 circuits that are based on Clifford+T gates can easily
                 be made fault tolerant, but the T gate is very costly
                 to implement. As a result, reducing T-count has become
                 an important optimization goal. Further, quantum
                 circuits with many qubits are difficult to realize,
                 making designs that save qubits and produce no garbage
                 outputs desirable. In this work, we present a T-count
                 optimized quantum square root circuit with only $ 2 s n
                 + 1 $ qubits and no garbage output. To make a fair
                 comparison against existing work, the Bennett's garbage
                 removal scheme is used to remove garbage output from
                 existing works. We determined that our proposed design
                 achieves an average T-count savings of 43.44\%,
                 98.95\%, 41.06\%, and 20.28\% as well as qubit savings
                 of 85.46\%, 95.16\%, 90.59\%, and 86.77\% compared to
                 existing works.",
  acknowledgement = ack-nhfb,
  articleno =    "36",
  fjournal =     "ACM Journal on Emerging Technologies in Computing
                 Systems (JETC)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J967",
}

@Article{Myland:2018:JEF,
  author =       "Jan C. Myland and Keith B. Oldham",
  title =        "{Jacobian} elliptic functions describe the properties
                 of the diffuse charge region in narrow electrochemical
                 cells",
  journal =      j-J-MATH-CHEM,
  volume =       "56",
  number =       "4",
  pages =        "1184--1205",
  month =        apr,
  year =         "2018",
  CODEN =        "JMCHEG",
  DOI =          "https://doi.org/10.1007/s10910-017-0847-4",
  ISSN =         "0259-9791 (print), 1572-8897 (electronic)",
  ISSN-L =       "0259-9791",
  bibdate =      "Tue Mar 6 07:08:26 MST 2018",
  bibsource =    "http://link.springer.com/journal/10910/56/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathchem.bib",
  URL =          "https://link.springer.com/article/10.1007/s10910-017-0847-4",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Chemistry",
  journal-URL =  "http://link.springer.com/journal/10910",
  journalabr =   "J. Math. Chem.",
}

@Article{Navas-Palencia:2018:FAA,
  author =       "Guillermo Navas-Palencia",
  title =        "Fast and accurate algorithm for the generalized
                 exponential integral {$ E_\nu (x) $} for positive real
                 order",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "77",
  number =       "2",
  pages =        "603--630",
  month =        feb,
  year =         "2018",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-017-0331-z",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Thu Jan 25 09:50:15 MST 2018",
  bibsource =    "http://link.springer.com/journal/11075/77/2;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-017-0331-z",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Navas-Palencia:2018:HPC,
  author =       "Guillermo Navas-Palencia",
  title =        "High-precision computation of the confluent
                 hypergeometric functions via {Franklin--Friedman}
                 expansion",
  journal =      j-ADV-COMPUT-MATH,
  volume =       "44",
  number =       "??",
  pages =        "1--19",
  year =         "2018",
  CODEN =        "ACMHEX",
  DOI =          "https://doi.org/10.1007/s10444-017-9565-5",
  ISSN =         "1019-7168 (print), 1572-9044 (electronic)",
  ISSN-L =       "1019-7168",
  bibdate =      "Sat Feb 3 16:58:03 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in Computational Mathematics",
  journal-URL =  "http://link.springer.com/journal/10444",
  keywords =     "Arbitrary-precision arithmetic; confluent
                 hypergeometric functions; Franklin--Friedman expansion;
                 generalized exponential integer $E_\nu(z) = z^{\nu - 1}
                 U(\nu, \nu, z)$; Kummer function $U(a,b,z)$; modified
                 Bessel function $K_\nu(z)$; uniform series expansion",
  xxnote =       "[03-Feb-2018]: online, but not yet assigned
                 volume/number/pages.",
}

@Article{Pakes:2018:LFN,
  author =       "Anthony G. Pakes",
  title =        "The {Lambert} {$W$} function, {Nuttall}'s integral,
                 and the {Lambert} law",
  journal =      j-STAT-PROB-LETT,
  volume =       "139",
  number =       "??",
  pages =        "53--60",
  month =        aug,
  year =         "2018",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/j.spl.2018.03.015",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  bibdate =      "Thu Nov 8 12:34:02 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/statproblett2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715218301354",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
}

@Article{Patterson:2018:SCS,
  author =       "T. N. L. Patterson",
  title =        "Sines, Cosines, Square Roots, and Binary Bits",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "125",
  number =       "8",
  pages =        "750--754",
  year =         "2018",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2018.1498695",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 17:59:05 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "28 Sep 2018",
}

@Article{Punta:2018:CFL,
  author =       "Jessica A. Del Punta and Gustavo Gasaneo and Lorenzo
                 U. Ancarani",
  title =        "On the {Laguerre} Representation of {Coulomb}
                 Functions and the Relation to Orthogonal Polynomials",
  chapter =      "4",
  journal =      j-ADV-QUANTUM-CHEM,
  volume =       "76",
  pages =        "79--101",
  year =         "2018",
  CODEN =        "AQCHA9",
  DOI =          "https://doi.org/10.1016/bs.aiq.2017.06.005",
  ISSN =         "0065-3276",
  ISSN-L =       "0065-3276",
  bibdate =      "Thu Feb 1 07:08:30 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advquantumchem.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S0065327617300643",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in Quantum Chemistry",
  journal-URL =  "http://www.sciencedirect.com/science/bookseries/00653276",
  keywords =     "Coulomb functions; Laguerre basis; Orthogonal
                 polynomials",
}

@Article{Qi:2018:DME,
  author =       "Hongyuan Qi and Jinchen Xu and Shaozhong Guo",
  title =        "Detection of the maximum error of mathematical
                 functions",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "74",
  number =       "11",
  pages =        "6275--6290",
  month =        nov,
  year =         "2018",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-018-2552-x",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Thu Oct 10 15:31:09 MDT 2019",
  bibsource =    "http://link.springer.com/journal/11227/74/11;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@PhdThesis{Saint-Genies:2018:EFT,
  author =       "Hugues de Lassus Saint-Geni{\`e}s",
  title =        "Elementary functions: towards automatically generated,
                 efficient, and vectorizable implementations",
  type =         "{Ph.D.} thesis",
  school =       "Universit{\'e} de Perpignan",
  address =      "Perpignan, France",
  pages =        "xxxviii + 128",
  day =          "17",
  month =        jul,
  year =         "2018",
  bibdate =      "Tue Mar 01 06:09:03 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://tel.archives-ouvertes.fr/tel-01841424/document",
  acknowledgement = ack-nhfb,
}

@Article{Schneider:2018:NFP,
  author =       "Barry I. Schneider and Javier Segura and Amparo Gil
                 and Xiaoxu Guan and Klaus Bartschat",
  title =        "A new {Fortran 90} program to compute regular and
                 irregular associated {Legendre} functions (new version
                 announcement)",
  journal =      j-COMP-PHYS-COMM,
  volume =       "225",
  number =       "??",
  pages =        "192--193",
  month =        apr,
  year =         "2018",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2017.12.013",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Wed Feb 28 14:39:27 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465517304186",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Walczyk:2018:IAF,
  author =       "Cezary J. Walczyk and Leonid V. Moroz and Jan L.
                 Cie{\'s}li{\'n}ski",
  title =        "Improving the accuracy of the fast inverse square root
                 algorithm",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--21",
  day =          "17",
  month =        feb,
  year =         "2018",
  DOI =          "https://doi.org/10.48550/arXiv.1802.06302",
  bibdate =      "Wed Dec 20 07:55:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/1802.06302",
  abstract =     "We present improved algorithms for fast calculation of
                 the inverse square root for single-precision
                 floating-point numbers. The algorithms are much more
                 accurate than the famous fast inverse square root
                 algorithm and have the same or similar computational
                 cost. The main idea of our work consists in modifying
                 the Newton-Raphson method and demanding that the
                 maximal error is as small as possible. Such
                 modification is possible when the distribution of
                 Newton-Raphson corrections is not symmetric (e.g., if
                 they are non-positive functions).",
  acknowledgement = ack-nhfb,
}

@Article{Xue:2018:RCL,
  author =       "Changfeng Xue and Shaozhong Deng",
  title =        "Recursive Computation of Logarithmic Derivatives,
                 Ratios, and Products of Spheroidal Harmonics and
                 Modified {Bessel} Functions and Applications",
  journal =      j-J-SCI-COMPUT,
  volume =       "75",
  number =       "1",
  pages =        "128--156",
  month =        oct,
  year =         "2018",
  CODEN =        "JSCOEB",
  DOI =          "https://doi.org/10.1007/s10915-017-0527-3",
  ISSN =         "0885-7474 (print), 1573-7691 (electronic)",
  ISSN-L =       "0885-7474",
  bibdate =      "Fri Mar 29 16:29:33 MDT 2019",
  bibsource =    "http://link.springer.com/journal/10915/75/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jscicomput.bib",
  URL =          "https://link.springer.com/article/10.1007/s10915-017-0527-3;
                 https://link.springer.com/content/pdf/10.1007/s10915-017-0527-3.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Scientific Computing",
  journal-URL =  "http://link.springer.com/journal/10915",
}

@Article{Alonso:2019:CMT,
  author =       "Pedro Alonso and Jes{\'u}s Peinado and Javier
                 Ib{\'a}{\~n}ez and Jorge Sastre and Emilio Defez",
  title =        "Computing matrix trigonometric functions with {GPUs}
                 through {Matlab}",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "75",
  number =       "3",
  pages =        "1227--1240",
  month =        mar,
  year =         "2019",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-018-2354-1",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Thu Oct 10 15:31:18 MDT 2019",
  bibsource =    "http://link.springer.com/journal/11227/75/3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@InProceedings{Arzelier:2019:EAE,
  author =       "Denis Arzelier and Florent Br{\'e}hard and Mioara
                 Joldes",
  title =        "Exchange Algorithm for Evaluation and Approximation
                 Error-Optimized Polynomials",
  crossref =     "Takagi:2019:ISC",
  pages =        "30--37",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00014",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Machine implementation of mathematical functions often
                 relies on polynomial approximations. The particularity
                 is that rounding errors occur both when representing
                 the polynomial coefficients on a finite number of bits,
                 and when evaluating it in finite precision. Hence, for
                 finding the best polynomial (for a given fixed degree,
                 norm and interval), one has to consider both types of
                 errors: approximation and evaluation. While efficient
                 algorithms were already developed for taking into
                 account the approximation error, the evaluation part is
                 usually a posteriori handled, in an ad-hoc manner.
                 Here, we formulate a semi-infinite linear optimization
                 problem whose solution is the best polynomial with
                 respect to the supremum norm of the sum of both errors.
                 This problem is then solved with an iterative exchange
                 algorithm, which can be seen as an extension of the
                 well-known Remez algorithm. A discussion and comparison
                 of the obtained results on different examples are
                 finally presented.",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation algorithms; Approximation error;
                 approximation error; approximation error-optimized
                 polynomials; ARITH-26; Digital arithmetic; evaluation
                 error; exchange algorithm; function approximation;
                 Indexes; Input variables; iterative exchange algorithm;
                 iterative methods; learning (artificial intelligence);
                 libm; linear programming; machine implementation;
                 mathematical functions; mathematics computing;
                 optimisation; Optimization; polynomial approximation;
                 polynomial approximations; polynomial coefficients;
                 Programming; remez algorithm; Remez algorithm;
                 semi-infinite programming; semiinfinite linear
                 optimization problem",
}

@Article{Batista:2019:ECM,
  author =       "Milan Batista",
  title =        "\pkg{Elfun18} --- a collection of {MATLAB} functions
                 for the computation of elliptic integrals and
                 {Jacobian} elliptic functions of real arguments",
  journal =      j-SOFTWAREX,
  volume =       "10",
  number =       "??",
  pages =        "Article 100245",
  month =        jul # "\slash " # dec,
  year =         "2019",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.softx.2019.100245",
  ISSN =         "2352-7110",
  ISSN-L =       "2352-7110",
  bibdate =      "Fri Apr 9 16:04:36 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/softwarex.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S2352711018302796",
  acknowledgement = ack-nhfb,
  fjournal =     "SoftwareX",
  journal-URL =  "https://www.sciencedirect.com/journal/softwarex/issues",
}

@TechReport{Bernstein:2019:FCT,
  author =       "Daniel J. Bernstein and Bo-Yin Yang",
  title =        "Fast constant-time gcd computation and modular
                 inversion",
  institution =  "International Association for Cryptologic Research",
  address =      "????",
  pages =        "1--59",
  day =          "13",
  month =        apr,
  year =         "2019",
  bibdate =      "Tue May 24 07:23:13 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://eprint.iacr.org/2019/266.pdf",
  abstract =     "This paper introduces streamlined constant-time
                 variants of Euclid's algorithm, both for polynomial
                 inputs and for integer inputs. As concrete
                 applications, this paper saves time in (1) modular
                 inversion for Curve25519, which was previously believed
                 to be handled much more efficiently by Fermat's method,
                 and (2) key generation for the ntruhrss701 and
                 sntrup4591761 lattice-based cryptosystems",
  acknowledgement = ack-nhfb,
  keywords =     "algorithm design; branchless algorithms; constant-time
                 computations; Curve25519; Euclid's algorithm; gcd;
                 greatest common divisor; modular inversion; modular
                 reciprocal; NTRU",
}

@Article{Bujanda:2019:CEC,
  author =       "Blanca Bujanda and Jos{\'e} and L. L{\'o}pez and Pedro
                 J. Pagola",
  title =        "Convergent expansions of the confluent hypergeometric
                 functions in terms of elementary functions",
  journal =      j-MATH-COMPUT,
  volume =       "88",
  number =       "318",
  pages =        "1773--1789",
  month =        apr,
  year =         "2019",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/mcom/3389",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Jul 14 06:45:40 MDT 2020",
  bibsource =    "http://www.ams.org/mcom/2019-88-318;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "https://www.ams.org/journals/mcom/2019-88-318/S0025-5718-2018-03389-0;
                 https://www.ams.org/journals/mcom/2019-88-318/S0025-5718-2018-03389-0/S0025-5718-2018-03389-0.pdf;
                 https://www.ams.org/mathscinet/search/authors.html?authorName=Lopez%2C%20Jose%20L.;
                 https://www.ams.org/mathscinet/search/authors.html?mrauthid=636519;
                 https://www.ams.org/mathscinet/search/authors.html?mrauthid=806866",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Campos-Pinto:2019:APP,
  author =       "Martin Campos-Pinto and Fr{\'e}d{\'e}rique Charles and
                 Bruno Despr{\'e}s",
  title =        "Algorithms For Positive Polynomial Approximation",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "57",
  number =       "1",
  pages =        "148--172",
  month =        "????",
  year =         "2019",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/17M1131891",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  bibdate =      "Mon Mar 18 13:37:59 MDT 2019",
  bibsource =    "http://epubs.siam.org/http://epubs.siam.org/toc/sjnaam/57/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjnumeranal2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  onlinedate =   "January 2019",
}

@Article{Cardoso:2019:CMG,
  author =       "Jo{\~a}o R. Cardoso and Amir Sadeghi",
  title =        "Computation of matrix gamma function",
  journal =      j-BIT-NUM-MATH,
  volume =       "59",
  number =       "2",
  pages =        "343--370",
  month =        jun,
  year =         "2019",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-018-00744-1",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Fri Sep 6 09:16:11 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/s10543-018-00744-1",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Fedotov:2019:CWM,
  author =       "Alexander Fedotov and Fr{\'e}d{\'e}ric Klopp",
  title =        "The Complex {WKB} Method for Difference Equations and
                 {Airy} Functions",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "51",
  number =       "6",
  pages =        "4413--4447",
  month =        "????",
  year =         "2019",
  CODEN =        "SJMAAH",
  DOI =          "https://doi.org/10.1137/18M1228694",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  bibdate =      "Fri Apr 24 15:47:49 MDT 2020",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/51/6;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmathana2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
  onlinedate =   "January 2019",
}

@Article{Green:2019:DFE,
  author =       "Kevin R. Green and Tanner A. Bohn and Raymond J.
                 Spiteri",
  title =        "Direct Function Evaluation versus Lookup Tables: When
                 to Use Which?",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "41",
  number =       "3",
  pages =        "C194--C218",
  month =        "????",
  year =         "2019",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/18M1201421",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Thu Oct 10 06:58:05 MDT 2019",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/41/3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2019",
}

@Article{Horyachyy:2019:SEF,
  author =       "Oleh Horyachyy and Leonid Moroz and Viktor Otenko",
  title =        "Simple Effective Fast Inverse Square Root Algorithm
                 with Two Magic Constants",
  journal =      "International Journal of Computing",
  volume =       "18",
  number =       "4",
  pages =        "461--470",
  month =        dec,
  year =         "2019",
  ISSN =         "1727-6209 (print), 2312-5381 (electronic)",
  ISSN-L =       "1727-6209",
  bibdate =      "Thu Feb 11 11:01:47 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.computingonline.net/computing/article/view/1616;
                 https://www.researchgate.net/publication/349173096_SIMPLE_EFFECTIVE_FAST_INVERSE_SQUARE_ROOT_ALGORITHM_WITH_TWO_MAGIC_CONSTANTS",
  acknowledgement = ack-nhfb,
  keywords =     "FISR algorithm; floating-point arithmetic; FMA
                 function; Householder.; IEEE 754 standard; initial
                 approximation; inverse square root; magic constant;
                 maximum relative error; Newton-Raphson",
}

@Article{Johansson:2019:CHF,
  author =       "Fredrik Johansson",
  title =        "Computing Hypergeometric Functions Rigorously",
  journal =      j-TOMS,
  volume =       "45",
  number =       "3",
  pages =        "30:1--30:26",
  month =        aug,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3328732",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 3 17:49:22 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3328732",
  abstract =     "We present an efficient implementation of
                 hypergeometric functions in arbitrary-precision
                 interval arithmetic. The functions $_0 F_1$, $_1 F_1$,
                 $_2 F_1$, and $_2 F_0$ (or the Kummer $U$-function) are
                 supported for unrestricted complex parameters and
                 argument, and, by extension, we cover exponential and
                 trigonometric integrals, error functions, Fresnel
                 integrals, incomplete gamma and beta functions, Bessel
                 functions, Airy functions, Legendre functions, Jacobi
                 polynomials, complete elliptic integrals, and other
                 special functions. The output can be used directly for
                 interval computations or to generate provably correct
                 floating-point approximations in any format.
                 Performance is competitive with earlier
                 arbitrary-precision software and sometimes orders of
                 magnitude faster. We also partially cover the
                 generalized hypergeometric function $_p F_q$ and
                 computation of high-order parameter derivatives.",
  acknowledgement = ack-nhfb,
  articleno =    "30",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lemire:2019:FRD,
  author =       "Daniel Lemire and Owen Kaser and Nathan Kurz",
  title =        "Faster remainder by direct computation: Applications
                 to compilers and software libraries",
  journal =      j-SPE,
  volume =       "49",
  number =       "6",
  pages =        "953--970",
  month =        jun,
  year =         "2019",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.2689",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat Oct 12 09:43:47 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/spe.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software --- Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  keywords =     "integer division; integer remainder",
  onlinedate =   "27 February 2019",
}

@InProceedings{Melquiond:2019:FVS,
  author =       "Guillaume Melquiond and Raphael Rieu-Helft",
  title =        "Formal Verification of a State-of-the-Art Integer
                 Square Root",
  crossref =     "Takagi:2019:ISC",
  pages =        "183--186",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00041",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present the automatic formal verification of a
                 state-of-the-art algorithm from the GMP library that
                 computes the square root of a 64-bit integer. Although
                 it uses only integer operations, the best way to
                 understand the program is to view it as a fixed-point
                 arithmetic algorithm that implements Newton's method.
                 The C code is short but intricate, involving magic
                 constants and intentional arithmetic overflows. We have
                 verified the algorithm using the Why3 tool and
                 automated solvers such as Gappa.",
  acknowledgement = ack-nhfb,
  keywords =     "64-bit integer; Approximation algorithms; ARITH-26;
                 automatic formal verification; C code; C language;
                 Convergence; Digital arithmetic; electronic engineering
                 computing; fixed point arithmetic; Fixed-point
                 arithmetic; fixed-point arithmetic algorithm; floating
                 point arithmetic; Floors; Formal verification; GMP
                 library; integer operations; integer square root;
                 intentional arithmetic overflows; Libraries; Newton
                 method; program verification; programming; Tools; Why3
                 tool",
}

@Article{Miyajima:2019:VCM,
  author =       "Shinya Miyajima",
  title =        "Verified computation for the matrix {Lambert} {$W$}
                 function",
  journal =      j-APPL-MATH-COMP,
  volume =       "362",
  number =       "??",
  pages =        "Article 124555",
  day =          "1",
  month =        dec,
  year =         "2019",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Sep 6 09:21:26 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S0096300319305387",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Nemes:2019:AEI,
  author =       "Gerg{\H{o}} Nemes and Adri B. Olde Daalhuis",
  title =        "Asymptotic expansions for the incomplete gamma
                 function in the transition regions",
  journal =      j-MATH-COMPUT,
  volume =       "88",
  number =       "318",
  pages =        "1805--1827",
  month =        apr,
  year =         "2019",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/mcom/3391",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Jul 14 06:45:40 MDT 2020",
  bibsource =    "http://www.ams.org/mcom/2019-88-318;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "https://www.ams.org/journals/mcom/2019-88-318/S0025-5718-2018-03391-9;
                 https://www.ams.org/journals/mcom/2019-88-318/S0025-5718-2018-03391-9/S0025-5718-2018-03391-9.pdf;
                 https://www.ams.org/mathscinet/search/authors.html?authorName=Nemes%2C%20Gergo;
                 https://www.ams.org/mathscinet/search/authors.html?mrauthid=293428",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Parhi:2019:CAF,
  author =       "Keshab K. Parhi and Yin Liu",
  title =        "Computing Arithmetic Functions Using Stochastic Logic
                 by Series Expansion",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "7",
  number =       "1",
  pages =        "44--59",
  month =        jan # "\slash " # mar,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/TETC.2016.2618750",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  abstract =     "Stochastic logic implementations of complex arithmetic
                 functions, such as trigonometric, exponential, and
                 sigmoid, are derived based on truncated versions of
                 their Maclaurin series expansions. This paper makes
                 three contributions. First, it is shown that a
                 polynomial can be implemented using multiple levels of
                 NAND gates based on Horner's rule, if the coefficients
                 are alternately positive and negative and their
                 magnitudes are monotonically decreasing. Truncated
                 Maclaurin series expansions of arithmetic functions are
                 used to generate polynomials which satisfy these
                 constraints. The input and output in these functions
                 are represented by unipolar representation. Functions
                 including sine, cosine, tangent hyperbolic, logarithm
                 and exponential can be implemented using this method.
                 Second, for a polynomial that does not satisfy these
                 constraints, it still can be implemented based on
                 Horner's rule if each factor of the polynomial
                 satisfies these constraints. It is shown that functions
                 such as $ \sin \pi x / \pi $, $ e^{-a x} $, $ \tanh a x
                 $ and $ \sigmoid (a x^3) $ (for values of $ a > 1$) can
                 be implemented using stochastic logic using
                 factorization in combination with Horner's rule. Third,
                 format conversion is proposed for arithmetic functions
                 with input and output represented in different formats,
                 such as $ \cos \pi x$ given $ x \in [0, 1]$ and $
                 \sigmoid (x)$ given $ x \in [ - 1, 1]$. Polynomials are
                 transformed to equivalent forms that naturally exploit
                 format conversions. The proposed stochastic logic
                 circuits outperform the well-known Bernstein polynomial
                 based and finite-state-machine (FSM) based
                 implementations. Furthermore, the hardware complexity
                 and the critical path of the proposed implementations
                 are less than the well-known Bernstein polynomial based
                 and FSM based implementations for most cases",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@Article{Qi:2019:CMD,
  author =       "Feng Qi and Ai-Qi Liu",
  title =        "Completely monotonic degrees for a difference between
                 the logarithmic and psi functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "361",
  number =       "??",
  pages =        "366--371",
  day =          "1",
  month =        dec,
  year =         "2019",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Fri Sep 6 08:23:29 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2015.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S0377042719302298",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Shterenlikht:2019:QIF,
  author =       "A. Shterenlikht",
  title =        "On Quality of Implementation of {Fortran 2008} Complex
                 Intrinsic Functions on Branch Cuts",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "11:1--11:9",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3301318",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3301318",
  abstract =     "Branch cuts in complex functions have important uses
                 in fracture mechanics, jet flow, and aerofoil analysis.
                 This article introduces tests for validating Fortran
                 2008 complex functions-LOG, SQRT, ASIN, ACOS, ATAN,
                 ASINH, ACOSH, and ATANH-on branch cuts with arguments
                 of all 3 IEEE floating-point binary formats: binary32,
                 binary64, and binary128, including signed zero and
                 signed infinity. Multiple test failures were revealed,
                 such as wrong signs of results or unexpected overflow,
                 underflow, or NaN. We conclude that the quality of
                 implementation of these Fortran 2008 intrinsics in many
                 compilers is not yet sufficient to remove the need for
                 special code for branch cuts. The electronic appendix
                 contains the full test results with 8 Fortran 2008
                 compilers: GCC, Flang, Cray, Oracle, PGI, Intel, NAG,
                 and IBM, detailed derivations of the values of these
                 functions on branch cuts and conformal maps of the
                 branch cuts, to be used as a reference. The tests and
                 the results are freely available from
                 https://cmplx.sourceforge.io. This work will be of
                 interest to engineers who use complex functions, as
                 well as to compiler and math library developers.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Volkova:2019:SAI,
  author =       "Anastasia Volkova and Jean-Michel Muller",
  title =        "Semi-Automatic Implementation of the Complementary
                 Error Function",
  crossref =     "Takagi:2019:ISC",
  pages =        "167--174",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00039",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The normal and complementary error functions are
                 ubiquitous special functions for any mathematical
                 library. They have a wide range of applications.
                 Practical applications call for customized
                 implementations that have strict accuracy requirements.
                 Accurate numerical implementation of these functions
                 is, however, non-trivial. In particular, the
                 complementary error function erfc for large positive
                 arguments heavily suffers from cancellation, which is
                 largely due to its asymptotic behavior. We provide a
                 semi-automatic code generator for the erfc function
                 which is parameterized by the user-given bound on the
                 relative error. Our solution exploits the asymptotic
                 expression of erfc and leverages the automatic code
                 generator Metalibm that provides accurate polynomial
                 approximations. A fine-grained a priori error analysis
                 provides a libm developer with the required accuracy
                 for each step of the evaluation. In critical parts, we
                 exploit double-word arithmetic to achieve
                 implementations that are fast, yet accurate up to 50
                 bits, even for large input arguments. We demonstrate
                 that for high required accuracies the automatically
                 generated code has performance comparable to that of
                 the standard libm and for lower ones our code
                 demonstrated roughly 25\% speedup.",
  acknowledgement = ack-nhfb,
  keywords =     "a priori error analysis; ARITH-26; asymptotic
                 behavior; asymptotic expression; complementary error
                 functions; Digital arithmetic; Error analysis; error
                 analysis; error function; floating-point arithmetic;
                 Generators; Libraries; Lips; mathematical library;
                 Metalibm; normal error functions; polynomial
                 approximation; polynomial approximations; program
                 compilers; semi-automated code generation;
                 semiautomatic code generator; semiautomatic
                 implementation; Standards; Tools; ubiquitous special
                 functions",
}

@Article{Zaghloul:2019:RO,
  author =       "Mofreh R. Zaghloul",
  title =        "Remark on {`Algorithm 680: Evaluation of the Complex
                 Error Function': Cause and Remedy for the Loss of
                 Accuracy Near the Real Axis}",
  journal =      j-TOMS,
  volume =       "45",
  number =       "2",
  pages =        "24:1--24:3",
  month =        apr,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3309681",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3309681",
  abstract =     "In this remark, we identify the cause of the loss of
                 accuracy in the computation of the Faddeyeva function,
                 $ w(z) $, near the real axis when using Algorithm 680.
                 We provide a simple correction to this problem that
                 allows us to restore this code as one of the important
                 reference routines for accuracy comparisons.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Abergel:2020:AFA,
  author =       "R{\'e}my Abergel and Lionel Moisan",
  title =        "{Algorithm 1006}: Fast and Accurate Evaluation of a
                 Generalized Incomplete Gamma Function",
  journal =      j-TOMS,
  volume =       "46",
  number =       "1",
  pages =        "10:1--10:24",
  month =        mar,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3365983",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 7 10:39:23 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3365983",
  abstract =     "We present a computational procedure to evaluate the
                 integral $ \int^y_x s^{p - 1} e^{- \mu s} \, d s $ for
                 $ 0 \leq x < y \leq + \infty $, $ \mu = \pm 1 $, $ p >
                 0 $, which generalizes the lower $ (x = 0) $ and upper
                 $ (y = + \infty) $ incomplete gamma functions. To allow
                 for large values of $x$, $y$, and $p$ while avoiding
                 under\slash overflow issues in the standard double
                 precision floating point arithmetic, we use an explicit
                 normalization that is much more efficient than the
                 classical ratio with the complete gamma function. The
                 generalized incomplete gamma function is estimated with
                 continued fractions, with integrations by parts, or,
                 when $ x \approx y$, with the Romberg numerical
                 integration algorithm. We show that the accuracy
                 reached by our algorithm improves a recent
                 state-of-the-art method by two orders of magnitude, and
                 it is essentially optimal considering the limitations
                 imposed by floating point arithmetic. Moreover, the
                 admissible parameter range of our algorithm $ (0 \leq
                 p, x, y \leq 10^{15})$ is much larger than competing
                 algorithms, and its robustness is assessed through
                 massive usage in an image processing application.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Adell:2020:RAE,
  author =       "Jos{\'e} A. Adell and Alberto Lekuona",
  title =        "Rational approximation to {Euler}'s constant at a
                 geometric rate of convergence",
  journal =      j-MATH-COMPUT,
  volume =       "89",
  number =       "325",
  pages =        "2553--2561",
  month =        jan,
  year =         "2020",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/mcom/3528",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Jul 14 07:56:12 MDT 2020",
  bibsource =    "http://www.ams.org/mcom/2020-89-325;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2020.bib",
  URL =          "https://www.ams.org/AMSMathViewer;
                 https://www.ams.org/journals/mcom/2020-89-325/S0025-5718-2020-03528-5;
                 https://www.ams.org/journals/mcom/2020-89-325/S0025-5718-2020-03528-5/S0025-5718-2020-03528-5.pdf;
                 https://www.ams.org/mathscinet/search/authors.html?mrauthid=340766;
                 https://www.ams.org/mathscinet/search/authors.html?mrauthid=663604",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Chin:2020:PPW,
  author =       "Wooyoung Chin",
  title =        "A Probabilistic Proof of a {Wallis}-type Formula for
                 the Gamma Function",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "127",
  number =       "1",
  pages =        "75--79",
  year =         "2020",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2020.1668708",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Dec 13 15:45:45 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "19 Dec 2019",
}

@Article{Ewart:2020:PES,
  author =       "Timoth{\'e}e Ewart and Francesco Cremonesi and Felix
                 Sch{\"u}rmann and Fabien Delalondre",
  title =        "Polynomial Evaluation on Superscalar Architecture,
                 Applied to the Elementary Function $ e^x $",
  journal =      j-TOMS,
  volume =       "46",
  number =       "3",
  pages =        "28:1--28:22",
  month =        sep,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3408893",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Sep 26 07:28:19 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3408893",
  abstract =     "The evaluation of small degree polynomials is critical
                 for the computation of elementary functions. It has
                 been extensively studied and is well documented. In
                 this article, we evaluate existing methods for
                 polynomial evaluation on superscalar architecture. In
                 addition, we have completed this work with a
                 factorization method, which is surprisingly neglected
                 in the literature. This work focuses on out-of-order
                 Intel processors, amongst others, of which
                 computational units are available. Moreover, we applied
                 our work on the elementary function $ e^x $ that
                 requires, in the current implementation, an evaluation
                 of a polynomial of degree 10 for a satisfying precision
                 and performance. Our results show that the
                 factorization scheme is the fastest in benchmarks, and
                 that latency and throughput are intrinsically dependent
                 on each other on superscalar architecture.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gil:2020:NEA,
  author =       "A. Gil and J. Segura and N. M. Temme",
  title =        "Numerical evaluation of {Airy}-type integrals arising
                 in uniform asymptotic analysis",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "371",
  number =       "??",
  pages =        "Article 112717",
  month =        jun,
  year =         "2020",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Wed May 13 06:58:32 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704272030008X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Gimbutas:2020:EAF,
  author =       "Zydrunas Gimbutas and Shidong Jiang and Li-Shi Luo",
  title =        "Evaluation of {Abramowitz} functions in the right half
                 of the complex plane",
  journal =      j-J-COMPUT-PHYS,
  volume =       "405",
  number =       "??",
  pages =        "Article 109169",
  day =          "15",
  month =        mar,
  year =         "2020",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/j.jcp.2019.109169",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Mar 9 18:28:24 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0021999119308745",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991",
  keywords =     "Abramowitz functions; Laurent series; Least squares
                 method",
  remark =       "The Abramowitz functions of order n, defined by $
                 J_n(z) = \int_0^\infty t^n \exp ( - t^2 - z / t) \, d t
                 $, for $ n \in \mathbb {Z} $.",
}

@Article{Godunov:2020:ACC,
  author =       "A. Godunov",
  title =        "Algorithms for Calculating Correctly Rounded
                 Exponential Function in Double-Precision Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "69",
  number =       "9",
  pages =        "1388--1400",
  month =        sep,
  year =         "2020",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2020.2972901",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Aug 12 14:58:16 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  abstract =     "Correct rounding provides the best approximation of
                 the exponential function by double-precision numbers.
                 To obtain the correctly rounded exponential of some
                 arguments, the exponential should be calculated with
                 high accuracy. For small arguments, even higher
                 accuracy is required. This article presents simple and
                 very fast algorithms for small arguments. Yet another
                 algorithm presented here demonstrates a good maximum
                 execution time, which may be important for critical
                 applications. This algorithm can be combined with some
                 other already existing algorithms to achieve the best
                 maximum and average execution times. All proposed
                 algorithms calculate the correctly rounded exponential
                 function for all rounding modes and use only
                 double-precision arithmetic for computation. In the
                 argument reduction step, precalculated tables are used.
                 Test implementations of these algorithms were developed
                 in C language and are portable. Full proofs are
                 presented either in this article itself or in its
                 appendices.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Harper:2020:AGH,
  author =       "J. F. Harper",
  title =        "Asymptotics of a {Gauss} hypergeometric function with
                 two large parameters: a new case",
  journal =      j-ANZIAM-J,
  volume =       "62",
  number =       "4",
  pages =        "446--452",
  month =        oct,
  year =         "2020",
  CODEN =        "AJNOA2",
  DOI =          "https://doi.org/10.1017/S1446181119000166",
  ISSN =         "1446-1811 (print), 1446-8735 (electronic)",
  ISSN-L =       "1446-1811",
  bibdate =      "Fri May 14 17:04:43 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/anziamj.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.cambridge.org/core/journals/anziam-journal/article/asymptotics-of-a-gauss-hypergeometric-function-with-two-large-parameters-a-new-case/32B40986E7DB85F500FC9024F846E527",
  acknowledgement = ack-nhfb,
  ajournal =     "ANZIAM J.",
  fjournal =     "The ANZIAM Journal. The Australian \& New Zealand
                 Industrial and Applied Mathematics Journal",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
  onlinedate =   "10 December 2019",
}

@Article{Hrycak:2020:ELP,
  author =       "Tomasz Hrycak and Sebastian Schmutzhard",
  title =        "Evaluation of {Legendre} polynomials by a three-term
                 recurrence in floating-point arithmetic",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "40",
  number =       "1",
  pages =        "587--605",
  month =        jan,
  year =         "2020",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/dry079",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  bibdate =      "Sat Feb 29 14:22:43 MST 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib",
  URL =          "http://academic.oup.com/imajna/article/40/1/587/5162990",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@Article{Jablonski:2020:IAC,
  author =       "A. Jablonski",
  title =        "Improved algorithm for calculating high accuracy
                 values of the {Chandrasekhar} function",
  journal =      j-COMP-PHYS-COMM,
  volume =       "251",
  number =       "??",
  pages =        "Article 107237",
  month =        jun,
  year =         "2020",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2020.107237",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri May 29 07:03:02 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465520300709",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Johansson:2020:CLW,
  author =       "Fredrik Johansson",
  title =        "Computing the {Lambert $W$} function in
                 arbitrary-precision complex interval arithmetic",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "83",
  number =       "1",
  pages =        "221--242",
  month =        jan,
  year =         "2020",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-019-00678-x",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Jan 22 08:40:22 MST 2020",
  bibsource =    "http://link.springer.com/journal/11075/83/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@InCollection{Johansson:2020:FSL,
  author =       "Fredrik Johansson",
  title =        "{FunGrim}: A Symbolic Library for Special Functions",
  crossref =     "Bigatti:2020:MSI",
  pages =        "315--323",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-52200-1_31",
  bibdate =      "Sat Sep 23 06:47:37 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Johnson:2020:EAHa,
  author =       "Jeff Johnson",
  title =        "Efficient, arbitrarily high precision hardware
                 logarithmic arithmetic for linear algebra",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--8",
  day =          "14",
  month =        may,
  year =         "2020",
  bibdate =      "Tue Jul 06 18:17:13 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/pdf/2004.09313.pdf",
  abstract =     "The logarithmic number system (LNS) is arguably not
                 broadly used due to exponential circuit overheads for
                 summation tables relative to arithmetic precision.
                 Methods to reduce this overhead have been proposed, yet
                 still yield designs with high chip area and power
                 requirements. Use remains limited to lower precision or
                 high multiply/add ratio cases, while much of linear
                 algebra (near 1:1 multiply/add ratio) does not
                 qualify.\par

                 We present a dual-base approximate logarithmic
                 arithmetic comparable to floating point in use, yet
                 unlike LNS it is easily fully pipelined, extendable to
                 arbitrary precision with $ O(n^2) $ overhead, and
                 energy efficient at a 1:1 multiply/add ratio.Compared
                 to float32 or float64 vector inner product with FMA,
                 our design is respectively $ 2.3 \times $ and $ 4.6
                 \times $ more energy efficient in 7 nm CMOS. It depends
                 on exp and log evaluation $ 5.4 \times $ and $ 3.2
                 \times $ more energy efficient, at $ 0.23 \times $ and
                 $ 0.37 \times $ the chip area for equivalent accuracy
                 versus standard hyperbolic CORDIC using shift-and-add
                 and approximated ODE integration in the style of Revol
                 and Yakoubsohn. This technique is a novel alternative
                 for low power, high precision hardened linear algebra
                 in computer vision, graphics and machine learning
                 applications.",
  acknowledgement = ack-nhfb,
  keywords =     "approximate arithmetic; elementary function
                 evaluation; hardware linear algebra; logarithmic
                 arithmetic",
  remark =       "Published in \cite{Johnson:2020:EAHb}.",
}

@InProceedings{Johnson:2020:EAHb,
  author =       "Jeff Johnson",
  title =        "Efficient, arbitrarily high precision hardware
                 logarithmic arithmetic for linear algebra",
  crossref =     "Cornea:2020:ISC",
  pages =        "25--32",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00013",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The logarithmic number system (LNS) is arguably not
                 broadly used due to exponential circuit overheads for
                 summation tables relative to arithmetic precision.
                 Methods to reduce this overhead have been proposed, yet
                 still yield designs with high chip area and power
                 requirements. Use remains limited to lower precision or
                 high multiply/add ratio cases, while much of linear
                 algebra (near 1:1 multiply/add ratio) does not qualify.
                 We present a dual-base approximate logarithmic
                 arithmetic comparable to floating point in use, yet
                 unlike LNS it is easily fully pipelined, extendable to
                 arbitrary precision with $ O(n^2) $ overhead, and
                 energy efficient at a 1:1 multiply/add ratio. Compared
                 to float32 or float64 vector inner product with FMA,
                 our design is respectively $ 2.3 \times $ and $ 4.6
                 \times $ more energy efficient in 7 nm CMOS. It depends
                 on exp and log evaluation 5.4 and $ 3.2 \times $ more
                 energy efficient, at $ 0.23 \times $ and $ 0.37 \times
                 $ the chip area for equivalent accuracy versus standard
                 hyperbolic CORDIC using shift-and-add and approximated
                 ODE integration in the style of Revol and Yakoubsohn.
                 This technique is a novel alternative for low power,
                 high precision hardened linear algebra in computer
                 vision, graphics and machine learning applications.",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; approximate arithmetic; Clocks; elementary
                 function evaluation; Hardware; hardware linear algebra;
                 Linear algebra; logarithmic arithmetic; Pipeline
                 processing; Read only memory; Switches",
}

@Book{Korotkov:2020:IRE,
  author =       "N. E. (Nikola{\'y}i Efimovich) Korotkov and Alexander
                 N. Korotkov",
  title =        "Integrals Related to the Error Function",
  publisher =    "CRC Press, Taylor and Francis Group",
  address =      "Boca Raton, FL, USA",
  pages =        "xx + 227",
  year =         "2020",
  ISBN =         "0-367-40820-1 (hardcover), 0-367-80923-0 (e-book),
                 1-000-03307-4 (e-book), 1-000-03308-2 (Mobipocket
                 e-book), 1-000-03309-0 (e-Pub)",
  ISBN-13 =      "978-0-367-40820-6 (hardcover), 978-0-367-80923-2
                 (e-book), 978-1-000-03307-6 (e-book), 978-1-000-03308-3
                 (Mobipocket e-book), 978-1-000-03309-0 (e-Pub)",
  LCCN =         "QA308 .K67 2020",
  bibdate =      "Fri Feb 5 17:54:22 MST 2021",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "\booktitle{Integrals Related to the Error Function}
                 presents a table of integrals related to the error
                 function, including indefinite and improper definite
                 integrals. Most of the formulas in this book have not
                 been presented in other tables of integrals or have
                 been presented only for some special cases of
                 parameters or for integration only along the real axis
                 of the complex plane. Many of the integrals presented
                 here cannot be obtained using a computer (except via an
                 approximate numerical integration). Additionally, for
                 improper integrals, this book emphasizes the necessary
                 and sufficient conditions for the validity of the
                 presented formulas, including trajectory for going to
                 infinity on the complex plane; such conditions are
                 usually not given in computer-assisted analytical
                 integration and often not presented in the previously
                 published tables of integrals. Features The first book
                 in English language to present a comprehensive
                 collection of integrals related to the error function
                 Useful for researchers whose work involves the error
                 function (e.g., via probability integrals in
                 communication theory). Additionally, it can also be
                 used by broader audience.",
  acknowledgement = ack-nhfb,
  subject =      "Integrals; Tables; Error functions",
  tableofcontents = "Indefinite integrals \\
                 Definite integrals \\
                 Appendix: Some useful formulas for obtaining other
                 integrals.",
}

@Article{Muller:2020:EFA,
  author =       "Jean-Michel Muller",
  title =        "Elementary Functions and Approximate Computing",
  journal =      j-PROC-IEEE,
  volume =       "108",
  number =       "12",
  pages =        "2136--2149",
  month =        dec,
  year =         "2020",
  CODEN =        "IEEPAD",
  DOI =          "https://doi.org/10.1109/jproc.2020.2991885",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Tue Mar 1 06:07:02 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}

@Article{Naterop:2020:HRN,
  author =       "L. Naterop and A. Signer and Y. Ulrich",
  title =        "{handyG} --- Rapid numerical evaluation of generalised
                 polylogarithms in {Fortran}",
  journal =      j-COMP-PHYS-COMM,
  volume =       "253",
  number =       "??",
  pages =        "Article 107165",
  month =        aug,
  year =         "2020",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2020.107165",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Jun 19 07:19:48 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465520300230",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@TechReport{Pornin:2020:OBG,
  author =       "Thomas Pornin",
  title =        "Optimized Binary {GCD} for Modular Inversion",
  type =         "Report",
  number =       "??",
  institution =  "International Association for Cryptologic Research",
  address =      "????",
  pages =        "16",
  day =          "23",
  month =        aug,
  year =         "2020",
  bibdate =      "Mon May 30 07:10:10 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://eprint.iacr.org/2020/972.pdf",
  abstract =     "In this short note, we describe a practical
                 optimization of the well-known extended binary GCD
                 algorithm, for the purpose of computing modular
                 inverses. The method is conceptually simple and is
                 applicable to all odd moduli (including non-prime
                 moduli). When implemented for inversion in the field of
                 integers modulo the prime $ 2^{255} - 19 $, on a recent
                 x86 CPU (Coffee Lake core), we compute the inverse in
                 6253 cycles, with a fully constant-time
                 implementation.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Raveendran:2020:NPF,
  author =       "Aneesh Raveendran and Sandra Jean and J. Mervin and D.
                 Vivian and David Selvakumar",
  editor =       "{IEEE}",
  booktitle =    "{2020 33rd International Conference on VLSI Design and
                 2020 19th International Conference on Embedded Systems
                 (VLSID), Bengaluru, India, 4--8 January 2020}",
  title =        "A Novel Parametrized Fused Division and Square-Root
                 {POSIT} Arithmetic Architecture",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "207--212",
  month =        jan,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/vlsid49098.2020.00053",
  ISBN =         "1-72815-701-3",
  ISBN-13 =      "978-1-72815-701-6",
  ISSN =         "1063-9667 (print), 2380-6923 (electronic)",
  ISSN-L =       "1063-9667",
  bibdate =      "Fri Dec 15 07:29:26 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Shibata:2020:SPV,
  author =       "Naoki Shibata and Francesco Petrogalli",
  title =        "{SLEEF}: A Portable Vectorized Library of {C} Standard
                 Mathematical Functions",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "31",
  number =       "6",
  pages =        "1316--1327",
  month =        jun,
  year =         "2020",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/TPDS.2019.2960333",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Thu Feb 20 10:08:58 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=71",
  keywords =     "elementary functions; floating-point arithmetic;
                 Parallel and vector implementations; SIMD processors",
}

@Article{Wakhare:2020:TCJ,
  author =       "Tanay Wakhare and Christophe Vignat",
  title =        "{Taylor} coefficients of the {Jacobi} $ \theta_3 (q) $
                 function",
  journal =      j-J-NUMBER-THEORY,
  volume =       "216",
  number =       "??",
  pages =        "280--306",
  month =        nov,
  year =         "2020",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2020.03.002",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Sat Aug 8 09:41:52 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X20300858",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Xiao:2020:PAH,
  author =       "Feibao Xiao and Feng Liang and Bin Wu and Junzhe Liang
                 and Shuting Cheng and Guohe Zhang",
  title =        "Posit Arithmetic Hardware Implementations with The
                 Minimum Cost Divider and Square Root",
  journal =      j-ELECTRONICS,
  volume =       "9",
  number =       "10",
  pages =        "1622:1--1622:16",
  month =        oct,
  year =         "2020",
  DOI =          "https://doi.org/10.3390/electronics9101622",
  ISSN =         "2079-9292",
  ISSN-L =       "2079-9292",
  bibdate =      "Fri Dec 15 07:25:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics",
  journal-URL =  "https://www.mdpi.com/journal/electronics",
}

@Article{Akram:2021:XFA,
  author =       "Riad Akram and Shantanu Mandal and Abdullah Muzahid",
  title =        "{XMeter}: Finding Approximable Functions and
                 Predicting Their Accuracy",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "70",
  number =       "7",
  pages =        "1081--1093",
  month =        jul,
  year =         "2021",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2020.3005083",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jun 10 15:51:57 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Misc{Bailey:2021:PMN,
  author =       "David H. Bailey",
  title =        "\pkg{MPFUN2020}: A new thread-safe arbitrary precision
                 package,",
  howpublished = "Web document",
  pages =        "54",
  day =          "18",
  month =        may,
  year =         "2021",
  bibdate =      "Mon Dec 05 07:32:16 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.davidhbailey.com/dhbpapers/mpfun2020.pdf",
  abstract =     "Numerous research studies have arisen, particularly in
                 mathematical physics and experimental mathematics, that
                 require extremely high numeric precision. Such
                 precision greatly magnifies computer run times, so
                 software packages to support high-precision computing
                 must be designed for thread-based parallel
                 processing.

                 This paper describes a new arbitrary precision software
                 package (``MPFUN2020'') that features several
                 significant improvements over an earlier package. It
                 comes in two versions: a self-contained all-Fortran
                 version, and a version based on the MPFR package, which
                 is even faster. Both versions feature: (a) a completely
                 thread-safe design, so user codes can be converted for
                 parallel execution at the application level; (b) a
                 full-featured high-level Fortran interface, so that
                 most applications can be converted to multiprecision
                 with relatively minor changes to source code; (c) full
                 support for both real and complex datatypes; (d) a wide
                 variety of transcendental functions and special
                 functions; (e) run-time checking and other facilities
                 to overcome problems with converting double precision
                 constants and data; (f) a medium precision datatype,
                 which improves performance and reduces memory cost on
                 large variable precision applications; and (g)
                 interoperability --- with a simple restriction,
                 application codes written for one version can be run
                 with the other without change.",
  acknowledgement = ack-nhfb,
}

@Article{Borges:2021:AIA,
  author =       "Carlos F. Borges",
  title =        "{Algorithm 1014}: an Improved Algorithm for {\tt
                 hypot(x,y)}",
  journal =      j-TOMS,
  volume =       "47",
  number =       "1",
  pages =        "9:1--9:12",
  month =        jan,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3428446",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jan 7 10:31:04 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/julia.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3428446",
  abstract =     "We develop fast and accurate algorithms for evaluating
                 $ \sqrt {x^2 + y^2} $ for two floating-point numbers
                 $x$ and $y$. Library functions that perform this
                 computation are generally named {\tt hypot(x,y)}. We
                 compare five approaches that we will develop in this
                 article to the current resident library function that
                 is delivered with Julia 1.1 and to the code that has
                 been distributed with the C math library for decades.
                 We will investigate the accuracy of our algorithms by
                 simulation.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Borges:2021:CRN,
  author =       "Carlos F. Borges",
  title =        "A Correctly Rounded {Newton} Step for the Reciprocal
                 Square Root",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--8",
  day =          "28",
  month =        dec,
  year =         "2021",
  bibdate =      "Fri Sep 22 16:08:53 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/2112.14321",
  abstract =     "The reciprocal square root is an important computation
                 for which many sophisticated algorithms exist (see for
                 example \cite{Moroz,863046,863031} and the references
                 therein). A common theme is the use of Newton's method
                 to refine the estimates. In this paper we develop a
                 correctly rounded Newton step that can be used to
                 improve the accuracy of a naive calculation (using
                 methods similar to those developed in \cite{borges})
                 The approach relies on the use of the fused
                 multiply-add (FMA) which is widely available in
                 hardware on a variety of modern computer architectures.
                 We then introduce the notion of {\em weak rounding} and
                 prove that our proposed algorithm meets this standard.
                 We then show how to leverage the exact Newton step to
                 get a Halley's method compensation which requires one
                 additional FMA and one additional multiplication. This
                 method appears to give correctly rounded results
                 experimentally and we show that it can be combined with
                 a square root free method for estimating the reciprocal
                 square root to get a method that is both very fast (in
                 computing environments with a slow square root) and,
                 experimentally, highly accurate.",
  acknowledgement = ack-nhfb,
}

@Article{Borges:2021:FCA,
  author =       "Carlos F. Borges",
  title =        "Fast compensated algorithms for the reciprocal square
                 root, the reciprocal hypotenuse, and {Givens}
                 rotations",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--11",
  day =          "23",
  month =        feb,
  year =         "2021",
  bibdate =      "Fri Sep 22 16:05:47 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/2103.08694",
  abstract =     "The reciprocal square root is an important computation
                 for which many very sophisticated algorithms exist (see
                 for example \cite{863046,863031} and the references
                 therein). In this paper we develop a simple
                 differential compensation (much like those developed in
                 \cite{borges}) that can be used to improve the accuracy
                 of a naive calculation. The approach relies on the use
                 of the fused multiply-add (FMA) which is widely
                 available in hardware on a variety of modern computer
                 architectures. We then demonstrate how to combine this
                 approach with a somewhat inaccurate but fast square
                 root free method for estimating the reciprocal square
                 root to get a method that is both fast (in computing
                 environments with a slow square root) and,
                 experimentally, highly accurate. Finally, we show how
                 this same approach can be extended to the reciprocal
                 hypotenuse calculation and, most importantly, to the
                 construction of Givens rotations.",
  acknowledgement = ack-nhfb,
}

@Article{Iacono:2021:BEF,
  author =       "Roberto Iacono",
  title =        "Bounding the Error Function",
  journal =      j-COMPUT-SCI-ENG,
  volume =       "23",
  number =       "4",
  pages =        "65--68",
  year =         "2021",
  CODEN =        "CSENFA",
  DOI =          "https://doi.org/10.1109/MCSE.2021.3083778",
  ISSN =         "1521-9615 (print), 1558-366X (electronic)",
  ISSN-L =       "1521-9615",
  bibdate =      "Thu Jul 29 07:00:57 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computscieng.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Prompted by previous work published in this magazine,
                 in this article we focus on the derivation of global
                 analytical bounds for the error function of a real
                 argument. Using an integral representation of this
                 function, we obtain two simple and accurate lower
                 bounds, which complement a well-known upper bound given
                 long ago by P{\'o}lya.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing in Science and Engineering",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}

@Article{Johansson:2021:APC,
  author =       "Fredrik Johansson",
  title =        "Arbitrary-Precision Computation of the Gamma
                 Function",
  journal =      "arXiv.org",
  pages =        "1--51",
  day =          "17",
  month =        sep,
  year =         "2021",
  DOI =          "https://doi.org/10.48550/arXiv.2109.0839",
  bibdate =      "Sun Dec 04 11:01:23 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://arxiv.org/abs/2109.08392",
  abstract =     "We discuss the best methods available for computing
                 the gamma function $ \Gamma (z) $ in
                 arbitrary-precision arithmetic with rigorous error
                 bounds. We address different cases: rational,
                 algebraic, real or complex arguments; large or small
                 arguments; low or high precision; with or without
                 precomputation. The methods also cover the log-gamma
                 function $ \log \Gamma (z) $, the digamma function $
                 \psi (z) $, and derivatives $ \Gamma^{(n)}(z) $ and $
                 \psi^{(n)}(z) $. Besides attempting to summarize the
                 existing state of the art, we present some new
                 formulas, estimates, bounds and algorithmic
                 improvements and discuss implementation results.",
  acknowledgement = ack-nhfb,
}

@Article{Kang:2021:NEE,
  author =       "Hongchao Kang and Hong Wang",
  title =        "Numerical evaluation and error analysis of many
                 different oscillatory {Bessel} transforms via confluent
                 hypergeometric function",
  journal =      j-APPL-NUM-MATH,
  volume =       "160",
  number =       "??",
  pages =        "23--41",
  month =        feb,
  year =         "2021",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Tue Dec 29 07:52:55 MST 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0168927420302932",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
}

@Article{Langdon:2021:GID,
  author =       "William B. Langdon and Oliver Krauss",
  title =        "Genetic Improvement of Data for Maths Functions",
  journal =      j-TELO,
  volume =       "1",
  number =       "2",
  pages =        "7:1--7:30",
  month =        jun,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3461016",
  ISSN =         "2688-299X (print), 2688-3007 (electronic)",
  ISSN-L =       "2688-299X",
  bibdate =      "Sat Aug 21 15:11:10 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/telo.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3461016",
  abstract =     "We use continuous optimisation and manual code changes
                 to evolve up to 1024 Newton--Raphson numerical values
                 embedded in an open source GNU C library glibc square
                 root sqrt to implement a double precision cube root
                 routine cbrt, binary logarithm log2 and reciprocal
                 square root function for C in seconds. The GI inverted
                 square root $ x{-1 / 2} $ is far more accurate than
                 Quake's InvSqrt, Quare root. GI shows potential for
                 automatically creating mobile or low resource mote
                 smart dust bespoke custom mathematical libraries with
                 new functionality.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Evolutionary Learning and
                 Optimization",
  journal-URL =  "https://dl.acm.org/loi/telo",
}

@Article{Lipovetsky:2021:BRI,
  author =       "Stan Lipovetsky",
  title =        "Book Review: {{\booktitle{Integrals Related to the
                 Error Function}}, by Nikolai E. Korotkov and Alexander
                 N. Korotkov. Boca Raton, FL: Chapman and Hall\slash CRC
                 Press, Taylor \& Francis Group, 2020, 228 pp., \$140.00
                 (hardback), \$46.36 (eBook), ISBN: 978-0-367-40820-6
                 (hardback)}",
  journal =      j-TECHNOMETRICS,
  volume =       "62",
  number =       "4",
  pages =        "560--560",
  year =         "2021",
  CODEN =        "TCMTA2",
  DOI =          "https://doi.org/10.1080/00401706.2020.1825632",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  bibdate =      "Fri Feb 5 17:42:52 MST 2021",
  bibsource =    "http://www.tandf.co.uk/journals/titles/00401706.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/technometrics2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
  journal-URL =  "http://www.tandfonline.com/loi/utch20",
  onlinedate =   "23 Oct 2020",
}

@TechReport{MPFR:2021:MLA,
  author =       "{The MPFR Team}",
  title =        "The {MPFR} Library: Algorithms and Proofs",
  type =         "Report",
  institution =  "????",
  address =      "????",
  pages =        "69",
  day =          "5",
  month =        nov,
  year =         "2021",
  bibdate =      "Tue Mar 14 13:13:13 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.mpfr.org/algorithms.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Snyder:2021:CRA,
  author =       "W. Van Snyder",
  title =        "Corrigendum: {Remark on Algorithm 723: Fresnel
                 Integrals}",
  journal =      j-TOMS,
  volume =       "47",
  number =       "4",
  pages =        "37:1--37:1",
  month =        dec,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3452336",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 29 06:58:41 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Snyder:1993:AFI}.",
  URL =          "https://dl.acm.org/doi/10.1145/3452336",
  abstract =     "There are mistakes and typographical errors in Remark
                 on Algorithm 723: Fresnel Integrals, which appeared in
                 ACM Transactions on Mathematical Software 22, 4
                 (December 1996). This remark corrects those errors. The
                 software provided to Collected Algorithms of the ACM
                 was correct.",
  acknowledgement = ack-nhfb,
  articleno =    "37",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Walczyk:2021:IAF,
  author =       "Cezary J. Walczyk and Leonid V. Moroz and Jan L.
                 Cie{\'s}li{\'n}ski",
  title =        "Improving the Accuracy of the Fast Inverse Square Root
                 by Modifying {Newton--Raphson} Corrections",
  journal =      j-ENTROPY,
  volume =       "23",
  number =       "1",
  pages =        "86:1--86:20",
  month =        jan,
  year =         "2021",
  CODEN =        "ENTRFG",
  DOI =          "https://doi.org/10.3390/e23010086",
  ISSN =         "1099-4300",
  ISSN-L =       "1099-4300",
  bibdate =      "Wed Dec 20 07:52:39 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Entropy",
  journal-URL =  "https://www.mdpi.com/journal/entropy/",
}

@Misc{Anonymous:2022:DLM,
  author =       "Anonymous",
  title =        "Digital Library of Mathematical Functions: Date:
                 2010",
  howpublished = "NIST Web site",
  day =          "14",
  month =        mar,
  year =         "2022",
  bibdate =      "Wed Oct 25 18:20:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://dlmf.nist.gov/;
                 https://www.nist.gov/mathematics-statistics/digital-library-mathematical-functions",
  abstract =     "In 2010, NIST released the Digital Library of
                 Mathematical Functions (DLMF), an online successor to
                 the classic Abramowitz and Stegun \booktitle{Handbook
                 of Mathematical
                 Functions}. [\cite{Abramowitz:1964:HMF}]",
  acknowledgement = ack-nhfb,
  remark =       "From the site: ``By the late 1990s it [the 1964
                 Handbook] was still the most widely distributed and
                 cited publication of all time, regularly seeing more
                 than 2000 citations per year.''",
}

@InProceedings{Borges:2022:HLA,
  author =       "Carlos F. Borges and Claude-Pierre Jeannerod and
                 Jean-Michel Muller",
  title =        "High-level algorithms for correctly-rounded reciprocal
                 square roots",
  crossref =     "IEEE:2022:ISC",
  pages =        "18--25",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00013",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}

@InProceedings{Bruguera:2022:LLH,
  author =       "Javier D. Bruguera",
  title =        "Low-Latency and High-Bandwidth Pipelined Radix-64
                 Division and Square Root Unit",
  crossref =     "IEEE:2022:ISC",
  pages =        "10--17",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00012",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
}

@Article{Causley:2022:GFI,
  author =       "Matthew F. Causley",
  title =        "The gamma function via interpolation",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "90",
  number =       "2",
  pages =        "687--707",
  month =        jun,
  year =         "2022",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-021-01204-8",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Sun May 8 06:36:19 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-021-01204-8",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Cojean:2022:GML,
  author =       "Terry Cojean and Yu-Hsiang Mike Tsai and Hartwig
                 Anzt",
  title =        "{Ginkgo} --- a math library designed for platform
                 portability",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "111",
  number =       "??",
  pages =        "??--??",
  month =        jul,
  year =         "2022",
  CODEN =        "PACOEJ",
  DOI =          "https://doi.org/10.1016/j.parco.2022.102902",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  bibdate =      "Mon May 9 07:06:37 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167819122000096",
  abstract =     "In an era of increasing computer system diversity, the
                 portability of software from one system to another
                 plays a central role. Software portability is important
                 for the software developers as many software projects
                 have a lifetime longer than a specific system, e.g., a
                 supercomputer, and it is important for the domain
                 scientists that realize their scientific application in
                 a software framework and want to be able to run on one
                 or another system. On a high level, there exist two
                 approaches for realizing platform portability: (1)
                 implementing software using a portability layer
                 leveraging any technique which always generates
                 specific kernels from another language or through an
                 interface for running on different architectures; and
                 (2) providing backends for different hardware
                 architectures, with the backends typically differing in
                 how and in which programming language functionality is
                 realized due to using the language of choice for each
                 hardware (e.g., CUDA kernels for NVIDIA GPUs, SYCL
                 (DPC++) kernels to targeting Intel GPUs and other
                 supported hardware, \ldots). In practice, these two
                 approaches can be combined in applications to leverage
                 their respective strengths. In this paper, we present
                 how we realize portability across different hardware
                 architectures for the Ginkgo library by following the
                 second strategy and the goal to not only port to new
                 hardware architectures but also achieve good
                 performance. We present the Ginkgo library design,
                 separating algorithms from hardware-specific kernels
                 forming the distinct hardware executors, and report our
                 experience when adding execution backends for NVIDIA,
                 AMD, and Intel GPUs. We also present the performance we
                 achieve with this approach for distinct hardware
                 backends.",
  acknowledgement = ack-nhfb,
  articleno =    "102902",
  fjournal =     "Parallel Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191",
}

@InProceedings{Gao:2022:TFI,
  author =       "Zhanyuan Gao and Laiping Zhao and Haonan Chen",
  editor =       "{IEEE}",
  booktitle =    "{2022 IEEE\slash ACIS 22nd International Conference on
                 Computer and Information Science (ICIS)}",
  title =        "A Trigonometric Function Instruction Set Extension
                 Method Based on {RISC-V}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "119--126",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ICIS54925.2022.9882453",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hao:2022:DVP,
  author =       "Jiangwei Hao and Jinchen Xu and YuanYuan Xia",
  title =        "Design of variable precision transcendental function
                 automatic generator",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "78",
  number =       "2",
  pages =        "2196--2218",
  month =        feb,
  year =         "2022",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-021-03937-8",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Mon Feb 28 16:44:34 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
  URL =          "https://link.springer.com/article/10.1007/s11227-021-03937-8",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Supercomputing",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@Article{Howard:2022:AAA,
  author =       "Roy M. Howard",
  title =        "Arbitrarily Accurate Analytical Approximations for the
                 Error Function",
  journal =      "Mathematical and Computational Applications",
  volume =       "27",
  number =       "1",
  pages =        "14",
  month =        feb,
  year =         "2022",
  DOI =          "https://doi.org/10.3390/mca27010014",
  ISSN =         "2297-8747",
  bibdate =      "Sat Feb 17 12:10:52 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Lim:2022:OPA,
  author =       "Jay P. Lim and Santosh Nagarakatte",
  title =        "One polynomial approximation to produce correctly
                 rounded results of an elementary function for multiple
                 representations and rounding modes",
  journal =      j-PACMPL,
  volume =       "6",
  number =       "POPL",
  pages =        "3:1--3:28",
  month =        jan,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3498664",
  ISSN =         "2475-1421 (electronic)",
  ISSN-L =       "2475-1421",
  bibdate =      "Thu May 26 06:32:48 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3498664",
  abstract =     "Mainstream math libraries for floating point (FP) do
                 not produce correctly rounded results for all inputs.
                 In contrast, CR-LIBM and RLIBM provide correctly
                 rounded implementations for a specific FP
                 representation with one rounding mode. Using such
                 libraries for a representation with a new rounding mode
                 or with different precision will result in wrong
                 results due to double rounding. This paper proposes a
                 novel method to generate a single polynomial
                 approximation that produces correctly rounded results
                 for all inputs for multiple rounding modes and multiple
                 precision configurations. To generate a correctly
                 rounded library for n-bits, our key idea is to generate
                 a polynomial approximation for a representation with
                 n+2-bits using the round-to-odd mode. We prove that the
                 resulting polynomial approximation will produce
                 correctly rounded results for all five rounding modes
                 in the standard and for multiple representations with
                 k-bits such that $ |E| + 1 < k \leq n $, where $ |E| $
                 is the number of exponent bits in the representation.
                 Similar to our prior work in the RLIBM project, we
                 approximate the correctly rounded result when we
                 generate the library with n+2-bits using the
                 round-to-odd mode. We also generate polynomial
                 approximations by structuring it as a linear
                 programming problem but propose enhancements to
                 polynomial generation to handle the round-to-odd mode.
                 Our prototype is the first 32-bit float library that
                 produces correctly rounded results with all rounding
                 modes in the IEEE standard for all inputs with a single
                 polynomial approximation. It also produces correctly
                 rounded results for any FP configuration ranging from
                 10-bits to 32-bits while also being faster than
                 mainstream libraries.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "Proceedings of the ACM on Programming Languages
                 (PACMPL)",
  journal-URL =  "https://dl.acm.org/loi/pacmpl",
  keywords =     "correct rounding; elementary functions",
}

@InProceedings{Oh:2022:EPA,
  author =       "Hyun Woo Oh and Won Sik Jeong and Seung Eun Lee",
  editor =       "{IEEE}",
  booktitle =    "{2022 19th International SoC Design Conference
                 (ISOCC)}",
  title =        "Evaluation of Posit Arithmetic on Machine Learning
                 based on Approximate Exponential Functions",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "358--359",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ISOCC56007.2022.10031524",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Takekawa:2022:FPC,
  author =       "Takashi Takekawa",
  title =        "Fast parallel calculation of modified {Bessel}
                 function of the second kind and its derivatives",
  journal =      j-SOFTWAREX,
  volume =       "17",
  number =       "??",
  pages =        "??--??",
  month =        jan,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.softx.2021.100923",
  ISSN =         "2352-7110",
  ISSN-L =       "2352-7110",
  bibdate =      "Mon Feb 28 10:41:25 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/softwarex.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S2352711021001655",
  acknowledgement = ack-nhfb,
  articleno =    "100923",
  fjournal =     "SoftwareX",
  journal-URL =  "https://www.sciencedirect.com/journal/softwarex/issues",
}

@Article{Ananthanarayan:2023:EAD,
  author =       "B. Ananthanarayan and Souvik Bera and S. Friot and O.
                 Marichev and Tanay Pathak",
  title =        "On the evaluation of the {Appell} {$ F_2 $} double
                 hypergeometric function",
  journal =      j-COMP-PHYS-COMM,
  volume =       "284",
  number =       "??",
  pages =        "Article 108589",
  month =        mar,
  year =         "2023",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2022.108589",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 06:01:54 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465522003083",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Blanchard:2023:NMD,
  author =       "Jeffrey D. Blanchard and Marc Chamberland",
  title =        "{Newton}'s Method Without Division",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "130",
  number =       "7",
  pages =        "606--617",
  year =         "2023",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2022.2093573",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Fri Aug 25 08:24:37 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "04 Aug 2023",
}

@Article{Gil:2023:EGF,
  author =       "Amparo Gil and Andrzej Odrzywo{\l}ek and Javier Segura
                 and Nico M. Temme",
  title =        "Evaluation of the generalized {Fermi--Dirac} integral
                 and its derivatives for moderate\slash large values of
                 the parameters",
  journal =      j-COMP-PHYS-COMM,
  volume =       "283",
  number =       "??",
  pages =        "Article 108563",
  month =        feb,
  year =         "2023",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2022.108563",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Dec 5 09:16:39 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S001046552200282X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Pradhan:2023:ETB,
  author =       "Chetana Pradhan and Martin Letras and J{\"u}rgen
                 Teich",
  title =        "Efficient Table-based Function Approximation on
                 {FPGAs} Using Interval Splitting and {BRAM}
                 Instantiation",
  journal =      j-TECS,
  volume =       "22",
  number =       "4",
  pages =        "73:1--73:??",
  month =        jul,
  year =         "2023",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3580737",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Thu Aug 10 07:21:24 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3580737",
  abstract =     "This article proposes a novel approach for the
                 generation of memory-efficient table-based function
                 approximation circuits for edge devices in general and
                 FPGAs in particular. Given a function $ f(x) $ to be
                 approximated in a given interval $ [x_0, x_0 + a) $ and
                 a maximum approximation error $ E_a $, the goal is to
                 determine a function table implementation with a
                 minimized memory footprint, i.e., number of entries
                 that need to be stored. Rather than state-of-the-art
                 work performing an equidistant sampling of the given
                 interval by so-called breakpoints and using linear
                 interpolation between two adjacent breakpoints to
                 determine $ f(x) $ at the maximum error bound, we
                 propose and compare three algorithms for splitting the
                 given interval into sub-intervals to reduce the
                 required memory footprint drastically based on the
                 observation that in sub-intervals of low gradient, a
                 coarser sampling grid may be assumed while guaranteeing
                 the maximum interpolation error bound $ E_a $.
                 Experiments on elementary mathematical functions show
                 that a large fraction in memory footprint may be saved.
                 Second, a hardware architecture implementing the
                 sub-interval selection, breakpoint lookup, and
                 interpolation at a latency of just 9 clock cycles is
                 introduced. Third, for each generated circuit design,
                 BRAMs are automatically instantiated rather than
                 synthesizing the reduced footprint function table using
                 LUT primitives, providing an additional degree of
                 resource efficiency. The approach presented here for
                 FPGAs can equally be applied to other circuit
                 technologies for fast and, at the same time,
                 memory-optimized function approximation at the edge.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Embed. Comput. Syst.",
  articleno =    "73",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "https://dl.acm.org/loi/tecs",
}

@Article{Slevinsky:2023:RAE,
  author =       "Richard M. Slevinsky and Hassan Safouhi",
  title =        "A recursive algorithm for an efficient and accurate
                 computation of incomplete {Bessel} functions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "92",
  number =       "1",
  pages =        "973--983",
  month =        jan,
  year =         "2023",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-022-01438-0",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Jan 30 12:22:09 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-022-01438-0",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Harris:2024:UDS,
  author =       "David Harris and James Stine and Milo Ercegovac and
                 Alberto Nannarelli and Katherine Parry and Cedar
                 Turek",
  title =        "Unified Digit Selection for Radix-4 Recurrence
                 Division and Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "73",
  number =       "1",
  pages =        "292--300",
  month =        jan,
  year =         "2024",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2023.3305760",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Dec 27 15:37:27 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "division; square root; SRT; minimally-redundant radix-4; RISC-V",
}

@Article{Zaghloul:2024:CFI,
  author =       "Mofreh R. Zaghloul and Leen Alrawas",
  title =        "Calculation of {Fresnel} integrals of real and complex
                 arguments up to 28 significant digits",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "95",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2024",
  DOI =          "https://doi.org/10.1007/s11075-023-01654-2",
  bibdate =      "Tue Feb 20 15:46:52 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  accepted =     "23 August 2023",
  acknowledgement = ack-nhfb,
  keywords =     "complex cosine integral C(z); complex sine integral
                 S(z); Fresnel functions; real cosine integral C(x);
                 real sine integral S(x)",
  received =     "5 July 2023",
  remark =       "[20-Feb-2024] Available at journal Web site, but not
                 yet assigned to a journal volume.",
}

@Article{Zaghloul:2024:EMP,
  author =       "Mofreh R. Zaghloul",
  title =        "Efficient multiple-precision computation of the scaled
                 complementary error function and the {Dawson}
                 integral",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "95",
  number =       "3",
  pages =        "1291--1308",
  month =        mar,
  year =         "2024",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-023-01608-8",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Feb 14 08:54:32 MST 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-023-01608-8",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Dawson(x); erf(x); erfc(x)",
}

@Article{Zaghloul:2024:ENA,
  author =       "Mofreh R. Zaghloul",
  title =        "Efficient numerical algorithms for multi-precision and
                 multi-accuracy calculation of the error functions and
                 {Dawson} integral with complex arguments",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "95",
  number =       "??",
  pages =        "1--19",
  month =        "????",
  year =         "2024",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-023-01727-2",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Tue Feb 20 15:50:26 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Dawson(x); erf(x); erfc(x)",
  remark =       "[20-Feb-2024] Available at journal Web site, but not
                 yet assigned to a journal volume.",
}

%%% ====================================================================
%%% Cross-referenced entries must come last:
@Book{Knuth:1998:SA,
  author =       "Donald E. Knuth",
  title =        "Seminumerical Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Third",
  pages =        "xiii + 762",
  year =         "1998",
  ISBN =         "0-201-89684-2",
  ISBN-13 =      "978-0-201-89684-8",
  LCCN =         "QA76.6 .K64 1997",
  bibdate =      "Fri Jul 11 15:41:22 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/css.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
  price =        "US\$52.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
  tableofcontents = "3: Random Numbers / 1 \\
                 3.1. Introduction / 1 \\
                 3.2. Generating Uniform Random Numbers / 10 \\
                 3.2.1. The Linear Congruential Method / 10 \\
                 3.2 1.1. Choice of modulus / 12 \\
                 3.2.1.2 Choice of multiplier / 16 \\
                 3.2.1.3. Potency / 23 \\
                 3.2.2. Other Methods / 26 \\
                 3.3. Statistical Tests / 41 \\
                 3.3.1. General Test Procedures for Studying Random Data
                 / 41 \\
                 3.3.2. Empirical Tests / 61 \\
                 *3.3.3. Theoretical Tests / 80 \\
                 3.3.4. The Spectral Test / 93 \\
                 3.4. Other Types of Random Quantities / 119 \\
                 3.4 1. Numerical Distributions / 119 \\
                 3.4.2. Random Sampling and Shuffling / 142 \\
                 *3.5. What Is a Random Sequence? / 149 \\
                 3.6. Summary / 184 \\
                 4: Arithmetic / 194 \\
                 4.1. Positional Number Systems / 195 \\
                 4.2. Floating Point Arithmetic / 214 \\
                 4.2.1. Single-Precision Calculations / 214 \\
                 4.2 2. Accuracy of Floating Point Arithmetic / 229 \\
                 *4.2.3. Double-Precision Calculations / 246 \\
                 4.2.4. Distribution of Floating Point Numbers / 253 \\
                 4.3 Multiple Precision Arithmetic / 265 \\
                 4.3.1. The Classical Algorithms / 265 \\
                 *4.3.2. Modular Arithmetic / 284 \\
                 *4.3.3. How Fast Can We Multiply? / 294 \\
                 4.4. Radix Conversion / 319 \\
                 4.5. Rational Arithmetic / 330 \\
                 4.5.1. Fractions / 330 \\
                 4.5.2. The Greatest Common Divisor / 333 \\
                 *4.5.3. Analysis of Euclid's Algorithm / 356 \\
                 4.5.4. Factoring into Primes / 379 \\
                 4.6. Polynomial Arithmetic / 418 \\
                 4.6.1. Division of Polynomials / 420 \\
                 *4.6.2. Factorization of Polynomials / 439 \\
                 4.6.3. Evaluation of Powers / 461 \\
                 4.6.4. Evaluation of Polynomials / 485 \\
                 *4.7. Manipulation of Power Series / 525 \\
                 Answers to Exercises / 538 \\
                 Appendix A: Tables of Numerical Quantities / 726 \\
                 1. Fundamental Constants (decimal) / 726 \\
                 2; Fundamental Constants ( octal) / 727 \\
                 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
                 Numbers / 728 \\
                 Appendix B: Index to Notations / 730 \\
                 Index and Glossary / 735",
}

@Book{Borwein:2007:RHR,
  editor =       "Peter Borwein and Stephen Choi and Brendan Rooney and
                 Andrea Weirathmueller and others",
  title =        "The {Riemann Hypothesis}: a resource for the
                 afficionado and virtuoso alike",
  volume =       "27",
  publisher =    "Springer Science+Business Media, LLC",
  address =      "New York, NY, USA",
  pages =        "xiv + 533",
  year =         "2007",
  DOI =          "https://doi.org/10.1007/978-0-387-72126-2",
  ISBN =         "0-387-72125-8 (hardcover), 0-387-72126-6 (e-book)",
  ISBN-13 =      "978-0-387-72125-5 (hardcover), 978-0-387-72126-2
                 (e-book)",
  LCCN =         "QA246 .R53 2008",
  bibdate =      "Thu Sep 1 07:07:49 MDT 2022",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "CMS books in mathematics",
  URL =          "http://libanswers.liverpool.ac.uk/faq/182315",
  abstract =     "This book is an introduction to the theory surrounding
                 the Riemann Hypothesis. Part I serves as a compendium
                 of known results and as a primer for the material
                 presented in the 20 original papers contained in Part
                 II. The original papers place the material into
                 historical context and illustrate the motivations for
                 research on and around the Riemann Hypothesis. Several
                 of these papers focus on computation of the zeta
                 function, while others give proofs of the Prime Number
                 Theorem, since the Prime Number Theorem is so closely
                 connected to the Riemann Hypothesis. The text is
                 suitable for a graduate course or seminar or simply as
                 a reference for anyone interested in this extraordinary
                 conjecture.",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "To the Riemann Hypothesis \\
                 Why This Book \\
                 Analytic Preliminaries \\
                 Algorithms for Calculating ?(s) \\
                 Empirical Evidence \\
                 Equivalent Statements \\
                 Extensions of the Riemann Hypothesis \\
                 Assuming the Riemann Hypothesis and Its Extensions
                 \ldots{} \\
                 Failed Attempts at Proof \\
                 Formulas \\
                 Timeline \\
                 Original Papers \\
                 Expert Witnesses \\
                 The Experts Speak for Themselves",
  subject =      "Mathematics; History; Number theory;
                 Math{\'e}matiques; Histoire; Th{\'e}orie des nombres;
                 Mathematics.; Number theory.",
  tableofcontents = "Part 1: Introduction to the Riemann hypothesis \\
                 1: Why this book \\
                 1.1: The Holy Grail \\
                 1.2: Riemann's zeta and Liouville's lambda \\
                 1.3: The prime number theorem \\
                 2: Analytic preliminaries \\
                 2.1: The Riemann zeta function \\
                 2.2: Zero-free region \\
                 2.3: Counting the zeros of [cedilla](s) \\
                 2.4: Hardy's theorem \\
                 3: Algorithms for calculating [cedilla](s) \\
                 3.1: Euler--MacLaurin summation \\
                 3.2: Backlund \\
                 3.3: Hardy's function \\
                 3.4: The Riemann--Siegel formula \\
                 3.5: Gram's law \\
                 3.6: Turing \\
                 3.7: The Odlyzko--Sch{\"o}nhage algorithm \\
                 3.8: A simple algorithm for the zeta function \\
                 3.9: Further reading \\
                 4: Empirical evidence \\
                 4.1: Verification in an interval \\
                 4.2: A brief history of computational evidence \\
                 4.3: The Riemann hypothesis and random matrices \\
                 4.4: The Skewes number5: Equivalent statements \\
                 5.1: Number-theoretic equivalences \\
                 5.2: Analytic equivalences \\
                 5.3: Other equivalences \\
                 6: Extensions of the Riemann hypothesis \\
                 6.1: The Riemann hypothesis \\
                 6.2: The generalized Riemann hypothesis \\
                 6.3: The extended Riemann hypothesis \\
                 6.4: An equivalent extended Riemann hypothesis \\
                 6.5: Another extended Riemann hypothesis \\
                 6.6: The Grand Riemann hypothesis \\
                 7: Assuming the Riemann hypothesis and its extensions
                 \\
                 7.1: Another proof of the prime number theorem \\
                 7.2: Goldbach's conjecture \\
                 7.3: More Goldbach \\
                 7.4: Primes in a given interval \\
                 7.5: The least prime in arithmetic progressions \\
                 7.6: Primality testing \\
                 7.7: Artin's primitive root conjecture \\
                 7.8: Bounds on Dirichlet $L$-series \\
                 7.9: The Lindel{\"o}f hypothesis \\
                 7.10: Titchmarsh's [delta](T) function \\
                 7.11: Mean values of [cedilla](s)8: Failed attempts at
                 proof \\
                 8.1: Stieltjes and Mertens' conjecture \\
                 8.2: Hans Rademacher and false hopes \\
                 8.3: Tur{\'a}n's condition \\
                 8.4: Louis de Branges's approach \\
                 8.5: No really good idea \\
                 9: Formulas \\
                 10: Timeline \\
                 pt. 2: Original papers \\
                 11: Expert witnesses \\
                 11. 1: E. Bombieri (2000--2001) \\
                 11.2: P. Sarnak (2004) \\
                 11.3: J.B. Conrey (2003) \\
                 11.4: A. Ivi{\'c} (2003) \\
                 12: The experts speak for themselves \\
                 12.1: P.L. Chebyshev (1852) \\
                 12.2: B. Riemann (1859) \\
                 12.3: J. Hadamard (1896) \\
                 12.4: C. de la Vall{\'e}e Poussin (1899) \\
                 12.5: G.H. Hardy (1914) \\
                 12.6: G.H. Hardy (1915) \\
                 12.7: G.H. Hardy and J.E. Littlewood (1915) \\
                 12.8: A. Weil (1941) \\
                 12.9: P. Tur{\'a}n (1948) \\
                 12.10: A. Selberg (1949) \\
                 12.11: P. Erdo$\cdot$s (1949) \\
                 12.12: S. Skewes (1955) \\
                 12.13: C.B. Haselgrove (1958) \\
                 12.14: H. Montgomery (1973) \\
                 12.15: D.J. Newman (1980) \\
                 12.16: J. Korevaar (1982) \\
                 12.17: H. Daboussi (1984) \\
                 12.18: A. Hildebrand (1986) \\
                 12.19: D. Goldston and H. Montgomery (1987) \\
                 12.20: M. Agrawal, N. Kayal, and N. Saxena (2004) \\
                 References \\
                 References \\
                 Index",
}

@Proceedings{Bowden:1953:FTT,
  editor =       "{Baron} Bertram Vivian Bowden",
  booktitle =    "Faster Than Thought: a Symposium on Digital Computing
                 Machines",
  title =        "Faster Than Thought: a Symposium on Digital Computing
                 Machines",
  publisher =    "Sir Isaac Pitman and Sons, Ltd.",
  address =      "London, UK",
  pages =        "xix + 416 + 21",
  year =         "1953",
  LCCN =         "QA76.5 .B66",
  bibdate =      "Sun May 15 10:03:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "With a foreword by the Right Honourable the Earl of
                 Halsbury.",
  URL =          "https://archive.org/details/FasterThanThought",
  acknowledgement = ack-nhfb,
  listofcontributors = "Miss M. Audrey Bates, Ferranti Ltd., Moston,
                 Manchester (Chapter 25) \\
                 Dr. J. M. Bennett, Ferranti Ltd., Moston, Manchester
                 (Chapters 5, 17, 20) \\
                 Dr. A. D. Booth, Director of the Electronic Computation
                 Laboratory, Birkbeck College, London (Chapter 13) \\
                 Dr. B. V. Bowden, Ferranti Ltd., Moston, Manchester
                 (Chapters 1--4, 14, 22, 25, 26) \\
                 Mr. R. H. A. Carter, Telecommunications Research
                 Establishment, Malvern (M.O.S.) (Chapter 10) \\
                 Mr. E. H. Cooke-Yarborough, Atomic Energy Research
                 Establishment, Harwell (M.O.S.) (Chapter 9) \\
                 Mr. A. E. Glennie, Research Establishment, Fort
                 Halstead (M.O.S.) (Chapters 5, 19) \\
                 Dr. S. H. Hollingdale, Head of the Mathematical
                 Services Department, Royal Aircraft Establishment,
                 Farnborough (M.O.S.) \\
                 (Chapter 12) \\
                 Dr. T. Kilburn, Senior Lecturer, Electrical Engineering
                 Dept., Manchester University (Chapter 6) \\
                 Mr. S. Michaelson, Imperial College of Science and
                 Technology, London (Chapter 11) \\
                 Dr. G. Morton, Lecturer In Economics, London School of
                 Economics And Political Science (Chapter 23) \\
                 Mr. B. W. Pollard, Ferranti Ltd., Moston, Manchester
                 (Chapter 2) \\
                 Miss Cicely M. Popplewell, Staff Member of the Royal
                 Society Computing Laboratory, Manchester University
                 (Chapter 24) \\
                 Dr. D. G. Prinz, Ferranti Ltd., Moston, Manchester
                 (Chapter 15) \\
                 Dr. R. S. Scorer, Lecturer, Department of Meteorology,
                 Imperial College of Science and Technology, London
                 (Chapter 18) \\
                 Mr. J. B. Smith, Ferranti Ltd., Crewe Toll, Edinburgh
                 (Chapter 15) \\
                 Mr. R. Stuart-Williams, Sometime of Ferranti Ltd.,
                 Moston, Manchester, now at the R.C.A. Research
                 Laboratories, Princeton, New Jersey, U.S.A. (Chapter
                 16) \\
                 Mr. B. B. Swann, Ferranti Ltd., Moston, Manchester
                 (Chapter 21) \\
                 Mr. C. Strachey, National Research Development
                 Corporation (Chapter 25) \\
                 Dr. K. D. Tocher, Imperial College of Science and
                 Technology, London (Chapter 11) \\
                 Dr. A. M. Turing, F.R.S., Assistant Director of the
                 Royal Society Computing Laboratory, Manchester
                 University (Chapter 25) \\
                 Dr. A. M. Uttley, Telecommunications Research
                 Establishment, Malvern (M.O.S.) (Chapter 10) \\
                 Dr. M. V. Wilkes, Director of the University
                 Mathematical Laboratory, Cambridge (Chapter 17) \\
                 Professor F. C. Williams, O.B.E., F.R.S. (Professor of
                 Electrical Engineering) Director of the Royal Society
                 Computing Laboratory, Manchester University (Chapter 6)
                 \\
                 Chapter 8 is reprinted from \booktitle{Engineering} by
                 kind permission of the Publishers",
  listofplates = "Ada Augusta, Countess of Lovelace / Frontispiece \\
                 I. Charles Babbage / 12 \\
                 II. Part of Babbage's Difference Engine / 28 \\
                 III. Two Hollerith Punch Cards of the Type Used in the
                 A.C.E. / 29 \\
                 IV. The Magnetic Drum of the Manchester Machine / 60
                 \\
                 V. The Photo-Electric Tape-Reader of the Manchester
                 Machine / 112 \\
                 VI. A Typical Stored Pattern on a Cathode-Ray-Tube
                 Screen / 120 \\
                 VII. The First Manchester University Computer / 121 \\
                 VIII. A General View of the Manchester University
                 Computer Without Covers / 124 \\
                 IX. A General View of the Manchester University
                 Computer and Control Desk / 126 \\
                 X. The Control Desk of the Manchester University
                 Computer, Showing the Console / 127 \\
                 XI. A General View of the E.D.S.A.C. / 132 \\
                 XII. One Unit of the A.C.E. / 136 \\
                 XIII. A View of the A.C.E. Showing Delay Units / 138
                 \\
                 XIV. A View of the A.C.E. Showing the Hollerith
                 Equipment Used for Input and Output / 139 \\
                 XV. A Cathode-Ray-Tube Store Pattern / 148 \\
                 XVI. The Ferranti (Edinburgh) Logical Computer and
                 Feedback Computer / 188 \\
                 XVII. ``Nimrod'' at the Science Exhibition, South
                 Kensington / 200 \\
                 XVIII. The $b$ Patterson Projection of Whale Myoglobin
                 Printed in Contour Form / 204",
  remark-01 =    "Portrait of Ada Augusta, Countess of Lovelace, faces
                 title page.",
  remark-02 =    "Chapter authors are credited only in the List of
                 Contributors on page xv; their names, and order, fail
                 to appear on chapter papers. No author is credited for
                 Chapters 7 and 8",
  remark-03 =    "From page ix: ``The principles on which all modern
                 computing machines are based were enunciated more than
                 a hundred years ago by a Cambridge mathematician named
                 Charles Babbage, who devoted his life and fortune to an
                 unsuccessful attempt to construct one. Modern
                 developments in electronics have made his dream come
                 true in the last decade, and there are now a dozen or
                 more machines in the world which do all and more than
                 he expected.",
  remark-04 =    "From page ix: ``A rough count showed that about 150
                 digital computers are being built at this moment, most
                 of them in universities and other research
                 establishments. It will be interesting to see if these
                 machines play in the next decade the part of the
                 cyclotrons and high voltage generators in the
                 `thirties'.''",
  remark-05 =    "From page x: ``It seems probable that we shall have a
                 second Industrial Revolution on our hands before long.
                 The first one replaced men's muscles by machines, and
                 eve1y worker in England now has an average of more than
                 3 horse power to help him. In the next revolution
                 machines may replace men's brains and relieve them of
                 much of the drudgery and boredom which is now the lot
                 of so many white collar workers.''",
  remark-06 =    "From page x: ``Nowadays many of these dedicated men
                 spend their time in computing prime numbers. The search
                 for the largest known prime is a hobby which is at
                 least as useful and interesting as playing bridge, and
                 computing machines have helped enormously. The reader
                 will not be surprised to hear that nowadays the biggest
                 primes are found in America. The largest which has been
                 discovered so far (January, 1953) consists of 2281
                 consecutive `ones,' when it is expressed in the binary
                 scale (see page 33).''",
  remark-07 =    "From page xi: ``The early history of these machines
                 and the story of poor Babbage's struggles is very
                 interesting. We owe our best account of Babbage's
                 `Engines' to the Countess of Lovelace, who was a
                 mathematician of great competence and one of the very
                 few people who understood what Babbage was trying to
                 do. Her ideas are so modern that they have become of
                 great topical interest once again, and since her paper
                 has long been out of print (it appeared more than a
                 hundred years ago) it has been reproduced as an
                 appendix to this book. Lady Lovelace's grand-daughter,
                 the Right Hon. Lady Wentworth, has very kindly allowed
                 me to read many of Lady Lovelace's most interesting
                 papers; I was so surprised by the connexion that I
                 found between digital computers and thoroughbred horses
                 that I have given a brief account of the story, for
                 further details of which the reader is referred to Lady
                 Wentworth's own books.''",
  remark-08 =    "From page xi: ``After I had finished the book, I saw a
                 microfilm of a life of Babbage which had been written
                 by his executor, the late Mr. L. H. D. Buxton. Mr.
                 Whitwell of the Powers Samas Company found the
                 manuscript in the Museum of the History of Science in
                 Oxford. It contains a more detailed account of the
                 construction of Babbage's Engines than any I have seen
                 elsewhere, and it is to be hoped that the material will
                 some day be published.''",
  remark-09 =    "From page xiii: ``Much of this book derives from the
                 work of those prolific authors `Anon' and `Ibid' who
                 have done so much to put our English platitudes on a
                 sound literary basis.''",
  remark-10 =    "From page xiii: ``I must express my thanks to all my
                 collaborators; to Lord Halsbury for writing the
                 foreword; to Lady Wentworth who gave me so much
                 information about Lady Lovelace, and who allowed me to
                 reproduce the portrait which has been used as a
                 frontispiece. I am also indebted to Miss Draper who
                 read all the Lovelace paper; and gave me a great deal
                 of help. I must thank Miss Dyke for preparing the flow
                 sheets which I used in Chapter 22. Dr. Gilles and Mr.
                 Whitewell told me the story of Dr. Comrie; Dr. Bullard
                 found some of Babbage's writing in the archives of the
                 National Physical Laboratory; and Professor Aitken, Mr.
                 W. Klein, Dr. van Wijngaarten, Dr. Stokvis, Mr. Seeber,
                 Mr. Ferris and Dr. Gabor gave me much of the
                 information on which Chapter 26 is based. The Portrait
                 of Babbage is included by courtesy of the Director of
                 the Science Museum, South Kensington.''",
  remark-11 =    "From glossary entry on page 411: ``{\em Computor}.
                 `Bad spelling of Computer' --- Oxford English
                 Dictionary.''",
  remark-12 =    "From glossary entry on page 411: ``{\em Cybernetics}.
                 A word invented by Professor Wiener to describe the
                 field of control and communication theory, whether in
                 the machine or in the animal. None of the authors quite
                 understands what the word means, so it has not been
                 used in this book.",
  remark-13 =    "From glossary entry on page 412: ``{\em Hartree
                 Constant}. The time which is expected to elapse before
                 a particular electronic computing machine is finished
                 and working. It was Professor Hartree who first pointed
                 out that this estimated time usually remains constant
                 at about six months for a period of several years
                 during the development of a machine. This phenomenon
                 was well known to Babbage. Few engineers are worried
                 unless the `constant' shows signs of increasing
                 monotonically as the years go by.''",
  remark-14 =    "From glossary entry on page 413: ``{\em Mill}.
                 Babbage's name for the arithmetic unit of his
                 machine.''",
  remark-15 =    "From glossary entry on page 414: ``{\em Programmer}.
                 One who prepares programmes for a machine, `a harmless
                 drudge'.''",
  remark-16 =    "From glossary entry on page 414: ``{\em T{\"u}ring
                 Machine}. In 1936 Dr. Turing wrote a paper on the
                 design and the limitations of computing machines. For
                 this reason they are sometimes known by his name. The
                 umlaut is an unearned and undesirable addition, due,
                 presumably, to an impression that anything so
                 incomprehensible must be Teutonic.''",
  subject =      "Electronic digital computers",
  tableofcontents = "Foreword / v \\
                 Preface / vii \\
                 List of Contributors / xv \\
                 Part One: The History and Theory of Computing Machines
                 \\
                 1. A Brief History of Computation / B. V. Bowden / 3
                 \\
                 2. The Circuit Components of Digital Computers / B. V.
                 Bowden and B. W. Pollard / 32 \\
                 3. The Organization of a Typical Machine / B. V. Bowden
                 / 67 \\
                 4. The Construction, Performance and Maintenance of
                 Digital Computers / B. V. Bowden / 78 \\
                 5. Programming For High-Speed Digital Calculating
                 Machines / J. M. Bennett and A. E. Glennie / 101 \\
                 Part Two: Electronic Computing Machines in Britain and
                 America / \\
                 6. The University of Manchester Computing Machine / T.
                 Kilburn and F. C. Williams / 117 \\
                 7. Calculating Machine Development at Cambridge / 130
                 \\
                 8. Automatic Computation at the National Physical
                 Laboratory / 135 \\
                 9. The Harwell Electronic Digital Computer / E. H.
                 Cooke-Yarborough / 140 \\
                 10. The Telecommunications Research Establishment
                 Parallel Electronic Digital Computer / R. H. A. Carter
                 and A. M. Uttley / 144 \\
                 11. The Imperial College Computing Engine / S.
                 Michaelson and K. D. Tocher / 161 \\
                 12. The Royal Aircraft Establishment
                 Sequence-Controlled Calculator / S. H. Hollingdale /
                 165 \\
                 13. Calculating Machines at the Birkbeck College
                 Computation Laboratory / A. D. Booth / 170 \\
                 14. Computers in America / B. V. Bowden / 173 \\
                 Part Three: Applications of Electronic Computing
                 Machines \\
                 15. Machines for the Solution of Logical Problems / D.
                 G. Prinz and J. B. Smith / 181 \\
                 16. Special-Purpose Automatic Computers / R.
                 Stuart-Williams / 199 \\
                 17. Digital Computation and the Crystallographer / J.
                 M. Bennett and M. V. Wilkes / 203 \\
                 18. The Use of High-Speed Computing Machines in
                 Meteorology / R. S. Scorer / 210 \\
                 19. An Application to Ballistics / A. E. Glennie / 216
                 \\
                 20. Digital Computers and the Engineer / J. M. Bennett
                 / 223 \\
                 21. Machines in Government Calculations / B. B. Swann /
                 234 \\
                 22. The Application of Digital Computers to Business
                 and Commerce / B. V. Bowden / 246 \\
                 23. Electronic Machines and Economics / G. Morton / 272
                 \\
                 24. Problems of Dynamical Astronomy / Cicely M.
                 Popplewell / 282 \\
                 25. Digital Computers Applied to Games / M. Audrey
                 Bates, B. V. Bowden, C. Strachey, and A. M. Turing /
                 286 \\
                 26. Thought and Machine Processes / B. V. Bowden / 311
                 \\
                 Appendix 1: Extracts From \booktitle{Taylor's
                 Scientific Memoirs}, Vol. III / 341 \\
                 Appendix 2: Extracts From the \booktitle{Lovelace
                 Papers} / 409 \\
                 Glossary / 411 \\
                 Index / 415 \\
                 Insets \\
                 Flow Sheet For P.A.Y.E. Calculation / 254 \\
                 Computation of Bernoulli Numbers / 404",
}

@Book{Birkhoff:1954:SMM,
  editor =       "Garrett Birkhoff",
  booktitle =    "Studies in Mathematics and Mechanics Presented to
                 {Richard von Mises} by friends, colleagues, and
                 pupils",
  title =        "Studies in Mathematics and Mechanics Presented to
                 {Richard von Mises} by friends, colleagues, and
                 pupils",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "ix + 353",
  year =         "1954",
  ISBN =         "1-4832-6356-8",
  ISBN-13 =      "978-1-4832-6356-4",
  LCCN =         "QA3 .S853",
  bibdate =      "Fri Oct 20 10:13:10 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Studies in Mathematics and Mechanics is a collection
                 of studies presented to Professor Richard von Mises as
                 a token of reverence and appreciation on the occasion
                 of his seventieth birthday which occurred on April 19,
                 1953. von Mises' thought has been a stimulus in many
                 seemingly unconnected fields of mathematics, science,
                 and philosophy, to which he has contributed decisive
                 results and new formulations of fundamental concepts.
                 The book contains 42 chapters organized into five
                 parts. Part I contains papers on algebra, number theory
                 and geometry. These include a study of Poincar{\'e}'s
                 representation of a hyperbolic space on an Euclidean
                 half-space and elementary estimates for the least
                 primitive root. Part II on analysis includes papers on
                 a generalization of Green's Formula and its application
                 to the Cauchy problem for a hyperbolic equation, and
                 the fundamental solutions of a singular Beltrami
                 operator. Part III deals with theoretical mechanics and
                 covers topics such as turbulent flow, axially symmetric
                 flow, and oscillating wakes. The papers in Part IV
                 focus on applied mechanics. These include studies on
                 plastic flow under high stresses and the problem of
                 inelastic thermal stresses. Part V presents studies on
                 probability and statistics, including a finite
                 frequency theory of probability and the problem of
                 expansion of clusters of galaxies.",
  acknowledgement = ack-nhfb,
  subject-dates = "Richard von Mises (1883--1953)",
}

@Book{Langer:1959:NAP,
  editor =       "R. E. Langer",
  booktitle =    "On numerical approximation. {Proceedings of a
                 Symposium, Madison, April 21--23, 1958}",
  title =        "On numerical approximation. {Proceedings of a
                 Symposium, Madison, April 21--23, 1958}",
  publisher =    "The University of Wisconsin Press",
  address =      "Madison, WI, USA",
  pages =        "x + 462",
  year =         "1959",
  LCCN =         "QA3 .U45 no. 1",
  bibdate =      "Tue Jun 19 06:45:47 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Publication no. 1 of the Mathematics Research Center,
                 U.S. Army, the University of Wisconsin.",
  acknowledgement = ack-nhfb,
  subjects =     "statistics",
  tableofcontents = "1. On trends and problems in numerical
                 approximation / Ostrowski \\
                 2. Linear spaces and approximation theory / Buck \\
                 3. Operational methods in numerical analysis based on
                 rational approximations / Kopal \\
                 4. On the numerical integration of periodic analytic
                 functions / Davis \\
                 S. Some new divided difference algorithms in two
                 variables / Salzer \\
                 6. Numerical evaluation of multiple integrals / Hammer
                 \\
                 7. Optimal approximation and error bounds / Golomb and
                 Weinberger \\
                 8. The rationale of approximation / Sard \\
                 9. On extremal approximations / Walsh \\
                 10. Numerical methods of Tchebycheff approximation /
                 Stiefel \\
                 11. Minimax methods in table construction / Fox \\
                 12. Existence of essentially nonlinear families
                 suitable for oscillatory approximation / Motzkin \\
                 13. On variation diminishing approximation methods /
                 Schoenberg \\
                 14. Approximation by functions of fewer variables /
                 Golomb \\
                 15. Extremal approximations --- a summary / Miller \\
                 16. Survey of recent Russian literature on
                 approximation / Buck \\
                 17. The quotient--difference and epsilon algorithms /
                 Bauer \\
                 18. Some sufficient conditions for the existence of an
                 asymptotic formula or an asymptotic expansion / Rosser
                 \\
                 19. The estimation of (power) spectra and related
                 quantities / Tukey \\
                 20. Approximation in partial differential equations /
                 Collatz \\
                 21. Special polynomials in numerical analysis / Todd",
}

@Book{Ralston:1960:MMD,
  editor =       "Anthony Ralston and Herbert S. Wilf",
  booktitle =    "Mathematical methods for digital computers",
  title =        "Mathematical methods for digital computers",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "various",
  year =         "1960--1977",
  ISBN =         "0-471-70690-6",
  ISBN-13 =      "978-0-471-70690-8",
  LCCN =         "QA39 .R26",
  bibdate =      "Mon Jan 13 10:36:06 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Three volumes.",
  acknowledgement = ack-nhfb,
}

@Book{Abramowitz:1964:HMF,
  editor =       "Milton Abramowitz and Irene A. Stegun",
  key =          "NBS",
  booktitle =    "Handbook of Mathematical Functions with Formulas,
                 Graphs, and Mathematical Tables",
  title =        "Handbook of Mathematical Functions with Formulas,
                 Graphs, and Mathematical Tables",
  volume =       "55",
  publisher =    "U. S. Department of Commerce",
  address =      "Washington, DC, USA",
  pages =        "xiv + 1046",
  year =         "1964",
  LCCN =         "QA47.A161 1972; QA 55 A16h 1972",
  bibdate =      "Thu Jan 27 07:58:12 2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Tenth printing, with corrections (December 1972). This
                 book is also available online at
                 \path=http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP=
                 in bitmap image format.",
  series =       "Applied mathematics series",
  abstract =     "This book is a compendium of mathematical formulas,
                 tables, and graphs. It contains a table of analytical
                 integrals, differential equations, and numerical
                 series; and includes tables of trigonometric and
                 hyperbolic functions, tables for numerical integration,
                 rules for differentiation and integration, and
                 techniques for point interpolation and function
                 approximation. Additionally, it devotes a entire
                 section to mathematical and physical constants as
                 fractions and powers of Pi, e, and prime numbers; and
                 discusses statistics by presenting combinatorial
                 analysis and probability functions.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Mathematical constants / David S. Liepman \\
                 Physical constants and conversion factors / A. G.
                 McNish \\
                 Elementary analytical methods / Milton Abramowitz \\
                 Elementary transcendental functions: logarithmic,
                 exponential, circular and hyperbolic functions / Ruth
                 Zucker \\
                 Exponential integral and related functions / Walter
                 Gautschi and William F. Cahill \\
                 Gamma function and related functions / Philip J. Davis
                 \\
                 Error function and Fresnel integrals / Walter Gautschi
                 \\
                 Legendre functions / Irene A. Stegun \\
                 Bessel functions of integer order / F. W. J. Olver \\
                 Bessell functions of fractional order / H. A.
                 Antosiewicz \\
                 Integrals of Bessel functions / Yudell L. Luke \\
                 Struve functions and related functions / Milton
                 Abramowitz \\
                 Confluent hypergeometric functions / Lucy Joan Slater
                 \\
                 Coulomb wave functions / Milton Abramowitz \\
                 Hypergeometric functions / Fritz Oberhettinger \\
                 Jacobian elliptic functions and theta functions;
                 Elliptic integrals / L. M. Milne-Thomson \\
                 Weierstrass elliptic and related functions / Thomas H.
                 Southard \\
                 Parabolic cylinder functions / J. C. P. Miller\ldots{}
                 Mathieu functions / Gertrude Blanch \\
                 Spheroidal wave functions / Arnold N. Lowan \\
                 Orthogonal polynomials / Urs W. Hochstrasser \\
                 Bernoulli and Euler polynomials, Riemann zeta function
                 / Emilie V. Haynesworth and Karl Goldberg \\
                 Combinatorial analysis / K. Goldberg, M. Newman and E.
                 Haynesworth \\
                 Numerical interpolation, differentiation and
                 integration / Philip J. Davis and Ivan Polonsky \\
                 Probability functions / Marvin Zelen and Norman C.
                 Severo \\
                 Miscellaneous functions / Irene A. Stegun \\
                 Scales of notation / S. Peavy and A. Schopf \\
                 Laplace transforms",
}

@Book{Magnus:1966:FTS,
  author =       "Wilhelm Magnus and Fritz Oberhettinger and Raj Pal
                 Soni",
  booktitle =    "Formulas and theorems for the special functions of
                 mathematical physics",
  title =        "Formulas and theorems for the special functions of
                 mathematical physics",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Third",
  pages =        "viii + 508",
  year =         "1966",
  LCCN =         "QA1 G88 v. 52, 1966",
  bibdate =      "Sat Oct 30 18:23:25 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  note =         "See errata
                 \cite{Cohl:2012:TEF,Szmytkowski:2013:EBT}.",
  acknowledgement = ack-nhfb,
}

@Proceedings{AFIPS:1969:ACPb,
  key =          "AFIPS FJCC '69",
  booktitle =    "1969 Fall Joint Computer Conference, November 18--20,
                 1969, Las Vegas, Nevada",
  title =        "1969 Fall Joint Computer Conference, November 18--20,
                 1969, Las Vegas, Nevada",
  volume =       "35",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "807",
  year =         "1969",
  LCCN =         "TK7885.A1 J6 1969",
  bibdate =      "Sat Sep 24 01:06:00 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "AFIPS conference proceedings",
  acknowledgement = ack-nhfb,
}

@Proceedings{AFIPS:1971:ACP,
  key =          "AFIPS SJCC '71",
  booktitle =    "1971 Spring Joint Computer Conference, May 18--20,
                 1971, Atlantic City, New Jersey",
  title =        "1971 Spring Joint Computer Conference, May 18--20,
                 1971, Atlantic City, New Jersey",
  volume =       "38",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "631",
  year =         "1971",
  LCCN =         "????",
  bibdate =      "Fri Sep 16 10:47:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "AFIPS conference proceedings",
  acknowledgement = ack-nj # " and " # ack-nhfb,
}

@Book{Rice:1971:MS,
  author =       "John R. Rice",
  booktitle =    "Mathematical Software",
  title =        "Mathematical Software",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xvii + 515",
  year =         "1971",
  ISBN =         "0-12-587250-X",
  ISBN-13 =      "978-0-12-587250-8",
  LCCN =         "QA1 .M26",
  bibdate =      "Thu Sep 15 18:56:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Based on the proceedings of the Mathematical Software
                 Symposium held at Purdue University, Lafayette,
                 Indiana, USA, April 1--3, 1970.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Askey:1975:TAS,
  editor =       "Richard Askey",
  booktitle =    "{Theory and application of special functions:
                 proceedings of an advanced seminar sponsored by the
                 Mathematics Research Center, the University of
                 Wisconsin-Madison, March 31--April 2, 1975}",
  title =        "{Theory and application of special functions:
                 proceedings of an advanced seminar sponsored by the
                 Mathematics Research Center, the University of
                 Wisconsin-Madison, March 31--April 2, 1975}",
  number =       "35",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xi + 560",
  year =         "1975",
  ISBN =         "0-12-064850-4",
  ISBN-13 =      "978-0-12-064850-4",
  LCCN =         "QA3 .U45 no. 35 QA351",
  bibdate =      "Sat Oct 30 07:41:32 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Publication of the Mathematics Research Center, the
                 University of Wisconsin",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  meetingname =  "Advanced Seminar on Special Functions, Madison, Wis.,
                 1975.",
  subject =      "Functions, Special; Congresses",
}

@Proceedings{Miller:1975:TNA,
  editor =       "John J. H. Miller",
  booktitle =    "Topics in numerical analysis: proceedings of the Royal
                 Irish Academy Conference on Numerical Analysis, 1972,
                 1974, 1976",
  title =        "Topics in numerical analysis: proceedings of the Royal
                 Irish Academy Conference on Numerical Analysis, 1972,
                 1974, 1976",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "various",
  year =         "1975",
  ISBN =         "0-12-496950-X",
  ISBN-13 =      "978-0-12-496950-6",
  LCCN =         "QA297 .R69 1973",
  bibdate =      "Mon Jan 13 10:41:13 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Traub:1976:ACC,
  editor =       "J. F. (Joseph Frederick) Traub",
  booktitle =    "{Analytic computational complexity: Proceedings of the
                 Symposium on Analytic Computational Complexity, held by
                 the Computer Science Department, Carnegie-Mellon
                 University, Pittsburgh, Pennsylvania, on April 7--8,
                 1975}",
  title =        "{Analytic computational complexity: Proceedings of the
                 Symposium on Analytic Computational Complexity, held by
                 the Computer Science Department, Carnegie-Mellon
                 University, Pittsburgh, Pennsylvania, on April 7--8,
                 1975}",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "ix + 239",
  year =         "1976",
  ISBN =         "0-12-697560-4",
  ISBN-13 =      "978-0-12-697560-4",
  LCCN =         "QA297.S9151 1975",
  bibdate =      "Mon Jan 13 10:18:33 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Cowell:1977:PMS,
  editor =       "Wayne Cowell",
  booktitle =    "{Portability of Numerical Software Workshop, Oak
                 Brook, Illinois, June 21--23, 1976}",
  title =        "{Portability of Numerical Software Workshop, Oak
                 Brook, Illinois, June 21--23, 1976}",
  volume =       "57",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 539",
  year =         "1977",
  ISBN =         "0-387-08446-0",
  ISBN-13 =      "978-0-387-08446-6",
  LCCN =         "QA297 .W65 1976",
  bibdate =      "Sat Sep 24 00:24:09 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Lecture Notes in Computer Science",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  remark =       "Workshop organized by Argonne National Laboratory.",
}

@Proceedings{IEEE:1978:PSC,
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the Symposium on Computer Arithmetic
                 {(4th: 1978: Santa Monica, CA)}",
  title =        "Proceedings of the Symposium on Computer Arithmetic
                 {(4th: 1978: Santa Monica, CA)}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 274",
  year =         "1978",
  ISSN =         "1063-6889",
  LCCN =         "QA76.6 .S919a",
  bibdate =      "Mon May 19 15:22:15 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "IEEE catalog no. 78 CH1412-6C.",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic --- Congresses.; Electronic
                 digital computers --- Programming --- Congresses.;
                 Floating-point arithmetic --- Congresses.",
}

@Proceedings{Alefeld:1980:PSE,
  editor =       "G. Alefeld and R. D. Grigorieff and R. Albrecht and U.
                 Kulisch and F. Stummel",
  booktitle =    "{Fundamentals of numerical computation
                 (computer-oriented numerical analysis). Proceedings of
                 a conference held June 5--8, 1979, on the occasion of
                 the centennial of the Technical University of Berlin}",
  title =        "{Fundamentals of numerical computation
                 (computer-oriented numerical analysis). Proceedings of
                 a conference held June 5--8, 1979, on the occasion of
                 the centennial of the Technical University of Berlin}",
  volume =       "2",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "229",
  year =         "1980",
  ISBN =         "0-387-81566-X",
  ISBN-13 =      "978-0-387-81566-4",
  ISSN =         "0344-8029",
  LCCN =         "QA297 .F84",
  bibdate =      "Mon Jan 13 10:20:47 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Computing. Supplementum",
  acknowledgement = ack-nhfb,
}

@Proceedings{Dieudonne:1980:SFL,
  editor =       "Jean Dieudonn{\'e}",
  booktitle =    "{Special functions and linear representations of Lie
                 groups}",
  title =        "{Special functions and linear representations of Lie
                 groups}",
  volume =       "42",
  publisher =    "Published for the Conference Board of the Mathematical
                 Sciences by the American Mathematical Society",
  address =      "Providence, RI, USA",
  pages =        "iii + 59",
  year =         "1980",
  ISBN =         "0-8218-1692-6",
  ISBN-13 =      "978-0-8218-1692-9",
  LCCN =         "????",
  bibdate =      "Sat Oct 30 17:14:47 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  series =       "Regional conference series in mathematics",
  acknowledgement = ack-nhfb,
  remark =       "Expository lectures from the CBMS regional conference
                 held at East Carolina University, March 5--9, 1979.",
}

@Proceedings{Lavington:1980:IPP,
  editor =       "Simon Hugh Lavington",
  booktitle =    "Information Processing 80: Proceedings of {IFIP}
                 Congress 80, Tokyo, Japan, October 6--9, 1980,
                 Melbourne, Australia, October 14--17, 1980",
  title =        "Information Processing 80: Proceedings of {IFIP}
                 Congress 80, Tokyo, Japan, October 6--9, 1980,
                 Melbourne, Australia, October 14--17, 1980",
  publisher =    pub-ENH,
  address =      pub-ENH:adr,
  pages =        "xiii + 1070",
  year =         "1980",
  ISBN =         "0-444-86034-7",
  ISBN-13 =      "978-0-444-86034-7",
  LCCN =         "QA 75.5 I57 1980",
  bibdate =      "Thu Sep 01 23:09:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1981:PIS,
  editor =       "{IEEE}",
  booktitle =    "Proceedings: 5th Symposium on Computer Arithmetic, May
                 18-19, 1981, University of Michigan, Ann Arbor,
                 Michigan",
  title =        "Proceedings: 5th Symposium on Computer Arithmetic, May
                 18-19, 1981, University of Michigan, Ann Arbor,
                 Michigan",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "vii + 278",
  year =         "1981",
  LCCN =         "QA76.9.C62 S95 1981",
  bibdate =      "Mon May 19 13:17:13 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "IEEE Catalog No. 81CH1630-3. Computer Society Order
                 No. 347.",
  acknowledgement = ack-nhfb,
  xxISBN =       "none",
}

@Proceedings{IEEE:1981:PSC,
  key =          "IEEE CA5 '81",
  booktitle =    "Proceedings: 5th Symposium on Computer Arithmetic, May
                 18--19, 1981, University of Michigan, Ann Arbor,
                 Michigan",
  title =        "Proceedings: 5th Symposium on Computer Arithmetic: May
                 18--19, 1981, University of Michigan, Ann Arbor,
                 Michigan",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "vii + 278",
  year =         "1981",
  LCCN =         "QA 76.6 S985t 1981",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 81CH1630-C.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5; Computer arithmetic and logic units ---
                 Congresses.; Electronic digital computers ---
                 Programming --- Congresses.; Floating-point arithmetic
                 Congresses.",
  xxISBN =       "(none)",
}

@Proceedings{Mulvey:1982:EMP,
  editor =       "J. M. Mulvey",
  booktitle =    "{Evaluating Mathematical Programming Techniques:
                 Proceedings of a Conference Held at the National Bureau
                 of Standards, Boulder, Colorado, January 5--6, 1981}",
  title =        "{Evaluating Mathematical Programming Techniques:
                 Proceedings of a Conference Held at the National Bureau
                 of Standards, Boulder, Colorado, January 5--6, 1981}",
  volume =       "199",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xi + 379",
  year =         "1982",
  ISBN =         "0-387-11495-5",
  ISBN-13 =      "978-0-387-11495-8",
  LCCN =         "QA402.5 .E94 1982",
  bibdate =      "Thu Nov 17 06:36:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Lecture Notes in Economics and Mathematical Systems",
  acknowledgement = ack-nhfb,
}

@Proceedings{Hwang:1985:PSC,
  editor =       "Kai Hwang",
  booktitle =    "Proceedings: 7th Symposium on Computer Arithmetic,
                 June 4--6, 1985, University of Illinois, Urbana,
                 Illinois",
  title =        "Proceedings: 7th Symposium on Computer Arithmetic,
                 June 4--6, 1985, University of Illinois, Urbana,
                 Illinois",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 343",
  year =         "1985",
  ISBN =         "0-8186-0632-0 (paperback), 0-8186-8632-4 (hard),
                 0-8186-4632-2 (microfiche)",
  ISBN-13 =      "978-0-8186-0632-8 (paperback), 978-0-8186-8632-0
                 (hard), 978-0-8186-4632-4 (microfiche)",
  LCCN =         "QA76.9.C62 S95 1985",
  bibdate =      "Thu Sep 08 00:11:41 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 85CH2146-9. IEEE Computer Society
                 order number 632.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-7",
}

@Proceedings{IEEE:1985:ERC,
  key =          "IEEE Region 5 '85",
  booktitle =    "1985 {IEEE} Region 5 Conference, March 13--15, 1985,
                 Holiday Inn Civic Center, Lubbock, Texas",
  title =        "1985 {IEEE} Region 5 Conference, March 13--15, 1985,
                 Holiday Inn Civic Center, Lubbock, Texas",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "vi + 71",
  year =         "1985",
  LCCN =         "TK 7801 N56 1985",
  bibdate =      "Thu Sep 15 18:50:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxISBN =       "(none)",
}

@Proceedings{Marron:1985:FEP,
  editor =       "J. S. Marron",
  booktitle =    "{Function estimates: proceedings of a conference held
                 July 28--August 3, 1985}",
  title =        "{Function estimates: proceedings of a conference held
                 July 28--August 3, 1985}",
  volume =       "59",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "ix + 178",
  year =         "1985",
  ISBN =         "0-8218-5062-8",
  ISBN-13 =      "978-0-8218-5062-6",
  ISSN =         "0271-4132 (print), 1098-3627 (electronic)",
  LCCN =         "QA276.8 .C651 1985",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Held at Humboldt State University, Arcata,
                 California.",
  series =       "Contemporary mathematics (American Mathematical
                 Society)",
  acknowledgement = ack-nhfb,
  bibno =        "18241",
  catcode =      "G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation",
  genterm =      "algorithms; theory",
  guideno =      "1986-12215",
  procdate =     "July 28--Aug. 3, 1985",
  procloc =      "Arcata, CA",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Proceedings{Miranker:1985:ASC,
  editor =       "Willard L. Miranker and Richard A. Toupin",
  booktitle =    "Accurate Scientific Computations: Symposium, Bad
                 Neuenahr, {FRG}, March 12--14, 1985: Proceedings",
  title =        "Accurate Scientific Computations: Symposium, Bad
                 Neuenahr, {FRG}, March 12--14, 1985: Proceedings",
  volume =       "235",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 205",
  year =         "1985",
  DOI =          "https://doi.org/10.1007/3-540-16798-6",
  ISBN =         "0-387-16798-6",
  ISBN-13 =      "978-0-387-16798-5",
  LCCN =         "QA76.95 .A231 1986",
  bibdate =      "Sat Sep 03 12:24:08 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
}

@Proceedings{Miranker:1986:ASC,
  editor =       "Willard L. Miranker and Richard A. Toupin",
  booktitle =    "Accurate scientific computations: symposium, Bad
                 Neuenahr, {FRG}, March 12--14, 1985: proceedings",
  title =        "Accurate scientific computations: symposium, Bad
                 Neuenahr, {FRG}, March 12--14, 1985: proceedings",
  volume =       "235",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 205",
  year =         "1986",
  CODEN =        "LNCSD9",
  ISBN =         "0-387-16798-6 (USA: paperback)",
  ISBN-13 =      "978-0-387-16798-5 (USA: paperback)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "QA76.95 .A231 1986",
  bibdate =      "Fri Apr 12 07:14:49 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Symposium sponsored by IBM Deutschland.",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  keywords =     "mathematics --- data processing --- congresses;
                 numerical calculations --- congresses",
}

@Proceedings{ACM:1987:UAA,
  editor =       "{ACM}",
  booktitle =    "Using Ada: {ACM} {SIGAda} international conference,
                 Boston, Massachusetts, December 8--11, 1987",
  title =        "Using Ada: {ACM} {SIGAda} international conference,
                 Boston, Massachusetts, December 8--11, 1987",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "viii + 240",
  year =         "1987",
  ISBN =         "0-89791-243-8",
  ISBN-13 =      "978-0-89791-243-3",
  LCCN =         "QA 76.73 A35 U85 1987",
  bibdate =      "Mon May 19 13:18:54 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Iserles:1987:SAN,
  editor =       "A. Iserles and M. J. D. Powell",
  booktitle =    "The State of the Art in Numerical Analysis:
                 Proceedings of the Joint {IMA}\slash {SIAM} Conference
                 on the State of the Art in Numerical Analysis held at
                 the University of Birmingham, 14--18 April 1986",
  title =        "The State of the Art in Numerical Analysis:
                 Proceedings of the Joint {IMA}\slash {SIAM} Conference
                 on the State of the Art in Numerical Analysis held at
                 the University of Birmingham, 14--18 April 1986",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xiv + 719",
  year =         "1987",
  ISBN =         "0-19-853614-3",
  ISBN-13 =      "978-0-19-853614-7",
  LCCN =         "QA297 .S781 1987",
  bibdate =      "Thu Sep 08 00:41:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  price =        "UK\pounds55.00, US\$77.50",
  acknowledgement = ack-nj # " and " # ack-nhfb,
}

@Proceedings{Mason:1987:AAB,
  editor =       "J. C. Mason and M. G. Cox",
  booktitle =    "{Algorithms for approximation: based on the
                 proceedings of the IMA Conference on Algorithms for the
                 Approximation of Functions and Data, held at the Royal
                 Military College of Science, Shrivenham, July 1985}",
  title =        "{Algorithms for approximation: based on the
                 proceedings of the IMA Conference on Algorithms for the
                 Approximation of Functions and Data, held at the Royal
                 Military College of Science, Shrivenham, July 1985}",
  volume =       "10",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "xvi + 694 + 8",
  year =         "1987",
  ISBN =         "0-19-853612-7",
  ISBN-13 =      "978-0-19-853612-3",
  LCCN =         "QA221 .A5361 1987; QA221 .I47 1985",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/r/ruhe-axel.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$90",
  series =       "The Institute of Mathematics and Its Applications
                 conference series, new series",
  acknowledgement = ack-nhfb,
  bibno =        "39820",
  catcode =      "G.1.2; G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Approximation; G.1.2
                 Elementary function approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "theory; algorithms",
  guideno =      "1987-16080",
  meetingname =  "IMA Conference on Algorithms for the Approximation of
                 Functions and Data (1985: Royal Military College of
                 Science, Shrivenham)",
  procdate =     "The Institute of mathematics and its applications
                 conference series; 10 July 1985",
  procloc =      "Shrivenham, UK",
  sub =          "Proceedings of the IMA Conference on Algorithms for
                 the approximation of functions",
  subject =      "Approximation theory; Data processing; Congresses; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
  tableofcontents = "Preface / v \\
                 Contributors / xiii \\
                 \\
                 I Development of Algorithms \\
                 \\
                 1. Spline Approximation and Smoothing \\
                 \\
                 G. T. Anthony and M. G. Cox / The fitting of extremely
                 large data sets by bivariate splines / 5 \\
                 W. Dahmen / Subdivision algorithms --- recent results,
                 some extensions and further developments / 21 \\
                 P. Dierckx / Fast algorithms for smoothing data over a
                 disc or a sphere using tensor product splines / 51 \\
                 T. Lyche and K. M{\o}rken / A discrete approach to knot
                 removal and degree reduction algorithms for splines /
                 67 \\
                 R. H. J. Gmelig Meyling / On algorithms and
                 applications for bivariate B-splines / 83 \\
                 \\
                 2. Spline Interpolation and Shape Preservation \\
                 \\
                 R. E. Carlson / Shape preserving interpolation / 97 \\
                 M. G. Cox and H. M. Jones / Shape preserving spline
                 approximation in the $\ell_1$-norm / 115 \\
                 J. A. Gregory / A review of curve interpolation with
                 shape control / 131 \\
                 \\
                 3. Multivariate Interpolation \\
                 \\
                 M. J. D. Powell / Radial basis functions for
                 multivariable interpolation: a review / 143 \\
                 R. A. Lorentz / On the determinant of a bivariate
                 Birkhoff interpolation problem / 169 \\
                 A. Le Mehaute / Interpolation with piecewise
                 polynomials in more than one variable / 181 \\
                 \\
                 4. Least Square Methods \\
                 \\
                 R. Farwig / Multivariate interpolation of scattered
                 data by moving least squares methods / 193 \\
                 F. Yoshimoto / Least squares approximation by one-pass
                 methods with piecewise polynomials / 213 \\
                 \\
                 5. Rational Approximation \\
                 \\
                 L. N. Trefethen and M. H. Gutknecht / Pad{\'e}, stable
                 Pad{\'e}, and Chebyshev--Pad{\'e} approximation / 227
                 \\
                 P. T. Breuer / A new method for real rational uniform
                 approximation / 265 \\
                 C. B. Dunham / Rationals with repeated poles / 285 \\
                 A. Iserles and S. P. N{\o}rsett / Error control of
                 rational approximation with a matrix argument / 293 \\
                 \\
                 6. Complex and Nonlinear Approximation \\
                 \\
                 K. Madsen / General algorithms for discrete non-linear
                 parameter estimation / 309 \\
                 G. Opfer / Complex rational approximation with
                 numerical experiments / 327 \\
                 G. A. Watson / Data fitting by positive sums of
                 exponentials / 337 \\
                 J. C. Mason and P. Owen / Some simple algorithms for
                 constrained complex and rational approximation / 357
                 \\
                 \\
                 7. Computer-Aided Design and Blending \\
                 \\
                 L. L. Schumaker / Numerical aspects of spaces of
                 piecewise polynomials on triangulations / 373 \\
                 M. V. Golitschek / The $H$-sets of the blending
                 functions / 407 \\
                 D. Levin / Multidimensional reconstruction by
                 set-valued approximations/ 421 \\
                 \\
                 II Applications \\
                 \\
                 8. Applications in Numerical Analysis \\
                 \\
                 H. P. Blatt, A, Iserles and E. B. Saff / Remarks on the
                 behaviour of zeros of best approximating polynomials
                 and rational functions / 437 \\
                 J. Gilbert and W. A. Light / Multigrid methods and the
                 alternating algorithm / 447 \\
                 K. Jetter and J. St{\"o}ckler / On the computation of
                 Gauss--Birkhoff quadrature formulas / 459 \\
                 E. Schock / Error bounds for the solution of integral
                 equations by Galerkin-like methods / 471 \\
                 N. M. Temme / On the computation of the incomplete
                 gamma functions for large values of the parameters /
                 479 \\
                 \\
                 9. Applications in Partial Differential Equations \\
                 \\
                 J. R. Rice / Adaptive tensor product grids for singular
                 problems / 493 \\
                 W. Freeden / Harmonic splines for solving boundary
                 value problems of potential theory / 507 \\
                 D. C. Hanscomb / Recovery of fluid flow fields / 531
                 \\
                 L. Reichel / The selection of subspace and collocation
                 points in the boundary collocation method for some
                 plane elliptic boundary problems / 541 \\
                 \\
                 10. Applications in Other Disciplines \\
                 \\
                 L. Andersson, K. Holmstr{\"o}m and A. Ruhe / Complex
                 formation constants --- a problem from solution
                 chemistry / 557 \\
                 D. E. Roberts and P. R. Graves-Morris / The application
                 of generalised inverse rational interpolants in the
                 model analysis of vibrating structures I / 573 \\
                 A. Daman and J. C. Mason / A generalised
                 cross-validation method for meteorological data with
                 gaps / 595 \\
                 K. P. Jackson and J. C. Mason / The approximation by
                 complex functions of stresses in cracked domains / 6ll
                 \\
                 J. H. McDonnell / Equally spaced cubic splines for
                 representing time histories / 623 \\
                 B. L. Rahimi and S. W. Ellacott / Dynamic phase
                 analysis of heart anomalies / 641 \\
                 \\
                 III Software \\
                 \\
                 J. G. Hayes / NAG algorithms for the approximation of
                 functions and data / 653 \\
                 G. T. Anthony and M. G. Cox / The National Physical
                 Laboratory's Data Approximation Subroutine Library /
                 669 \\
                 \\
                 M. G. Cox (editor) / Panel Discussion / 689",
}

@Proceedings{USENIX:1988:UPC,
  editor =       "{USENIX Association}",
  booktitle =    "{USENIX} proceedings: {C++} Conference, Denver, {CO},
                 October 17--21, 1988",
  title =        "{USENIX} proceedings: {C++} Conference, Denver, {CO},
                 October 17--21, 1988",
  publisher =    pub-USENIX,
  address =      pub-USENIX:adr,
  pages =        "362",
  year =         "1988",
  bibdate =      "Sun Feb 18 07:46:09 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "C++ (Computer program language) --- Congresses.",
}

@Proceedings{ACM:1989:PAI,
  editor =       "{ACM}",
  booktitle =    "Proceedings of the {ACM-SIGSAM 1989} International
                 Symposium on Symbolic and Algebraic Computation, {ISSAC
                 '89}",
  title =        "{Proceedings of the ACM--SIGSAM 1989 International
                 Symposium on Symbolic and Algebraic Computation, ISSAC
                 '89}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "399",
  year =         "1989",
  ISBN =         "0-89791-325-6",
  ISBN-13 =      "978-0-89791-325-6",
  LCCN =         "QA76.95.I59 1989",
  bibdate =      "Tue Sep 17 06:46:18 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  confdate =     "17--19 July 1989",
  conflocation = "Portland, OR, USA",
  confsponsor =  "ACM",
  pubcountry =   "USA",
}

@Book{Campbell-Kelly:1989:WCB-3,
  editor =       "Martin Campbell-Kelly",
  booktitle =    "The works of {Charles Babbage}, Vol. 3, The analytical
                 engine and mechanical notation",
  title =        "The works of {Charles Babbage}, Vol. 3, The analytical
                 engine and mechanical notation",
  publisher =    "William Pickering",
  address =      "London, UK",
  pages =        "253",
  year =         "1989",
  ISBN =         "1-85196-503-3, 1-85196-005-8 (set)",
  ISBN-13 =      "978-1-85196-503-8, 978-1-85196-005-7 (set)",
  LCCN =         "????",
  MRclass =      "01A75 (68-03)",
  MRnumber =     "998151 (90g:01064)",
  MRreviewer =   "A. D. Booth",
  bibdate =      "Sat Jan 12 22:42:35 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.libris.kb.se:210/libr",
  acknowledgement = ack-nhfb,
  subject =      "Mathematics; Science; 1961; mathematics",
}

@Proceedings{Ercegovac:1989:PSC,
  editor =       "Milo{\v{s}} D. Ercegovac and Earl E. {Swartzlander,
                 Jr.}",
  booktitle =    "Proceedings: 9th Symposium on Computer Arithmetic:
                 September 6--8, 1989, Santa Monica, California, {USA}",
  title =        "Proceedings: 9th Symposium on Computer Arithmetic:
                 September 6--8, 1989, Santa Monica, California, {USA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xv + 247",
  year =         "1989",
  ISBN =         "0-8186-8963-3 (case), 0-8186-5963-7 (microfiche)",
  ISBN-13 =      "978-0-8186-8963-5 (case), 978-0-8186-5963-8
                 (microfiche)",
  LCCN =         "QA 76.9 C62 S95 1989",
  bibdate =      "Thu Sep 01 22:36:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "IEEE catalog no. 89CH2757-3.",
  acknowledgement = ack-nhfb,
  confdate =     "6-8 Sept. 1989",
  conflocation = "Santa Monica, CA, USA",
  confsponsor =  "IEEE; IFIP; Univ. California",
  pubcountry =   "USA",
}

@Proceedings{IEE:1989:EEC,
  editor =       "{IEE}",
  booktitle =    "{ECCTD 89}: European Conference on Circuit Theory and
                 Design, 5--8 September 1989: venue, University of
                 Sussex, Brighton, United Kingdom",
  title =        "{ECCTD} 89: European Conference on Circuit Theory and
                 Design, 5--8 September 1989: venue, University of
                 Sussex, Brighton, United Kingdom",
  publisher =    pub-IEE,
  address =      pub-IEE:adr,
  bookpages =    "xviii + 680",
  year =         "1989",
  ISBN =         "0-85296-383-1",
  ISBN-13 =      "978-0-85296-383-8",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 08:19:35 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Conference publication no. 308.",
  acknowledgement = ack-nhfb,
  confdate =     "5-8 Sept. 1989",
  conflocation = "Brighton, UK",
  confsponsor =  "IEE",
  pubcountry =   "UK",
}

@Proceedings{IEEE:1989:ASF,
  editor =       "{IEEE}",
  booktitle =    "30th annual Symposium on Foundations of Computer
                 Science, October 30--November 1, 1989, Research
                 Triangle Park, North Carolina",
  title =        "30th annual Symposium on Foundations of Computer
                 Science, October 30--November 1, 1989, Research
                 Triangle Park, North Carolina",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xvii + 632",
  year =         "1989",
  CODEN =        "ASFPDV",
  ISBN =         "0-8186-1982-1 (casebound), 0-8186-5982-3
                 (microfiche)",
  ISBN-13 =      "978-0-8186-1982-3 (casebound), 978-0-8186-5982-9
                 (microfiche)",
  ISSN =         "0272-5428",
  LCCN =         "QA 76 S979 1989; TK7885.A1 S92 1989",
  bibdate =      "Thu Dec 3 07:11:18 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Formerly called the Annual Symposium on Switching and
                 Automata Theory. IEEE catalog no. 89CH2808-4. Computer
                 Society order no. 1982.",
  acknowledgement = ack-nhfb,
  keywords =     "computational complexity --- congresses; electronic
                 data processing --- congresses; machine theory ---
                 congresses",
}

@Proceedings{IEEE:1989:PII,
  key =          "IEEE ICCD '89",
  booktitle =    "Proceedings: 1989 {IEEE} International Conference on
                 Computer Design: {VLSI} in Computer and Processors,
                 {ICCD} '89, Hyatt Regency Cambridge, Cambridge,
                 Massachusetts, October 2--4, 1989",
  title =        "Proceedings: 1989 {IEEE} International Conference on
                 Computer Design: {VLSI} in Computer and Processors,
                 {ICCD} '89, Hyatt Regency Cambridge, Cambridge,
                 Massachusetts, October 2--4, 1989",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xvii + 587",
  year =         "1989",
  ISBN =         "0-8186-1971-6 (paper), 0-8186-5971-8 (microfiche),
                 0-8186-8971-4 (case)",
  ISBN-13 =      "978-0-8186-1971-7 (paper), 978-0-8186-5971-3
                 (microfiche), 978-0-8186-8971-0 (case)",
  LCCN =         "TK 7888.4 I23 1989",
  bibdate =      "Wed Dec 13 18:26:58 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 89CH2794-6.",
  acknowledgement = ack-nj,
  confdate =     "2-4 Oct. 1989",
  conflocation = "Cambridge, MA, USA",
  confsponsor =  "IEEE",
}

@Proceedings{MacNair:1989:WSC,
  editor =       "Edward A. MacNair and Kenneth J. Musselman and Philip
                 Heidelberger",
  booktitle =    "{1989 Winter Simulation Conference proceedings:
                 December 4--6, 1989, the Capital Hilton Hotel,
                 Washington, DC}",
  title =        "{1989 Winter Simulation Conference proceedings:
                 December 4--6, 1989, the Capital Hilton Hotel,
                 Washington, DC}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "xx + 1139",
  pages =        "xx + 1139",
  year =         "1989",
  ISBN =         "0-911801-58-8",
  ISBN-13 =      "978-0-911801-58-3",
  LCCN =         "QA76.9.C65 W56 1989",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  note =         "IEEE order number 89CH2778-9.",
  URL =          "http://ieeexplore.ieee.org/servlet/opac?punumber=5823",
  acknowledgement = ack-nhfb,
  bibno =        "76750",
  catcode =      "I.6.3; G.1.6; G.3; G.1.2",
  CRclass =      "I.6.3 Applications; G.1.6 Optimization; G.1.2
                 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Computing Methodologies, SIMULATION AND MODELING,
                 Applications; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization; Mathematics of Computing,
                 PROBABILITY AND STATISTICS; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "algorithms; design; performance",
  guideno =      "1989-12012",
  procdate =     "December 4-6, 1989",
  procloc =      "Washington, D. C.",
  subject =      "I. Computing Methodologies; I.6 SIMULATION AND
                 MODELING; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS; G. Mathematics of Computing; G.3 PROBABILITY
                 AND STATISTICS; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}

@Proceedings{Megiddo:1989:PMP,
  editor =       "N. Megiddo",
  booktitle =    "Progress in Mathematical Programming: Interior-Point
                 and Related Methods",
  title =        "Progress in Mathematical Programming: Interior-Point
                 and Related Methods",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 158",
  year =         "1989",
  ISBN =         "0-387-96847-4",
  ISBN-13 =      "978-0-387-96847-6",
  LCCN =         "QA402.5 .P7851 1989",
  bibdate =      "Sat Nov 09 07:07:37 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the conference held at the Asilomar
                 conference center in Pacific Grove, California, March
                 1--4, 1987.",
  acknowledgement = ack-nhfb,
}

@Book{Srivastava:1989:UFF,
  editor =       "H. M. Srivastava and Shigeyoshi Owa",
  booktitle =    "Univalent functions, fractional calculus, and their
                 applications (K{\=o}riyama, 1988)",
  title =        "Univalent functions, fractional calculus, and their
                 applications ({K}{\=o}riyama, 1988)",
  publisher =    pub-ELLIS-HORWOOD,
  address =      pub-ELLIS-HORWOOD:adr,
  pages =        "404",
  year =         "1989",
  ISBN =         "0-470-21630-1, 0-7458-0701-1",
  ISBN-13 =      "978-0-470-21630-9, 978-0-7458-0701-0",
  LCCN =         "QA331 .U55 1989",
  bibdate =      "Mon Jan 13 09:52:29 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  price =        "UK\pounds 39.95",
  acknowledgement = ack-nhfb,
}

@Proceedings{Cray:1990:PCU,
  editor =       "????",
  key =          "Cray UG '90",
  booktitle =    "Proceedings Cray User Group",
  title =        "Proceedings Cray User Group",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  month =        "Spring",
  year =         "1990",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Thu Sep 08 08:56:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
}

@Proceedings{Mason:1990:AAI,
  editor =       "J. C. Mason and M. G. Cox",
  booktitle =    "{Algorithms for approximation II: based on the
                 proceedings of the Second International Conference on
                 Algorithms for Approximation, held at Royal Military
                 College of Science, Shrivenham, July 1988}",
  title =        "{Algorithms for approximation II: based on the
                 proceedings of the Second International Conference on
                 Algorithms for Approximation, held at Royal Military
                 College of Science, Shrivenham, July 1988}",
  publisher =    pub-CHAPMAN-HALL,
  address =      pub-CHAPMAN-HALL:adr,
  pages =        "514",
  year =         "1990",
  ISBN =         "0-412-34580-3",
  ISBN-13 =      "978-0-412-34580-7",
  LCCN =         "QA221 .I54 1988",
  bibdate =      "Thu Sep 01 23:55:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Algorithms for
                 Approximation (2nd: 1988: Royal Military College of
                 Science, Shrivenham, England)",
  subject =      "Approximation theory; Data processing; Congresses",
  tableofcontents = "Part One: Development of Algorithms / 1 \\
                 1. Spline Approximation / 3 \\
                 E. Arge, M. Dcehlen, T. Lyche and K. Morken /
                 Constrained spline approximation of functions and data
                 based on constrained knot removal / 4 \\
                 G. T. Anthony and M. G. Cox / Near real-time spline
                 fitting of long sequences of uniformly-spaced data / 21
                 \\
                 M. Bozzini and F. de Tisi / An algorithm for knot
                 location in bivariate least squares spline
                 approximation / 30 \\
                 M. G. Cox, P. M. Harris and H. M. Jones / A knot
                 placement strategy for least squares spline fitting
                 based on the use of local polynomial approximations /
                 37 \\
                 G. Opfer / An algorithm for nonlinear splines with
                 non-negativity constraints / 46 \\
                 C. Potier and C. Vercken / Spline curve fitting of
                 digitized contours / 54 \\
                 C. Rabut / A B-spline approximation algorithm for
                 quasi-interpolation or filtering / 62 \\
                 P. W. Smith / On knots and nodes for spline
                 interpolation / 72 \\
                 2. Polynomial and Piecewise Polynomial Approximation /
                 79 \\
                 W. Dahmen / A basis for certain spaces of multivariate
                 polynomials and exponentials / 80 \\
                 F. N. Fritschi / Monotone piecewise cubic data fitting
                 / 99 \\
                 M. Heilmann and M. W. M{\"u}ller / Direct and converse
                 results on simultaneous approximation by the method of
                 Bernstein--Durrmeyer operators / 107 \\
                 A. Iserles, P. E. Koch, S. P. N{\o}rsett and J. M.
                 Sanz-Serna / Orthogonality and approximation in a
                 Sobolev space / 117 \\
                 M. A. Lachance / Piecewise polynomial approximation of
                 polynomial curves / 125 \\
                 E. Quak and L. L. Schumaker / Calculation of the energy
                 of a piecewise polynomial surface / 134 \\
                 3. Interpolation / 145 \\
                 M. D. Buhmann and M. J. D. Powell / Radial basis
                 function interpolation on an infinite regular grid /
                 146 \\
                 L. Brutman / The Fourier operator of even order and its
                 application to an extremum problem in interpolation /
                 170 \\
                 N. Dyn and A. Ron / On multivariate polynomial
                 interpolation / 177 \\
                 N. Dyn, D. Levin and S. Rippen / Algorithms for the
                 construction of data dependent triangulations / 185 \\
                 C. Rademacher and K. Scherer / Algorithms for computing
                 best parametric cubic interpolation / 193 \\
                 4. Smoothing and Constraint Methods / 209 \\
                 M. Von Golitschek and L. L. Schumaker / Data fitting by
                 penalized least squares / 210 \\
                 K. W. Bosworth / A semiinfinite programming algorithm
                 for constrained best approximation / 228 \\
                 M. Bozzini and L. Lenarduzzi / Inference region for a
                 method of local approximation by using the residuals /
                 236 \\
                 5. Complex Approximation / 245 \\
                 G. A. Watson / Numerical methods for Chebyshev
                 approximation of complex-valued functions / 246 \\
                 P. T. P. Tang / A fast algorithm for linear complex
                 Chebyshev approximation / 265 \\
                 Part Two: Applications / 275 \\
                 6. Computer Aided Design and Geometric Modelling / 277
                 \\
                 N. Dyn, J. A. Gregory and D. Levin / Uniform
                 subdivision algorithms for curves and surfaces / 278
                 \\
                 T. B. Boffey, M. G. Cox, L. M. Delves and C. J.
                 Pursglove / Approximation by spheres / 296 \\
                 T. A. Foley / Interpolation of scattered data on a
                 spherical domain / 303 \\
                 A. B. Forbes / Least squares best fit geometric
                 elements / 311 \\
                 W. Freeden and J. C. Mason / Uniform piecewise
                 approximation on the sphere / 320 \\
                 7. Applications in Numerical Analysis / 335 \\
                 L. N. Trefethen / Approximation theory and numerical
                 linear algebra / 336 \\
                 M. Frontini, G. Rodriguez and S. Seatzu / An algorithm
                 for computing minimum norm solutions of the finite
                 moment problem / 361 \\
                 R. H. J. Gmelig Meyling / Numerical solution of the
                 biharmonic equation using different types of bivariate
                 spline functions / 369 \\
                 G. O. Olaofe / Quadrature solution of integral
                 equations: a uniform treatment of Fredholm and Volterra
                 equations / 377 \\
                 G. Walz / Increasing the convergence modulus of an
                 asymptotic expansion: an algorithm for numerical
                 differentiation / 387 \\
                 J. Williams / Approximation and parameter estimation in
                 ordinary differential equations / 395 \\
                 8. Applications in Other Disciplines / 405 \\
                 C. Zala and I. Barrodale / Applications of discrete
                 $L_1$ methods in science and engineering / 406 \\
                 J. C. Mason, A. E. Trefethen and S. J. Wilde /
                 Constrained complex approximation algorithms in
                 communication engineering / 424 \\
                 R. W. Allen and J. G. Metcalfe / Integration of
                 absolute amplitude from a decibel B-spline fit / 449
                 \\
                 M. G. Cox and H. M. Jones / A nonlinear least squares
                 data fitting problem arising in microwave measurement /
                 458 \\
                 J. C. Mason and S. J. Wilde / A complex minimax
                 algorithm for phase-only adaptation in antenna arrays /
                 466 \\
                 Part Three: Catalogue of Algorithms / 477 \\
                 E. Grosse / A catalogue of algorithms for approximation
                 / 479",
}

@Proceedings{Ullrich:1990:CCA,
  editor =       "Christian Ullrich",
  booktitle =    "Contributions to Computer Arithmetic and
                 Self-Validating Numerical Methods. (Proceedings of
                 {SCAN 89}, held in Basel, Oct. 2--6, 1989)",
  title =        "Contributions to Computer Arithmetic and
                 Self-Validating Numerical Methods. (Proceedings of
                 {SCAN} 89, held in Basel, Oct. 2--6, 1989)",
  volume =       "7",
  publisher =    pub-BALTZER,
  address =      pub-BALTZER:adr,
  pages =        "526",
  year =         "1990",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "QA76.9.C62 C664 1990",
  bibdate =      "Sat Nov 29 08:36:57 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
  series =       "IMACS annals on computing and applied mathematics",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic --- congresses; numerical analysis
                 --- congresses",
  xxbooktitle =  "SCAN-89, International Symposium on Scientific
                 Computing, Computer Arithmetic, and Numeric Validation
                 [October 1989, Basel, Switzerland]",
}

@Proceedings{Anonymous:1991:PIS,
  editor =       "Anonymous",
  booktitle =    "Proceedings of the International Symposium on
                 Supercomputing: Fukuoka, Japan, November 6--8, 1991",
  title =        "Proceedings of the International Symposium on
                 Supercomputing: Fukuoka, Japan, November 6--8, 1991",
  publisher =    "Kyushu University Press",
  address =      "Fukuoka, Japan",
  pages =        "iv + 261",
  year =         "1991",
  ISBN =         "4-87378-284-8",
  ISBN-13 =      "978-4-87378-284-3",
  LCCN =         "QA76.88.I 1991",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  searchkey =    "ti:elementary function",
}

@Proceedings{Bowers:1991:CCI,
  editor =       "K. L. (Kenneth L.) Bowers and J. (John) Lund",
  booktitle =    "{Computation and control II: proceedings of the second
                 Bozeman conference, Bozeman, Montana, August 1--7,
                 1990}",
  title =        "{Computation and control II: proceedings of the second
                 Bozeman conference, Bozeman, Montana, August 1--7,
                 1990}",
  volume =       "11",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "369",
  year =         "1991",
  ISBN =         "0-8176-3611-0",
  ISBN-13 =      "978-0-8176-3611-1",
  LCCN =         "TA329 .C644 1991",
  bibdate =      "Wed May 9 08:56:08 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$65.00",
  series =       "Progress in systems and control theory",
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
  subject =      "Engineering mathematics; Congresses; Feedback control
                 systems",
}

@Proceedings{IEEE:1991:PSA,
  editor =       "{IEEE}",
  booktitle =    "Proceedings, Supercomputing '91: Albuquerque, New
                 Mexico, November 18--22, 1991",
  title =        "Proceedings, Supercomputing '91: Albuquerque, New
                 Mexico, November 18--22, 1991",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxiii + 917",
  year =         "1991",
  ISBN =         "0-8186-9158-1 (IEEE case), 0-8186-2158-3 (IEEE paper),
                 0-8186-6158-5 (IEEE microfiche), 0-89791-459-7 (ACM)",
  ISBN-13 =      "978-0-8186-9158-4 (IEEE case), 978-0-8186-2158-1 (IEEE
                 paper), 978-0-8186-6158-7 (IEEE microfiche),
                 978-0-89791-459-8 (ACM)",
  LCCN =         "QA76.5 .S894 1991",
  bibdate =      "Fri Aug 30 08:01:51 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 University of California MELVYL catalog.",
  note =         "ACM order number 415913. IEEE Computer Society Press
                 order number 2158. IEEE catalog number 91CH3058-5.",
  acknowledgement = ack-nhfb,
  classification = "C5440 (Multiprocessor systems and techniques); C5470
                 (Performance evaluation and testing); C6110P (Parallel
                 programming)",
  keywords =     "combinatorial algorithms; data dependence; distributed
                 memory code generation; high school environment;
                 latency tolerance; memory access; numerical algorithms;
                 parallel processing; parallel programming; performance
                 evaluation; performance tools; processor design;
                 program analysis; storage hierarchy optimization;
                 supercomputer benchmarks; supercomputer congresses;
                 supercomputing; system issues",
}

@Proceedings{Koopman:1991:PST,
  editor =       "Philip J. {Koopman, Jr.}",
  booktitle =    "{The proceedings of the second and third annual
                 workshops for the ACM Special Interest Group on Forth:
                 SIGForth '90, February 16--18, 1990, Dallas, Texas
                 \ldots{} SIGForth '91, March 7--9, 1991, San Antonio,
                 Texas}",
  title =        "{The proceedings of the second and third annual
                 workshops for the ACM Special Interest Group on Forth:
                 SIGForth '90, February 16--18, 1990, Dallas, Texas
                 \ldots{} SIGForth '91, March 7--9, 1991, San Antonio,
                 Texas}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "ii + 134",
  year =         "1991",
  ISBN =         "0-89791-462-7",
  ISBN-13 =      "978-0-89791-462-8",
  LCCN =         "QA 76.73 F24 S53 1991",
  bibdate =      "Tue May 04 07:39:28 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ACM order number 817911.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Kornerup:1991:PIS,
  editor =       "Peter Kornerup and David W. Matula",
  booktitle =    "Proceedings: 10th {IEEE} Symposium on Computer
                 Arithmetic: June 26--28, 1991, Grenoble, France",
  title =        "Proceedings: 10th {IEEE} Symposium on Computer
                 Arithmetic: June 26--28, 1991, Grenoble, France",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 282",
  year =         "1991",
  ISBN =         "0-8186-9151-4 (case), 0-8186-6151-8 (microfiche),
                 0-7803-0187-0 (library binding)",
  ISBN-13 =      "978-0-8186-9151-5 (case), 978-0-8186-6151-8
                 (microfiche), 978-0-7803-0187-0 (library binding)",
  LCCN =         "QA76.9.C62 S95 1991",
  bibdate =      "Thu Sep 01 23:18:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Book{Lewin:1991:SPP,
  editor =       "Leonard Lewin",
  booktitle =    "Structural Properties of Polylogarithms",
  title =        "Structural Properties of Polylogarithms",
  volume =       "37",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "xviii + 412",
  year =         "1991",
  ISBN =         "0-8218-1634-9, 1-4704-1264-0 (e-book)",
  ISBN-13 =      "978-0-8218-1634-9, 978-1-4704-1264-7 (e-book)",
  ISSN =         "0076-5376",
  MRclass =      "33E20, 00B15, 11-02, 11F67, 11R70, 11R42, 19F27,
                 33-02, 33-06, 33B99",
  bibdate =      "Fri Jun 16 14:03:50 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Mathematical surveys and monographs",
  acknowledgement = ack-nhfb,
  editor-dates = "22-Jul-1919--13-Aug-2007",
  editor-url =   "https://en.wikipedia.org/wiki/Leonard_Lewin_(telecommunications_engineer)",
  subject =      "Logarithmic functions; Fonctions logarithmes;
                 Mathematics; Algebra; Intermediate; Logarithmic
                 functions; Fonctions logarithmes",
  tableofcontents = "Preface / xiii \\
                 Acknowledgments / xv \\
                 List of Contributors / xvii \\
                 \\
                 1: The Evolution of the Ladder Concept / L. Lewin / 1
                 \\
                 1.1 Early History / 1 \\
                 1.2 Functional Equations / 2 \\
                 1.3 More Recent Numerical Results / 4 \\
                 1.4 Current Developments / 6 \\
                 1.5 Base on the Unit Circle and Clausen Function
                 Ladders / 8 \\
                 References / 9 \\
                 \\
                 2: Dilogarithmic Ladders / L. Lewin / 11 \\
                 2.1 Derivation from Kummer's Functional Equation / 11
                 \\
                 2.2 Relation to Clausen's Function / 15 \\
                 2.3 A Three-Variable Dilogarithmic Functional Equation
                 / 17 \\
                 2.4 Functional Equations in the Complex Plane / 18 \\
                 2.5 Cyclotomic Equations and Rogers' Function / 20 \\
                 2.6 Accessible and Analytic Ladders / 21 \\
                 2.7 Inaccessible Ladders / 23 \\
                 References / 25 \\
                 \\
                 3: Polylogarithmic Ladders / M. Abouzahra and L. Lewin
                 / 27 \\
                 3.1 Kummer's Function and its Relation to the
                 Polylogarithm / 27 \\
                 3.2 Functional Equations for the Polylogarithm / 28 \\
                 3.3 A Generalization of Rogers' Function to the $n$th
                 Order / 31 \\
                 3.4 Ladder Order-Independence on Reduction of Order /
                 33 \\
                 3.5 Generic Ladders for the Base Equation $u^p + u^q =
                 1$ / 34 \\
                 3.6 Examples of Ladders for $n < 3$ / 40 \\
                 3.7 Examples of Ladders for $n < 4$ / 44 \\
                 3.8 Examples of Ladders for $n < 5$ / 45 \\
                 3.9 Polynomial Relations for Ladders / 46 \\
                 References / 47 \\
                 \\
                 4: Ladders in the Trans-Kummer Region / M. Abouzahra
                 and L. Lewin / 49 \\
                 4.1 Ladder Results to $n = 9$ for the Base p / 49 \\
                 4.2 Ladder Results to $n = 9$ for the Base co / 53 \\
                 4.3 Ladder Results to $n = 6$ for the Base 6 / 62 \\
                 4.4 The Nonexistence of Functional Equations at $n = 6$
                 with Arguments Limited to $\pm z^m (1 - z)^r (1 + z)^s$
                 / 65 \\
                 References / 67 \\
                 \\
                 5: Supemumary Ladders / M. Abouzahra and L. Lewin / 69
                 \\
                 5.1 The Concept of Supemumary Results / 69 \\
                 5.2 Supemumary Results for $p = 4$ / 71 \\
                 5.3 Supemumary Results for $p = 5$ / 76 \\
                 5.4 Supemumary Results for $p = 6$ / 78 \\
                 5.5 Supemumary Results for the Equation-family $u^{6m +
                 1} u^{6r - 1}$ = 1 / 80 \\
                 5.6 Supemumary Results for an Irreducible Quintic / 82
                 \\
                 5.7 Supemumary Ladders from a 15-Term Functional
                 Equation / 84 \\
                 5.8 Supemumary Ladders on the Unit Circle / 90 \\
                 References \\
                 6: Functional Equations and Ladders / L. Lewin / 97 \\
                 6.1 New Categories of Functional Equations / 97 \\
                 6.2 The $\rho$-family of Equations / 100 \\
                 6.3 The $\omega$-family of Equations / 109 \\
                 6.4 The $\theta$-family of Equations / 115 \\
                 Acknowledgements / 121 \\
                 References / 121 \\
                 \\
                 7: Multivariable Polylogarithm Identities / G. A. Ray /
                 123 \\
                 7.0 Introduction / 123 \\
                 7.1 A General Identity for the Dilogarithm / 123 \\
                 7.2 A General Identity for the Bloch-Wigner Function /
                 135 \\
                 7.3 A General Identity for the Trilogarithm and
                 $D_3(z)$ / 141 \\
                 7.4 Linear Power Relations among Dilogarithms / 147 \\
                 7.5 Cyclotomic Equations and Bases for Polylogarithm
                 Relations / 154 \\
                 7.6 Mahler's Measure and Salem/Pisot Numbers / 160 \\
                 7.7 Recent Results for Supemumary Ladders / 165 \\
                 References / 168 \\
                 \\
                 8: Functional Equations of Hyperlogarithms / G.
                 Wechsung / 171 \\
                 8.1 Hyperlogarithms / 171 \\
                 8.2 Logarithmic Singularities / 172 \\
                 8.3 The Linear Spaces LI$_n$ and PLI$_n$ / 176 \\
                 8.4 Functional Equations of Hyperlogarithms / 177 \\
                 8.5 A Reduction Problem / 181 \\
                 References / 184 \\
                 \\
                 9: Kummer-Type Functional Equations of Polylogarithms /
                 G. Wechsung / 185 \\
                 9.1 Automorphic Functions / 185 \\
                 9.2 Kummer-Type Functional Equations / 186 \\
                 9.3 A Method to Construct Functional Equations / 191
                 \\
                 9.4 The Nonexistence of a Kummer-Type Functional
                 Equation for $\Li_6$ / 197 \\
                 References / 203 \\
                 \\
                 10: The Basic Structure of Polylogarithmic Equations /
                 Z. Wojtkowiak / 205 \\
                 10.1 Introduction / 205 \\
                 10.2 Canonical Unipotent Connection on
                 $P^1(\mathbb{C})\{a_1, \ldots{}, a_{n+1}\}$ / 211 \\
                 10.3 Horizontal Sections / 213 \\
                 10.4 Easy Lemmas about Monodromy / 215 \\
                 10.5 Functional Equations / 216 \\
                 10.6 Functional Equations of Polylogarithms / 218 \\
                 10.7 Functional Equations of Lower Degree
                 Polylogarithms / 223 \\
                 10.8 Generalized Bloch Groups / 228 \\
                 Acknowledgements / 231 \\
                 References / 231 \\
                 \\
                 11: $K$-Theory, Cyclotomic Equations and Clausen's
                 Function / J. Browkin / 233 \\
                 11.1 Algebraic Background / 233 \\
                 11.2 Analytic Background / 238 \\
                 11.3 $K$-theoretic Background / 248 \\
                 11.4 Examples / 251 \\
                 11.5 Problems and Conjectures / 270 \\
                 References / 272 \\
                 \\
                 12: Function Theory of Polylogarithms / S. Bloch / 275
                 \\
                 \\
                 13: Partition Identities and the Dilogarithm / J. H.
                 Loxton / 287 \\
                 13.1 Introduction / 287 \\
                 13.2 Cyclotomic Equations / 290 \\
                 13.3 Accessible Relations / 291 \\
                 13.4 Partition Identities / 292 \\
                 13.5 Generalisations and Extensions / 297 \\
                 References / 299 \\
                 \\
                 14: The Dilogarithm and Volumes of Hyperbolic Polytopes
                 / R. Kellerhals / 301 \\
                 14.0 Introduction / 301 \\
                 14.1 A Particular Class of Hyperbolic Polytopes / 303
                 \\
                 14.2 The Volume of a rf-Truncated Orthoscheme / 309 \\
                 14.3 Applications / 321 \\
                 14.4 Further Aspects / 328 \\
                 References / 335 \\
                 \\
                 15: Introduction to Higher Logarithms / R. M. Hain and
                 R. MacPherson / 337 \\
                 15.1 The Problem of Generalizing the Logarithm and the
                 Dilogarithm / 337 \\
                 15.2 The Quest for Higher Logarithms / 340 \\
                 15.3 Higher Logarithms / 341 \\
                 15.4 The Higher Logarithm Bicomplex / 343 \\
                 15.5 Multivalued Deligne Cohomology / 346 \\
                 15.6 Higher Logarithms as Deligne Cohomology Classes /
                 350 \\
                 Acknowledgements 3 / 51 \\
                 References / 352 \\
                 \\
                 16: Some Miscellaneous Results / L. Lewin / 355 \\
                 16.1 Clausen's Function and the Di-Gamma Function for
                 Rational Arguments / 355 \\
                 16.2 An Infinite Integral of a Product of Two
                 Polylogarithms / 359 \\
                 16.3 Cyclotomic and Polylogarithmic Equations for a
                 Salem Number / 364 \\
                 16.4 New Functional Equations / 373 \\
                 References / 374 \\
                 \\
                 Appendix A. Special Values and Functional Equations of
                 Polylogarithms / D. Zagier / 377 \\
                 0. Introduction / 377 \\
                 1. The Basic Algebraic Relation and the Definition of
                 $\mathcal{A}_m(F)$ / 378 \\
                 2. Examples of Dilogarithm Relations / 383 \\
                 3. Examples for Higher Order Polylogarithms / 385 \\
                 4. Examples: Ladders / 387 \\
                 5. Existence of Relations among Polylogarithm Values of
                 Arbitrarily High Order / 390 \\
                 6. A Conjecture on Linear Independence / 391 \\
                 7. Functional Equations / 392 \\
                 References / 399 \\
                 \\
                 Appendix B. Summary of the Informal Polylogarithm
                 Workshop, November 17--18, 1990, MIT, Cambridge,
                 Massachusetts / 401 \\
                 R. MacPherson and H. Sah / List of Participants / 401
                 \\
                 Abbreviated Summary / 402 \\
                 Bibliography / 405 \\
                 Index / 409",
}

@Proceedings{EC2:1992:DJN,
  key =          "AEF'92",
  booktitle =    "{Deuxi{\`e}mes journ{\'e}es nationales: Les
                 applications des ensembles flous, en l'honneur du
                 Professeur A. Kaufmann, Nimes, 2--3 novembre 1992,
                 conference scientifique (English: Second national
                 conference: Application of Fuzzy Sets, in honor of
                 Professor A. Kaufman, Nimes, 2--3 November 1992,
                 scientific conference)}",
  title =        "{Deuxi{\`e}mes journ{\'e}es nationales: Les
                 applications des ensembles flous, en l'honneur du
                 Professeur A. Kaufmann, Nimes, 2--3 novembre 1992,
                 conference scientifique (English: Second national
                 conference: Application of Fuzzy Sets, in honor of
                 Professor A. Kaufman, Nimes, 2--3 November 1992,
                 scientific conference)}",
  publisher =    "EC2",
  address =      "Nanterre Cedex, France",
  pages =        "384",
  year =         "1992",
  ISBN =         "2-906899-78-X",
  ISBN-13 =      "978-2-906899-78-0",
  LCCN =         "????",
  bibdate =      "Wed Jan 10 07:40:53 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Richards:1992:HFD,
  editor =       "Donald St P. Richards",
  booktitle =    "{Hypergeometric functions on domains of positivity,
                 Jack polynomials, and applications: proceedings of an
                 AMS Special Session held March 22--23, 1991 in Tampa,
                 Florida}",
  title =        "{Hypergeometric functions on domains of positivity,
                 Jack polynomials, and applications: proceedings of an
                 AMS Special Session held March 22--23, 1991 in Tampa,
                 Florida}",
  volume =       "138",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "x + 259",
  year =         "1992",
  ISBN =         "0-8218-5159-4",
  ISBN-13 =      "978-0-8218-5159-3",
  ISSN =         "0271-4132 (print), 1098-3627 (electronic)",
  LCCN =         "QA353.H9 H97 1992",
  bibdate =      "Sat Oct 30 21:12:24 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Contemporary mathematics",
  acknowledgement = ack-nhfb,
  subject =      "Hypergeometric functions; Congresses",
}

@Book{Adams:1993:ACA,
  editor =       "E. Adams and U. Kulisch",
  booktitle =    "Scientific computing with automatic result
                 verification",
  title =        "Scientific computing with automatic result
                 verification",
  volume =       "189",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "x + 612",
  year =         "1993",
  ISBN =         "0-12-044210-8",
  ISBN-13 =      "978-0-12-044210-2",
  LCCN =         "QA76.S368 1993",
  bibdate =      "Mon Jan 13 09:58:58 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Mathematics in science and engineering",
  acknowledgement = ack-nhfb,
}

@Proceedings{Albrecht:1993:VNT,
  editor =       "R. Albrecht and G. Alefeld and H. J. Stetter",
  booktitle =    "Validation numerics: theory and applications",
  title =        "Validation numerics: theory and applications",
  volume =       "9",
  publisher =    pub-SPRINGER-WIEN,
  address =      pub-SPRINGER-WIEN:adr,
  pages =        "291",
  year =         "1993",
  CODEN =        "COSPDM",
  ISBN =         "0-387-82451-0 (New York), 3-211-82451-0 (Vienna)",
  ISBN-13 =      "978-0-387-82451-2 (New York), 978-3-211-82451-1
                 (Vienna)",
  ISSN =         "0344-8029",
  LCCN =         "QA297 .V27 1993",
  bibdate =      "Wed Oct 13 18:45:11 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Dedicated to Ulrich Kulisch on the occasion of his
                 60th birthday.",
  series =       j-COMPUTING-SUPPLEMENTUM,
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
}

@Proceedings{Allasia:1993:PIJ,
  editor =       "G. Allasia and Luighi Gatteshi and Francesco Lerda",
  booktitle =    "Proceedings of the International Joint Symposium on
                 Special Functions and Artificial Intelligence, (1993:
                 Turin, Italy)",
  title =        "Proceedings of the International Joint Symposium on
                 Special Functions and Artificial Intelligence, (1993:
                 Turin, Italy)",
  volume =       "2(1/4)",
  publisher =    "Baltzer Science Publishers",
  address =      "Amsterdam, The Netherlands",
  pages =        "474",
  year =         "1993",
  ISSN =         "1021-2655",
  LCCN =         "QA297 A614 v. 2, no. 1/4",
  bibdate =      "Sat Oct 30 18:57:57 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Annals of numerical mathematics",
  acknowledgement = ack-nhfb,
}

@Proceedings{Sincovec:1993:PSS,
  editor =       "Richard F. Sincovec and David E. Keyes and Michael R.
                 Leuze",
  booktitle =    "{Proceedings of the Sixth SIAM Conference on Parallel
                 Processing for Scientific Computing, held March 22--24,
                 1993, in Norfolk, VA, USA}",
  title =        "{Proceedings of the Sixth SIAM Conference on Parallel
                 Processing for Scientific Computing, held March 22--24,
                 1993, in Norfolk, VA, USA}",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xix + 1041 + iv",
  year =         "1993",
  ISBN =         "0-89871-315-3",
  ISBN-13 =      "978-0-89871-315-2",
  LCCN =         "QA76.58 .S55 1993 v.1-2",
  bibdate =      "Tue Oct 11 12:21:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Two volumes.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Swartzlander:1993:SCA,
  editor =       "Earl {Swartzlander, Jr.} and Mary Jane Irwin and
                 Graham Jullien",
  booktitle =    "Proceedings: 11th Symposium on Computer Arithmetic,
                 June 29--July 2, 1993, Windsor, Ontario",
  title =        "Proceedings: 11th Symposium on Computer Arithmetic,
                 June 29--July 2, 1993, Windsor, Ontario",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 284",
  year =         "1993",
  ISBN =         "0-7803-1401-8 (softbound), 0-8186-3862-1 (casebound),
                 0-8186-3861-3 (microfiche)",
  ISBN-13 =      "978-0-7803-1401-6 (softbound), 978-0-8186-3862-6
                 (casebound), 978-0-8186-3861-9 (microfiche)",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  LCCN =         "QA 76.9 C62 S95 1993",
  bibdate =      "Thu Sep 01 22:58:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "IEEE Transactions on Computers {\bf 43(8)}, 1994",
  acknowledgement = ack-nhfb,
}

@Proceedings{Brown:1994:PCL,
  editor =       "J. David Brown and Moody T. Chu and Donald C. Ellison
                 and Robert J. Plemmons",
  booktitle =    "{Proceedings of the Cornelius Lanczos International
                 Centenary Conference, Raleigh, North Carolina, December
                 12--17, 1993}",
  title =        "{Proceedings of the Cornelius Lanczos International
                 Centenary Conference, Raleigh, North Carolina, December
                 12--17, 1993}",
  volume =       "73",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "lxv + 644",
  year =         "1994",
  ISBN =         "0-89871-339-0",
  ISBN-13 =      "978-0-89871-339-8",
  LCCN =         "QC19.2 .C67 1993",
  bibdate =      "Wed Jun 8 14:42:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/einstein.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Proceedings in Applied Mathematics",
  acknowledgement = ack-nhfb,
  meetingname =  "Cornelius Lanczos International Centenary Conference
                 (1993:Raleigh, NC)",
  subject =      "Mathematical physics; Congresses; Astrophysics;
                 Mathematics; Lanczos, Cornelius; Physicists; Hungary;
                 Biography; Mathematicians",
  subject-dates = "1893--1974",
  tableofcontents = "The Life and Works of Cornelius Lanczos \\
                 \\
                 A Photographic Essay / / xvii \\
                 Cornelius Lanczos: A Biographical Essay / Barbara
                 Gellai / xxi \\
                 Cornelius Lanczos (1893-1974), and the Hungarian
                 Phenomenon in Science and Mathematics / Peter D. Lax /
                 xlix \\
                 The Roots of Cornelius Lanczos / George Marx / liii \\
                 Reminiscences of Cornelius Lanczos / Jon Todd / lviii
                 \\
                 Published Papers and Books of Cornelius Lanczos / / lx
                 \\
                 \\
                 Plenary Presentations: Computational Mathematics \\
                 \\
                 Lanczos and the FFT: A Discovery Before its Time /
                 James W. Cooley / 3 \\
                 Lanczos Algorithms for Large Scale Symmetric and
                 Nonsymmetric Matrix Eigenvalue Problems / Jane K.
                 Cullum / 11 \\
                 The Look-Ahead Lanczos Process for Nonsymmetric
                 Matrices and its Applications / Roland W Freund / 33
                 \\
                 The Lanczos and Conjugate Gradient Algorithms in Finite
                 Precision Arithmetic / Anne Greenbaum / 49 \\
                 The Lanczos Process and Pade Approximation / Martin H.
                 Gutknecht / 61 \\
                 The Tau Method and the Numerical Solution of
                 Differential Equations: Past Research and Recent
                 Research / Eduardo L. Ortiz / 77 \\
                 Krylov Subspace Processes, Krylov Subspace Methods, and
                 Iteration Polynomials / C. C. Paige / 83 \\
                 Do We Fully Understand the Symmetric Lanczos Algorithm
                 Yet? / Beresford N. Parlett / 93 \\
                 On Generalized Band Matrices and Their Inverses /
                 P{\'a}l R{\'o}sa, Francesco Romani, and Roberto
                 Bevilacqua / 109 \\
                 Theoretical Error Bounds and General Analysis of a Few
                 Lanczos-Type Algorithms / Youcef Saad / 123 \\
                 Lanczos and Linear Systems / G. W. Stewart / 135 \\
                 \\
                 Plenary Presentations: Theoretical Physics and
                 Astrophysics \\
                 \\
                 Integration on the Space of Connections Modulo Gauge
                 Transformations / Abbay Ashtekar, Donald Marolf, and
                 Jose Mourdo / 143 \\
                 Quasiclassical Domains in a Quantum Universe / James B.
                 Hartle / 161 \\
                 Gauge Invariant Energy-Momentum Tensor in Spinar
                 Electrodynamics / D. Petiot and Y. Takahashi / 173 \\
                 $\gamma$-Ray Bursts and Neutron Star Mergers / Tsvi
                 Piran / 187 \\
                 Lanczos's Early Contributions to Relativity and His
                 Relationship with Einstein / John Stachel / 201 \\
                 Topological Roots of Black Hole Entropy / Claudio
                 Teitelboim / 223 \\
                 Variational Principles, Local Symmetries, and Black
                 Hole Entropy / Robert M. Wald / 231 \\
                 \\
                 Mathematics Minisymposia \\
                 \\
                 Eigenvalue Computations: Theory and Algorithms / / 241
                 \\
                 Eigenvalue Computations: Applications / / 249 \\
                 Moments in Numerical Analysis / / 265 \\
                 Iterative Methods for Linear Systems / / 277 \\
                 Least Squares / / 301 \\
                 Software for Lanczos-based Algorithms / / 311 \\
                 Tau Method / / 335 \\
                 Chebyshev Polynomials / / 357 \\
                 Lanczos Methods in Control and Signal Processing / /
                 375 \\
                 Development of the FFT / / 393 \\
                 The FFT in Signal Processing / / 399 \\
                 Wavelets / / 411 \\
                 \\
                 Physics Minisymposia \\
                 \\
                 Computational Magnetohydrodynamics in Astrophysics / /
                 431 \\
                 Numerical Simulations of Collisionless Space Plasmas /
                 / 453 \\
                 Detection of Gravitational Radiation from Astrophysical
                 Sources / / 477 \\
                 Lanczos $H$-tensor / / 489 \\
                 Cosmic Censorship / / 513 \\
                 Cauchy Problem of General Relativity / / 527 \\
                 Black Hole Evaporation and Thermodynamics / / 543 \\
                 The Problem of Time in Quantum Gravity / / 555 \\
                 New Variables and Loop Quantization / / 571 \\
                 Decoherence and the Foundations of Quantum Mechanics /
                 / 589 \\
                 Open Questions in Particle Theory / / 603 \\
                 Supercollider Physics / / 621 \\
                 Symplectic Methods in Physics / / 633",
}

@Proceedings{Cuyt:1994:NNM,
  editor =       "Annie Cuyt",
  booktitle =    "Nonlinear numerical methods and rational approximation
                 {II}",
  title =        "Nonlinear numerical methods and rational approximation
                 {II}",
  volume =       "296",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "xviii + 446",
  year =         "1994",
  ISBN =         "0-7923-2967-8",
  ISBN-13 =      "978-0-7923-2967-1",
  LCCN =         "QA297 .N642 1994",
  bibdate =      "Wed Nov 3 09:30:14 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of an international conference held at the
                 University of Antwerp, Belgium, Sept. 5--11, 1993.",
  series =       "Mathematics and its applications",
  acknowledgement = ack-nhfb,
  keywords =     "approximation theory -- congresses; numerical analysis
                 -- congresses",
}

@Proceedings{Gautschi:1994:MCH,
  editor =       "Walter Gautschi",
  booktitle =    "{Mathematics of computation, 1943--1993: a
                 half-century of computational mathematics: Mathematics
                 of Computation 50th Anniversary Symposium, August
                 9--13, 1993, Vancouver, British Columbia}",
  title =        "{Mathematics of computation, 1943--1993: a
                 half-century of computational mathematics: Mathematics
                 of Computation 50th Anniversary Symposium, August
                 9--13, 1993, Vancouver, British Columbia}",
  volume =       "48",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "xix + 643",
  year =         "1994",
  ISBN =         "0-8218-0291-7, 0-8218-0353-0 (pt. 1), 0-8218-0354-9
                 (pt. 2)",
  ISBN-13 =      "978-0-8218-0291-5, 978-0-8218-0353-0 (pt. 1),
                 978-0-8218-0354-7 (pt. 2)",
  ISSN =         "0160-7634",
  LCCN =         "QA1 .A56 v.48 1994; QA297.M385 1993",
  MRclass =      "00B25 (11-06 65-06)",
  MRnumber =     "95j:00014",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/l/lehmer-derrick-henry.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1940.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  note =         "See also SIAM Review, September 1995, {\bf 37}(3), p.
                 483.",
  series =       "Proceedings of Symposia in Applied Mathematics",
  acknowledgement = ack-nhfb,
  author-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
  tableofcontents = "Preface / xi \\
                 Mathematics of Computation: A brief history / Eugene
                 Isaacson / xvii \\
                 \\
                 Part I. Symposium on Numerical Analysis \\
                 \\
                 Invited Papers \\
                 \\
                 On the development of multigrid methods and their
                 analysis / James H. Bramble / 5 \\
                 An introduction to inverse problems / Margaret Cheney /
                 21 \\
                 Algorithms for unconstrained optimization: A review of
                 recent developments / Donald Goldfarb / 33 \\
                 A survey of componentwise perturbation theory in
                 numerical linear algebra / Nicholas J. Higham / 49 \\
                 Numerical evaluation of special functions / D. W.
                 Lozier and F. W. J. Olver / 79 \\
                 A survey of numerical cubature over triangles / J. N.
                 Lyness and Ronald Cools / 127 \\
                 New trends in the use and analysis of integral
                 equations / J. C. Nedelec / 151 \\
                 Applications of multivariate splines / Larry L.
                 Schumaker / 177 \\
                 Initial value problems for ordinary differential
                 equations: Development of ideas, techniques, and
                 implementation / Hans J. Stetter / 205 \\
                 Multiresolution methods for partial differential
                 equations / Roger Temam / 225 \\
                 \\
                 Contributed Papers \\
                 \\
                 A comparison of techniques for solving ill-conditioned
                 problems arising from the immersed boundary method /
                 Loyce Adams and Zhiyun Yang / 243 \\
                 A mixed spectral-collocation and operator splitting
                 method for the Wigner-Poisson equation / Anton Arnold /
                 249 \\
                 Finite volume methods for irregular one-dimensional
                 grids / M. J. Berger, R. J. Leveque, and L. G. Stern /
                 255 \\
                 Linear rational interpolation of continuous functions
                 over an interval / Jean-Paul Berrut / 261 \\
                 A von Neumann reflection for the 2-D Burgers equation /
                 M. Brio and J. K. Hunter / 265 \\
                 Slow evolution from the boundary: A new stabilizing
                 constraint in ill-posed continuation problems / Alfred
                 S. Carasso / 269 \\
                 A finite element method for the 2D drift-diffusion
                 semiconductor model / Zhangxin Chen / 275 \\
                 Splitting functions and numerical analysis of WR-type
                 methods for evolutionary and stationary problems / S.
                 De Marchi, M. Vianello, and R. Zanovello / 281 \\
                 Error estimates for a quadrature rule for Cauchy
                 principal value integrals / Kai Diethelm / 287 \\
                 A numerical radius approach to stable difference
                 schemes for parabolic systems / Moshe Goldberg / 293
                 \\
                 An extension of the Olver-Sookne method for the
                 solution of second-order linear difference equations /
                 Takemitsu Hasegawa and Tatsuo Torii / 297 \\
                 The Faber polynomials for circular arcs / Matthew He /
                 301 \\
                 Finite element approximation for optimal control of
                 electrically conducting fluid flows / L. S. Hou and S.
                 S. Ravindran / 305 \\
                 ADI methods for heat equations with discontinuities
                 along an arbitrary interface / Zhilin Li and Anita Mayo
                 / 311 \\
                 Eigenvalue approximation of Fredholm integral operators
                 / E. B. Lin / 317 \\
                 Spectral methods for singular perturbation problems /
                 Wenbin Liu and Tao Tang / 323 \\
                 A quaternion-Jacobi method for symmetric matrices /
                 Niloufer Mackey / 327 \\
                 On constructing Chebyshev series solutions of
                 differential equations / Allan J. MacLeod / 333 \\
                 Multiquadric collocation methods in the numerical
                 solution of Volterra integral and integro-differential
                 equations / Athena Makroglou / 337 \\
                 Methods for solving large eigenvalue problems
                 associated with configuration interaction electronic
                 structure calculations / Kristyn J. Maschhoff / 343 \\
                 Computing limiting normals to real surfaces / Donal
                 O'Shea and Les Wilson / 349 \\
                 Orthogonal spline collocation solution of nonlinear
                 Schr{\"o}dinger equations / Mark P. Robinson / 355 \\
                 Who invented the computer? The debate from the
                 viewpoint of computer architecture / Ra{\'u}l Rojas /
                 361 \\
                 Locking and boundary layer effects in the finite
                 element approximation of the Reissner--Mindlin plate
                 model / Christoph Schwab and Manil Suri / 367 \\
                 Efficient spectral Galerkin methods for some elliptic
                 problems / Jie Shen / 373 \\
                 Periodic solutions of higher-order difference equations
                 in two independent variables / Qin Sheng and Ravi P.
                 Agarwal / 377 \\
                 Front tracking based on high-resolution wave
                 propagation methods / Keh-Ming Shyue / 383 \\
                 Time-splitting methods for nonhomogeneous conservation
                 laws / Tao Tang and Zhen-Huan Teng / 389 \\
                 Numerical aspects of uniform Airy-type asymptotic
                 expansions / N. M. Temme / 395 \\
                 Local dynamics and bifurcation consistencies of
                 continuous-time dynamical systems and their numerical
                 discretizations / Xin Wang, Edward K. Blum, and Qingnan
                 Li / 399 \\
                 Computing integrals of the complex error function / J.
                 A. C. Weideman / 403 \\
                 Quadratures for improper integrals and their
                 applications in integral equations / Yuesheng Xu and
                 Yunhe Zhao / 409 \\
                 Spline harmonic analysis and wavelet bases / Valery A.
                 Zheludev / 415 \\
                 \\
                 Part II. Minisymposium on Computational Number Theory
                 Dedicated to the memory of Derrick Henry Lehmer \\
                 \\
                 Invited Papers \\
                 \\
                 Algorithms for quadratic orders / Ingrid Biehl and
                 Johannes Buchmann / 425 \\
                 Analytic computations in number theory / Andrew M.
                 Odlyzko / 451 \\
                 The number field sieve / Carl Pomerance / 465 \\
                 Factoring integers before computers / H. C. Williams
                 and J. O. Shallit / 481 \\
                 \\
                 Contributed Papers \\
                 \\
                 Explicit bounds for primes in residue classes / Eric
                 Bach and Jonathan Sorenson / 535 \\
                 Ramanujan and Euler's constant / Richard P. Brent / 541
                 \\
                 Congruential sieves on FPGA computers / Nathan D.
                 Bronson and Duncan A. Buell / 547 \\
                 Lehmer pairs of zeros and the Riemann $\xi$-function /
                 George Csordas, Wayne Smith, and Richard S. Varga / 553
                 \\
                 A record Aliquot sequence / Andrew W. P. Guy and
                 Richard K. Guy / 557 \\
                 Implications of computational mathematics for the
                 philosophy of mathematics / Andrew J. Lazarus / 561 \\
                 Square roots of products of algebraic numbers / Peter
                 L. Montgomery / 567 \\
                 A locally parameterized version of Lehmer's problem /
                 Gary A. Ray / 573 \\
                 A new method for finding amicable pairs / H. J. J. te
                 Riele / 577 \\
                 Generalized Fermat numbers / Hans Riesel and Anders
                 Bj{\"o}rn / 583 \\
                 Evaluation of $\zeta_K(2)$ for some totally real
                 algebraic number fields K of degree 9 / Kisao Takeuchi
                 / 589 \\
                 The period of the Bell exponential integers modulo a
                 prime / Samuel S. Wagstaff, Jr. / 595 \\
                 Computing invariant polynomials of $p$-adic reflection
                 groups / Changsheng Xu / 599 \\
                 Author Index / 603 \\
                 Subject Index / 619",
}

@Proceedings{Mudge:1994:PTS,
  editor =       "Trevor N. Mudge and Bruce D. Shriver",
  booktitle =    "{Proceedings of the Twenty-Seventh Hawaii
                 International Conference on System Sciences Vol. I:
                 Architecture}",
  title =        "{Proceedings of the Twenty-Seventh Hawaii
                 International Conference on System Sciences Vol. I:
                 Architecture}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "various",
  year =         "1994",
  ISBN =         "0-8186-5050-8 (paper), 0-8186-5051-6 (microfiche)",
  ISBN-13 =      "978-0-8186-5050-5 (paper), 978-0-8186-5051-2
                 (microfiche)",
  LCCN =         "????",
  bibdate =      "Mon Jan 13 10:02:18 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "First of five volumes. IEEE Catalog No. 94TH0607-2.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Zahar:1994:ACF,
  editor =       "R. V. M. (Ramsay Vincent Michael) Zahar",
  booktitle =    "{Approximation and computation: a festschrift in honor
                 of Walter Gautschi: proceedings of the Purdue
                 conference, December 2--5, 1993}",
  title =        "{Approximation and computation: a festschrift in honor
                 of Walter Gautschi: proceedings of the Purdue
                 conference, December 2--5, 1993}",
  volume =       "119",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "xlvi + 591",
  year =         "1994",
  ISBN =         "0-8176-3753-2",
  ISBN-13 =      "978-0-8176-3753-8",
  LCCN =         "QA221 .A634 1994",
  bibdate =      "Wed May 9 09:01:57 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series of numerical mathematics",
  acknowledgement = ack-nhfb,
  subject =      "Approximation theory; Congresses; Orthogonal
                 polynomials; Numerical integration; Functions,
                 Special",
}

@Proceedings{Knowles:1995:PSC,
  editor =       "Simon Knowles and William H. McAllister",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, July 19--21, 1995, Bath, England",
  title =        "Proceedings of the 12th Symposium on Computer
                 Arithmetic, July 19--21, 1995, Bath, England",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xvi + 252",
  year =         "1995",
  ISBN =         "0-8186-7089-4 (paperback), 0-8186-7089-4 (case),
                 0-8186-7149-1 (microfiche), 0-8186-7089-4 (softbound),
                 0-7803-2949-X (casebound)",
  ISBN-13 =      "978-0-8186-7089-3 (paperback), 978-0-8186-7089-3
                 (case), 978-0-8186-7149-4 (microfiche),
                 978-0-8186-7089-3 (softbound), 978-0-7803-2949-2
                 (casebound)",
  LCCN =         "QA 76.9 C62 S95 1995",
  bibdate =      "Sun Mar 29 08:48:20 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Singh:1995:CRT,
  editor =       "Avtar Singh",
  booktitle =    "Conference record of the Twenty-Ninth Asilomar
                 Conference on Signals, Systems \& Computers: October
                 30--November 1, 1995 Pacific Grove, California",
  title =        "Conference record of the Twenty-Ninth Asilomar
                 Conference on Signals, Systems \& Computers: October
                 30--November 1, 1995 Pacific Grove, California",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "various",
  year =         "1995",
  ISBN =         "0-8186-7370-2",
  ISBN-13 =      "978-0-8186-7370-2",
  LCCN =         "TK7801 .A83 1995",
  bibdate =      "Sun Mar 29 08:51:26 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Two volumes.",
  acknowledgement = ack-nhfb,
}

@Proceedings{LakshmanYN:1996:IPI,
  editor =       "{Lakshman Y.N.}",
  booktitle =    "{ISSAC '96: Proceedings of the 1996 International
                 Symposium on Symbolic and Algebraic Computation, July
                 24--26, 1996, Zurich, Switzerland}",
  title =        "{ISSAC '96: Proceedings of the 1996 International
                 Symposium on Symbolic and Algebraic Computation, July
                 24--26, 1996, Zurich, Switzerland}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xvii + 313",
  year =         "1996",
  ISBN =         "0-89791-796-0",
  ISBN-13 =      "978-0-89791-796-4",
  LCCN =         "QA 76.95 I59 1996",
  bibdate =      "Thu Mar 12 08:00:14 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  sponsor =      "ACM; Special Interest Group in Symbolic and Algebraic
                 Manipulation (SIGSAM). ACM; Special Interest Group on
                 Numerical Mathematics (SIGNUM).",
}

@Book{Berggren:1997:PSB,
  editor =       "Lennart Berggren and Jonathan M. Borwein and Peter B.
                 Borwein",
  booktitle =    "Pi, a source book",
  title =        "Pi, a source book",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xix + 716",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-1-4757-2736-4",
  ISBN =         "0-387-94924-0, 1-4757-2736-4 (e-book), 1-4757-2738-0
                 (print), 3-540-94924-0",
  ISBN-13 =      "978-0-387-94924-6, 978-1-4757-2736-4 (e-book),
                 978-1-4757-2738-8 (print), 978-3-540-94924-4",
  LCCN =         "QA484 .P5 1997",
  bibdate =      "Fri Sep 2 17:41:50 MDT 2022",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib;
                 z3950.loc.gov:7090/Voyager",
  abstract =     "The aim of this book is to provide a complete history
                 of pi from the dawn of mathematical time to the
                 present. The story of pi reflects the most seminal, the
                 most serious and sometimes the silliest aspects of
                 mathematics, and a surprising amount of the most
                 important mathematics and mathematicians have
                 contributed to its unfolding. Pi is one of the few
                 concepts in mathematics whose mention evokes a response
                 of recognition and interest in those not concerned
                 professionally with the subject. Yet, despite this, no
                 source book on pi has been published. One of the
                 beauties of the literature on pi is that it allows for
                 the inclusion of very modern, yet still accessible,
                 mathematics. Mathematicians and historians of
                 mathematics will find this book indispensable. Teachers
                 at every level from the seventh grade onward will find
                 here ample resources for anything from special topic
                 courses to individual talks and special student
                 projects. The literature on pi included in this source
                 book falls into three classes: first a selection of the
                 mathematical literature of four millennia, second a
                 variety of historical studies or writings on the
                 cultural meaning and significance of the number, and
                 third, a number of treatments on pi that are fanciful,
                 satirical and/or whimsical.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject =      "Pi; Pi (Le nombre); Pi.; Pi (le nombre)",
  tableofcontents = "Preface / v \\
                 \\
                 Acknowledgments / ix \\
                 \\
                 Introduction / xvii \\
                 \\
                 1. The Rhind Mathematical Papyrus-Problem 50 ($\approx$
                 1650 B.C.) / A problem dealing with the area of a round
                 field of given diameter / 1 \\
                 \\
                 2. Engels. Quadrature of the Circle in Ancient Egypt
                 (1977) / A conjectural explanation of how the
                 mathematicians of ancient Egypt approximated the area
                 of a circle / 3 \\
                 \\
                 3. Archimedes. Measurement of a Circle ($\approx$ 250
                 BC) / The seminal work in which Archimedes presents the
                 first true algorithm for $\pi$ / 7 \\
                 \\
                 4. Phillips. Archimedes the Numerical Analyst (1981) /
                 A summary of Archimedes' work on the computation of
                 $\pi$ using modern notation / 15 \\
                 \\
                 5. Lam and Ang. Circle Measurements in Ancient China
                 (1986) / This paper discusses and contains a
                 translation of Liu Hui's (3rd century) method for
                 evaluating $\pi$ and also examines values for $\pi$
                 given by Zu Chongzhi (429--500) / 20 \\
                 \\
                 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane
                 and Solid Figures ($\approx$ 850) / This extract gives
                 an explicit statement and proof that the ratio of the
                 circumference to the diameter is constant / 36 \\
                 \\
                 7. M{\=a}dhava. The Power Series for Arctan and Pi
                 ($\approx$ 1400) / These theorems by a fifteenth
                 century Indian mathematician give Gregory's series for
                 arctan with remainder terms and Leibniz's series for
                 $\pi$ / 45 \\
                 \\
                 8. Hope-Jones. Ludolph (or Ludolff or Lucius) van
                 Ceulen (1938) / Correspondence about van Ceulen's
                 tombstone in reference to it containing some digits of
                 $\pi$ / 51 \\
                 \\
                 9. Vi{\'e}te. Variorum de Rebus Mathematicis Reponsorum
                 Liber VII (1593) / Two excerpts. One containing the
                 first infinite expression of $\pi$, obtained by
                 relating the area of a regular $2n$-gon to that of a
                 regular $n$-gon / 53 \\
                 \\
                 10. Wallis. Computation of $\pi$ by Successive
                 Interpolations (1655) / How Wallis derived the infinite
                 product for $\pi$ that bears his name / 68 \\
                 \\
                 11. Wallis. Arithmetica Infinitorum (1655) / An excerpt
                 including Prop. 189, 191 and an alternate form of the
                 result that gives Wm. Brounker's continued fraction
                 expression for $4/\pi$ / 78 \\
                 \\
                 12. Huygens. De Circuli Magnitudine Inventa (1724) /
                 Huygens's proof of W. Snell's discovery of improvements
                 in Archimedes' method of estimating the lengths of
                 circular arcs / 81 \\
                 \\
                 13. Gregory. Correspondence with John Collins (1671) /
                 A letter to Collins in which he gives his series for
                 arctangent, carried to the ninth power. / 87 \\
                 \\
                 14. Roy. The Discovery of the Series Formula for $\pi$
                 by Leibniz, Gregory, and Nilakantha (1990) / A
                 discussion of the discovery of the series $\pi/4 = 1 -
                 1/3 + 1/5, \cdots{}$ / 92 \\
                 \\
                 15. Jones. The First Use of $\pi$ for the Circle Ratio
                 (1706) / An excerpt from Jones' book, the Synopsis
                 Palmariorum Matheseos: or, a New Introduction to the
                 Mathematics, London, 1706 / 108 \\
                 \\
                 16. Newton. Of the Method of Fluxions and Infinite
                 Series (1737) / An excerpt giving Newton's calculation
                 of $\pi$ to 16 decimal places / 110 \\
                 \\
                 17. Euler. Chapter 10 of Introduction to Analysis of
                 the Infinite (On the Use of the Discovered Fractions to
                 Sum Infinite Series) (1748) / This includes many of
                 Euler's infinite series for $\pi$ and powers of $\pi$ /
                 112 \\
                 \\
                 18. Lambert. M{\'e}moire Sur Quelques
                 Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s
                 Transcendentes Circulaires et Logarithmiques (1761) /
                 An excerpt from Lambert's original proof of the
                 irrationality of $\pi$ / 129 \\
                 \\
                 19. Lambert. Irrationality of $\pi$ (1969) / A
                 translation and Struik's discussion of Lambert's proof
                 of the irrationality of $\pi$ / 141 \\
                 \\
                 20. Shanks. Contributions to Mathematics Comprising
                 Chiefly of the Rectification of the Circle to 607
                 Places of Decimals (1853) / Pages from Shank's report
                 of his monumental hand calculation of $\pi$ / 147 \\
                 \\
                 21. Hermite. Sur La Fonction Exponentielle (1873) / The
                 first proof of the transcendence of $e$ / 162 \\
                 \\
                 22. Lindemann. Ueber die Zahl $\pi$ (1882) / The first
                 proof of the transcendence of $\pi$ / 194 \\
                 \\
                 23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die
                 Ludolphsche Zahl'' (1885) / Weierstrass' proof of the
                 transcendence of $\pi$ / 207 \\
                 \\
                 24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und
                 $\pi$ (1893) / Hilbert's short and elegant
                 simplification of the transcendence proofs for $e$ and
                 $\pi$ / 226 \\
                 \\
                 25. Goodwin. Quadrature of the Circle (1894) / The
                 dubious origin of the attempted legislation of the
                 value of $\pi$ in Indiana / 230 \\
                 \\
                 26. Edington. House Bill No. 246, Indiana State
                 Legislature, 1897 (1935) / A summary of the action
                 taken by the Indiana State Legislature to fix the value
                 of $\pi$ (including a copy of the actual bill that was
                 proposed) / 231 \\
                 \\
                 27. Singmaster. The Legal Values of Pi (1985) / A
                 history of the attempt by Indiana to legislate the
                 value of $\pi$ / 236 \\
                 \\
                 28. Ramanujan. Squaring the Circle (1913) / A geometric
                 approximation to $\pi$ / 240 \\
                 \\
                 29. Ramanujan. Modular Equations and Approximations to
                 $\pi$ (1914) / Ramanujan's seminal paper on $\pi$ that
                 includes a number of striking series and algebraic
                 approximations / 241 \\
                 \\
                 30. Watson. The Marquis and the Land Agent: A Tale of
                 the Eighteenth Century (1933) / A Presidential address
                 to the Mathematical Association in which the author
                 gives an account of ``some of the elementary work on
                 arcs and ellipses and other curves which led up to the
                 idea of inverting an elliptic integral, and so laying
                 the foundations of elliptic functions and doubly
                 periodic functions generally.'' / 258 \\
                 \\
                 31. Ballantine. The Best (?) Formula for Computing
                 $\pi$ to a Thousand Places (1939) / An early attempt to
                 orchestrate the calculation of $\pi$ more cleverly /
                 271 \\
                 \\
                 32. Birch. An Algorithm for Construction of Arctangent
                 Relations (1946) / The object of this note is to
                 express $\pi / 4 $ as a sum of arctan relations in
                 powers of 10 / 274 \\
                 \\
                 33. Niven. A Simple Proof that $\pi$ Is Irrational
                 (1947) / A very concise proof of the irrationality of
                 $\pi$ / 276 \\
                 \\
                 34. Reitwiesner. An ENIAC Determination of $\pi$ and
                 $e$ to 2000 Decimal Places (1950) / One of the first
                 computer-based computations / 277 \\
                 \\
                 35. Schepler. The Chronology of Pi (1950) / A fairly
                 reliable outline of the history of $\pi$ from 3000 BC
                 to 1949 / 282 \\
                 \\
                 36. Mahler. On the Approximation of $\pi$ (1953) /
                 ``The aim of this paper is to determine an explicit
                 lower bound free of unknown constants for the distance
                 of $\pi$ from a given rational or algebraic number'' /
                 306 \\
                 \\
                 37. Wrench, Jr. The Evolution of Extended Decimal
                 Approximations to $\pi$ (1960) / A history of the
                 calculation of the digits of $\pi$ to 1960 \\
                 \\
                 38. Shanks and Wrench, Jr. Calculation of $\pi$ to
                 100,000 Decimals (1962) / A landmark computation of
                 $\pi$ to more than 100,000 places / 326 \\
                 \\
                 39. Sweeny. On the Computation of Euler's Constant
                 (1963) / The computation of Euler's constant to 3566
                 decimal places / 350 \\
                 \\
                 40. Baker. Approximations to the Logarithms of Certain
                 Rational Numbers (1964) / The main purpose of this deep
                 and fundamental paper is to ``deduce results concerning
                 the accuracy with which the natural logarithms of
                 certain rational numbers may be approximated by
                 rational numbers, or, more generally, by algebraic
                 numbers of bounded degree.'' / 359 \\
                 \\
                 41. Adams. Asymptotic Diophantine Approximations to $E$
                 (1966) / An asymptotic estimate for the rational
                 approximation to $e$ which disproves the conjecture
                 that $e$ behaves like almost all numbers in this
                 respect / 368 \\
                 \\
                 42. Mahler. Applications of Some Formulae by Hermite to
                 the Approximations of Exponentials of Logarithms (1967)
                 / An important extension of Hilbert's approach to the
                 study of transcendence / 372 \\
                 \\
                 43. Eves. In Mathematical Circles; A Selection of
                 Mathematical Stories and Anecdotes (excerpt) (1969) / A
                 collection of mathematical stories and anecdotes about
                 $\pi$ / 400 \\
                 \\
                 44. Eves. Mathematical Circles Revisited; A Second
                 Collection of Mathematical Stories and Anecdotes
                 (excerpt) (1971) / A further collection of mathematical
                 stories and anecdotes about $\pi$ / 402 \\
                 \\
                 45. Todd. The Lemniscate Constants (1975) / A unifying
                 account of some of the methods used for computing the
                 lemniscate constants / 412 \\
                 \\
                 46. Salamin. Computation of r Using
                 Arithmetic-Geometric Mean (1976) / The first
                 quadratically converging algorithm for $\pi$ based on
                 Gauss's AGM and on Legendre's relation for elliptic
                 integrals / 418 \\
                 \\
                 47. Brent. Fast Multiple-Precision Evaluation of
                 Elementary Functions (1976) / ``This paper contains the
                 `Gauss-Legendre' method and some different algorithms
                 for log and exp (using Landen transformations).'' / 424
                 \\
                 \\
                 48. Beukers. A Note on the Irrationality of $\zeta(2)$
                 and $\zetq(3)$ (1979) / A short and elegant recasting
                 of Ap{\'e}ry's proof of the irrationality of $\zeta(3)$
                 (and $\zeta(2)$) / 434 \\
                 \\
                 49. van der Poorten. A Proof that Euler Missed \ldots{}
                 Ap{\'e}ry's Proof of the Irrationality of $\zeta(3)$
                 (1979) / An illuminating account of Ap{\'e}ry's
                 astonishing proof of the irrationality of $\zeta(3)$ /
                 439 \\
                 \\
                 50. Brent and McMillan. Some New Algorithms for
                 High-Precision Computation of Euler's Constant (1980) /
                 Several new algorithms for high precision calculation
                 of Euler's constant, including one which was used to
                 compute 30,100 decimal places / 448 \\
                 \\
                 51. Apostol. A Proof that Euler Missed: Evaluating
                 $\zeta(2)$ the Easy Way (1983) / This note shows that
                 one of the double integrals considered by Beukers ([48]
                 in the table of contents) can be used to establish
                 directly that $\zeta(2) = \pi / 6$ / 456 \\
                 \\
                 52. O'Shaughnessy. Putting God Back in Math (1983) / An
                 article about the Institute of Pi Research, an
                 organization that ``pokes fun at creationists by
                 pointing out that even the Bible makes mistakes.'' /
                 458 \\
                 \\
                 53. Stern. A Remarkable Approximation to $\pi$ (1985) /
                 Justification of the value of $\pi$ in the Bible
                 through numerological interpretations / 460 \\
                 \\
                 54. Newman and Shanks. On a Sequence Arising in Series
                 for $\pi$ (1984) / More connections between $\pi$ and
                 modular equations / 462 \\
                 \\
                 55. Cox. The Arithmetic-Geometric Mean of Gauss (1984)
                 / An extensive study of the complex analytic properties
                 of the AGM / 481 \\
                 \\
                 56. Borwein and Borwein. The Arithmetic-Geometric Mean
                 and Fast Computation of Elementary Functions (1984) /
                 The relationship between the AGM iteration and fast
                 computation of elementary functions (one of the
                 by-products is an algorithm for $\pi$) / 537 \\
                 \\
                 57. Newman. A Simplified Version of the Fast Algorithms
                 of Brent and Salamin (1984) / Elementary algorithms for
                 evaluating $e^x$ and $\pi$ using the Gauss AGM without
                 explicit elliptic function theory / 553 \\
                 \\
                 58. Wagon. Is Pi Normal? (1985) / A discussion of the
                 conjecture that $\pi$ has randomly distributed digits /
                 557 \\
                 \\
                 59. Keith. Circle Digits: A Self-Referential Story
                 (1986) / A mnemonic for the first 402 decimal places of
                 $\pi$ / 560 \\
                 \\
                 60. Bailey. The Computation of $\pi$ to 29,360,000
                 Decimal Digits Using Borweins' Quartically Convergent
                 Algorithm (1988) / The algorithms used, both for $\pi$
                 and for performing the required multiple-precision
                 arithmetic / 562 \\
                 \\
                 61. Kanada. Vectorization of Multiple-Precision
                 Arithmetic Program and 201,326,000 Decimal Digits of 1
                 Calculation (1988) / Details of the computation and
                 statistical tests of the first 200 million digits of
                 $\pi$ / 576 \\
                 \\
                 62. Borwein and Borwein. Ramanujan and Pi (1988) / This
                 article documents Ramanujan's life, his ingenious
                 approach to calculating $\pi$, and how his approach is
                 now incorporated into modern computer algorithms / 588
                 \\
                 \\
                 63. Chudnovsky and Chudnovsky. Approximations and
                 Complex Multiplication According to Ramanujan (1988) /
                 This excerpt describes ``Ramanujan's original quadratic
                 period--quasiperiod relations for elliptic curves with
                 complex multiplication and their applications to
                 representations of fractions of $\pi$ and other
                 logarithms in terms of rapidly convergent nearly
                 integral (hypergeometric) series.'' / 596 \\
                 \\
                 64. Borwein, Borwein and Bailey. Ramanujan, Modular
                 Equations, and Approximations to Pi or How to Compute
                 One Billion Digits of Pi (1989) / An exposition of the
                 computation of $\pi$ using mathematics rooted in
                 Ramanujan's work / 623 \\
                 \\
                 65. Borwein, Borwein and Dilcher. Pi, Euler Numbers,
                 and Asymptotic Expansions (1989) / An explanation as to
                 why the slowly convergent Gregory series for $\pi$,
                 truncated at 500,000 terms, gives $\pi$ to 40 places
                 with only the 6th, 17th, 18th, and 29th places being
                 incorrect / 642 \\
                 \\
                 66. Beukers, B{\'e}zivin, and Robba. An Alternative
                 Proof of the Lindemann--Weierstrass Theorem (1990) /
                 The Lindemann--Weierstrass theorem as a by-product of a
                 criterion for rationality of solutions of differential
                 equations / 649 \\
                 \\
                 67. Webster. The Tail of Pi (1991) / Various anecdotes
                 about $\pi$ from the 14th annual IMO Lecture to the
                 Royal Society / 654 \\
                 \\
                 68. Eco. An excerpt from Foucault's Pendulum (1993) /
                 ``The unnumbered perfection of the circle itself.'' /
                 658 \\
                 \\
                 69. Keith. Pi Mnemonics and the Art of Constrained
                 Writing (1996) / A mnemonic for $\pi$ based on Edgar
                 Allen Poe's poem ``The Raven.'' / 659 \\
                 \\
                 70. Bailey, Borwein, and Plouffe. On the Rapid
                 Computation of Various Polylogarithmic Constants (1996)
                 / A fast method for computing individual digits of
                 $\pi$ in base 2 / 663 \\
                 Appendix I --- On the Early History of Pi / 677 \\
                 \\
                 Appendix II --- A Computational Chronology of Pi / 683
                 \\
                 \\
                 Appendix III --- Selected Formulae for Pi / 686 \\
                 \\
                 Bibliography / 690 \\
                 \\
                 Credits / 697 \\
                 \\
                 Index / 701",
}

@Proceedings{Boisvert:1997:QNS,
  editor =       "Ronald F. Boisvert",
  booktitle =    "Quality of Numerical Software: Assessment and
                 Enhancement. {Proceedings of the IFIP TC2/WG2.5 Working
                 Conference on the Quality of Numerical Software,
                 Assessment and Enhancement, Oxford, United Kingdom,
                 8--12 July 1996}",
  title =        "Quality of Numerical Software: Assessment and
                 Enhancement. {Proceedings of the IFIP TC2/WG2.5 Working
                 Conference on the Quality of Numerical Software,
                 Assessment and Enhancement, Oxford, United Kingdom,
                 8--12 July 1996}",
  publisher =    pub-CHAPMAN-HALL,
  address =      pub-CHAPMAN-HALL:adr,
  pages =        "vii + 384",
  year =         "1997",
  ISBN =         "0-412-80530-8",
  ISBN-13 =      "978-0-412-80530-1",
  LCCN =         "QA297 .I35 1996",
  bibdate =      "Fri Jul 09 05:58:30 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Lang:1997:ISC,
  editor =       "Tomas Lang and Jean-Michel Muller and Naofumi Takagi",
  booktitle =    "13th {IEEE} Symposium on Computer Arithmetic:
                 proceedings, July 6--9, 1997, Asilomar, California,
                 {USA}",
  title =        "13th {IEEE} Symposium on Computer Arithmetic:
                 proceedings, July 6--9, 1997, Asilomar, California,
                 {USA}",
  volume =       "13",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 291",
  year =         "1997",
  ISBN =         "0-8186-7846-1, 0-8186-7847-X, 0-8186-7848-8",
  ISBN-13 =      "978-0-8186-7846-2, 978-0-8186-7847-9,
                 978-0-8186-7848-6",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62 S95 1997",
  bibdate =      "Fri Mar 27 09:56:17 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "IEEE Computer Society order number PR07846. IEEE Order
                 Plan catalog number 97CB36091.",
  series =       "Symposium on Computer Arithmetic",
  acknowledgement = ack-nhfb,
  sponsor =      "IEEE.",
}

@Proceedings{Thiele:1997:IIC,
  editor =       "Lothar Thiele and others",
  booktitle =    "{IEEE International Conference on Application-Specific
                 Systems, Architectures and Processors: proceedings,
                 July 14--16, 1997, Z{\"u}rich, Switzerland}",
  title =        "{IEEE International Conference on Application-Specific
                 Systems, Architectures and Processors: proceedings,
                 July 14--16, 1997, Z{\"u}rich, Switzerland}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 540",
  year =         "1997",
  ISBN =         "0-8186-7959-X, 0-8186-7960-3, 0-8186-7958-1",
  ISBN-13 =      "978-0-8186-7959-9, 978-0-8186-7960-5,
                 978-0-8186-7958-2",
  LCCN =         "TK7874.6 .I57 1997eb; TK7874.6 .I57 1997; TK7874.6
                 .I58 1997",
  bibdate =      "Sun Mar 4 21:13:29 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Application-Specific
                 Systems, Architectures, and Processors (11th: 1997:
                 Z{\"u}rich, Switzerland)",
  remark =       "IEEE Computer Society Press order number PR07958. IEEE
                 catalog number 97TB100177",
  subject =      "Array processors; Congresses; Signal processing;
                 Digital techniques; Application-specific integrated
                 circuits",
}

@Proceedings{Rusev:1998:TMS,
  editor =       "Petur Rusev and I. Dimovski and Virginia Kiryakova",
  booktitle =    "{Transformation methods and special functions, Varna
                 '96: second international workshop: proceedings}",
  title =        "{Transformation methods and special functions, Varna
                 '96: second international workshop: proceedings}",
  publisher =    "Institute of Mathematics and Informatics, Bulgarian
                 Academy of Sciences",
  address =      "Sofia, Bulgaria",
  pages =        "vi + 613",
  year =         "1998",
  ISBN =         "954-8986-05-1",
  ISBN-13 =      "978-954-8986-05-2",
  LCCN =         "????",
  bibdate =      "Thu Dec 1 11:08:47 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  meetingname =  "International Workshop ``Transform Methods and Special
                 Functions'' (2nd: 1996: Varna, Bulgaria)",
  remark =       "``This second edition of the Workshops 'TM and SF' has
                 been devoted to the 100th anniversary of the eminent
                 Bulgarian mathematician Nikola Obreshkoff
                 (1896-1963)''--T.p. verso.",
  subject =      "Transformations (Mathematics); Differential equations;
                 Integral equations",
  tableofcontents = "On a generalization of the theorem on two constants
                 / G. Adamczyk \\
                 On a construction of the solutions of some elliptic
                 equations with generalized coefficients / A. Antonevich
                 \\
                 Some non-metrizable spaces of harmonic functions / G.
                 Balikov, I. Dimitrov \\
                 Duhamel-type representations of the solutions of
                 non-local boundary value problems for the fractional
                 diffusion-wave equation / E. Bazhlekova \\
                 Pointwise convergence for Hankel transform / J.
                 Betancour, L. Rodr\'iguez-Mesa \\
                 On fractional order continuity, integrability and
                 derivability of real functions / B. Bonilla, J.
                 Trujillo, M. Rivero \\
                 On the root functions of a nonlocal Sturm--Liouville
                 problem / N. Bozhinov \\
                 Mellin transform theory and the role of its
                 differential and integral operators / P. Butzer, S.
                 Jansche \\
                 Exact solution of some systems of non-selfadjoint
                 partial differential equations / D. Callebaut \\
                 Numerical computation of Lame functions / H.-J. Dobner,
                 S. Ritter \\
                 Some extremal problems for $p$-valent alpha-convex
                 functions / J. Dziok \\
                 Extension of a result on the convolution product of
                 distributions / B. Fisher, A. Kilicman \\
                 Simple algorithms for approximations of generalized
                 elliptic-type integrals / M. A. El-Gabali, Shyam L.
                 Kalla \\
                 On Zernicke polynomials / H.-J. Glaeske \\
                 Tomato salad problem in spherical stereology / R.
                 Gorenflo \\
                 On existence of solutions of ordinary differential
                 equations of fractional order / N. Hayek \ldots{} [et
                 al.] \\
                 Tauberian theorem for distributions / J. Jel\'inek \\
                 Radiation field integrals and their evaluation
                 techniques / Shyam L. Kalla, H. G. Khajah \\
                 On the product of distributions / A. Kami\'nski \\
                 On isotopies of algebras and triple systems / N. Kamiya
                 \\
                 Univalence criteria connected with arithmetic and
                 geometric means: I / S. Kanas, A. Lecko \\
                 Global and causal solutions of fractional linear
                 differential equations / S. Kempfle, H. Beyer \\
                 On the applications of Mikusinski's operational
                 calculus to the controllability of dynamical systems /
                 W. Kierat, K. Sk\'ornik \\
                 Application of fractional calculus to solve
                 Abel--Volterra nonlinear and linear integral equations
                 / A. Kilbas, M. Saigo \\
                 Note on linear operators and fractional calculus
                 operators in the univalent function theory / Yong Chan
                 Kim \\
                 Application of the generalized Mikhaylov criterion / S.
                 Krasinska \\
                 On some classes of holomorphic functions in the
                 half-plane / A. Lazi{\'n}ska \\
                 Expansions in series of Legendre functions / E. R.
                 Love, M. Hunter \\
                 Intersections with Gronwall methods / W. Luh \\
                 Applications of fractional calculus in mechanics / F.
                 Mainardi \\
                 Automorphisms in the commutant of the integration
                 operator in spaces of Lebesgue integrable functions /
                 S. Mincheva \\
                 Applications of fractional calculus operators to
                 univalent functions / S. Owa \\
                 Application of orthogonal polynomials to solution of
                 fractional integral equations / I. Podlubny \\
                 Remark on Watson transform / A. Prudnikov, U. Sk\'ornik
                 \\
                 Generalized operators of fractional
                 integro-differentiation in meaning of M. Saigo and
                 their applications / O. Repin \\
                 Fractional integrals and wavelet transformations / B.
                 Rubin, D. Ryabogin, E. Shamir \\
                 More generalization of fractional calculus / M. Saigo,
                 N. Maeda \\
                 On certain subclasses of analytic functions involving a
                 linear operator / H. Saitoh \\
                 On some sequence spaces / E. Savas \\
                 Class of integro-differential equations via fractional
                 calculus / N. Shawagfeh \\
                 On some extreme points of the unit ball / J. Sokol, W.
                 Szumny \\
                 Hyper-Bessel operators, differential equations,
                 functions, and integral transforms of 4th order / S.
                 Spirova \\
                 Some operational techniques in the theory of special
                 functions / H. M. Srivastava \\
                 Convolution in the theory of univalent functions / J.
                 Stankiewicz \\
                 Some extensions of the Rolle and Gauss--Lucas theorems
                 / T. Stoyanov \\
                 On infinitely divisible probability distributions and
                 integral equations / K. Takano \\
                 Generating functions related to pairs of inverse
                 functions / R. Tremblay, B. J. Fug\`ere \\
                 Integral transforms connected with the group
                 representations / N. Tretyakova \\
                 On some integral operators in the clas of functions
                 with negative coefficients / L. Trojnar-Spelina \\
                 On a new generalized Taylor's formula / J. Trujillo, M.
                 Rivero, B. Bonilla \\
                 Some properties of the finite Laplace transform / M.
                 Valbuena, L. Galue, I. Ali \\
                 Airy integral transform and the Paley--Wiener theorem /
                 Vu Kim Tuan \\
                 On starlike functions related with hyperbolic regions /
                 A. Wi{\'s}niowska \\
                 Editorial: Nikola Obreshkoff (1896--1963): biographical
                 data and 100 selected papers of Acad. N. Obreshkoff \\
                 Obreshkoff's generalization of Descartes rule / P.
                 Rusev \\
                 Obrechkoff's generalization of the Laplace and Meijer
                 transformations: origins and recent developments / I.
                 Dimovski, V. Kiryakova \\
                 Longstanding conjecture failed? / V. Kiryakova \\
                 Afterthoughts on interpretation of fractional
                 derivatives and integrals / R. Gorenflo \\
                 Modelling viscous damped oscillations by fractional
                 differential operators / S. Kempfle \\
                 Considerations on fractional calculus: interpretations
                 and applications / F. Mainardi \\
                 Introduction to the fractional calculus and some
                 applications / K. Oldham",
}

@Book{Bultheel:1999:ORF,
  editor =       "Adhemar Bultheel and Pablo Gonzales-Vera and Erik
                 Hendriksen and Olav Njastad",
  booktitle =    "Orthogonal Rational Functions",
  title =        "Orthogonal Rational Functions",
  volume =       "5",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xiv + 407",
  year =         "1999",
  ISBN =         "0-521-65006-2 (hardcover)",
  ISBN-13 =      "978-0-521-65006-9 (hardcover)",
  LCCN =         "QA404.5 .O75 1999",
  bibdate =      "Tue Mar 24 21:04:21 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Cambridge monographs on applied and computational
                 mathematics",
  URL =          "http://www.loc.gov/catdir/description/cam029/98011646.html;
                 http://www.loc.gov/catdir/toc/cam024/98011646.html",
  acknowledgement = ack-nhfb,
  subject =      "functions, orthogonal; functions of complex
                 variables",
}

@Proceedings{IEEE:1999:PIF,
  editor =       "IEEE",
  booktitle =    "Proceedings of the {IEEE} Forum on Research and
                 Technology Advances in Digital Libraries, May 19--21,
                 1999, Baltimore, Maryland",
  title =        "Proceedings of the {IEEE} Forum on Research and
                 Technology Advances in Digital Libraries, May 19--21,
                 1999, Baltimore, Maryland",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 217",
  year =         "1999",
  ISBN =         "0-7695-0219-9",
  ISBN-13 =      "978-0-7695-0219-9",
  LCCN =         "ZA4080 .F67 1999",
  bibdate =      "Fri Jul 09 06:32:32 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  xxeditor =     "Frances M. Titsworth",
}

@Proceedings{Koren:1999:ISC,
  editor =       "Israel Koren and Peter Kornerup",
  booktitle =    "14th {IEEE} Symposium on Computer Arithmetic:
                 proceedings: April 14--16, 1999, Adelaide, Australia",
  title =        "14th {IEEE} Symposium on Computer Arithmetic:
                 proceedings: April 14--16, 1999, Adelaide, Australia",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 274",
  year =         "1999",
  ISBN =         "0-7803-5609-8, 0-7695-0116-8, 0-7695-0118-4",
  ISBN-13 =      "978-0-7803-5609-2, 978-0-7695-0116-1,
                 978-0-7695-0118-5",
  ISSN =         "1063-6889",
  LCCN =         "QA76.6 .S887 1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "IEEE Computer Society Order Number PR00116. IEEE Order
                 Plan Catalog Number 99CB36336.",
  URL =          "http://computer.org/conferen/home/arith/;
                 http://www.ecs.umass.edu/ece/arith14/program.html",
  acknowledgement = ack-nhfb,
  annote =       "Also known as ARITH-14.",
  source =       "Computer arithmetic",
  sponsor =      "IEEE.",
}

@Proceedings{Luk:1999:PSA,
  editor =       "Franklin T. Luk",
  booktitle =    "Proceedings of {SPIE: Advanced signal processing
                 algorithms, architectures, and implementations IX:
                 19--21 July, 1999, Denver, Colorado}",
  title =        "Proceedings of {SPIE: Advanced signal processing
                 algorithms, architectures, and implementations IX:
                 19--21 July, 1999, Denver, Colorado}",
  volume =       "3807",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  pages =        "ix + 648",
  year =         "1999",
  ISBN =         "0-8194-3293-8",
  ISBN-13 =      "978-0-8194-3293-3",
  LCCN =         "TK5102.5 .A3325 1999; TK5102.5 .A3173 1999eb; TK5102.9
                 .A37 1999; TK5102.5; TS510 .S63",
  bibdate =      "Mon Mar 5 07:43:43 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  subject =      "Signal processing; Digital techniques; Congresses;
                 Algorithms; Computer architecture",
}

@Book{Berggren:2000:PSB,
  editor =       "Lennart Berggren and Jonathan Borwein and Peter
                 Borwein",
  booktitle =    "Pi: a source book",
  title =        "Pi: a source book",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xx + 736",
  year =         "2000",
  DOI =          "https://doi.org/10.1007/978-1-4757-3240-5",
  ISBN =         "0-387-98946-3 (hardcover)",
  ISBN-13 =      "978-0-387-98946-4 (hardcover)",
  LCCN =         "QA484 .P5 2000",
  MRclass =      "11-00 (01A05 01A75 11-03)",
  MRnumber =     "1746004",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  libnote =      "Not yet in my library.",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject =      "Pi (mathematical constant)",
  tableofcontents = "Preface / v \\
                 \\
                 Preface to the Second Edition / viii \\
                 Acknowledgments / ix \\
                 \\
                 Introduction / xvii \\
                 \\
                 1. The Rhind Mathematical Papyrus-Problem 50 ($\approx$
                 1650 B.C.) / A problem dealing with the area of a round
                 field of given diameter / 1 \\
                 \\
                 2. Engels. Quadrature of the Circle in Ancient Egypt
                 (1977) / A conjectural explanation of how the
                 mathematicians of ancient Egypt approximated the area
                 of a circle / 3 \\
                 \\
                 3. Archimedes. Measurement of a Circle ($\approx$ 250
                 BC) / The seminal work in which Archimedes presents the
                 first true algorithm for $\pi$ / 7 \\
                 \\
                 4. Phillips. Archimedes the Numerical Analyst (1981) /
                 A summary of Archimedes' work on the computation of
                 $\pi$ using modern notation / 15 \\
                 \\
                 5. Lam and Ang. Circle Measurements in Ancient China
                 (1986) / This paper discusses and contains a
                 translation of Liu Hui's (3rd century) method for
                 evaluating $\pi$ and also examines values for $\pi$
                 given by Zu Chongzhi (429--500) / 20 \\
                 \\
                 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane
                 and Solid Figures ($\approx$ 850) / This extract gives
                 an explicit statement and proof that the ratio of the
                 circumference to the diameter is constant / 36 \\
                 \\
                 7. M{\=a}dhava. The Power Series for Arctan and Pi
                 ($\approx$ 1400) / These theorems by a fifteenth
                 century Indian mathematician give Gregory's series for
                 arctan with remainder terms and Leibniz's series for
                 $\pi$ / 45 \\
                 \\
                 8. Hope-Jones. Ludolph (or Ludolff or Lucius) van
                 Ceulen (1938) / Correspondence about van Ceulen's
                 tombstone in reference to it containing some digits of
                 $\pi$ / 51 \\
                 \\
                 9. Vi{\'e}te. Variorum de Rebus Mathematicis Reponsorum
                 Liber VII (1593) / Two excerpts. One containing the
                 first infinite expression of $\pi$, obtained by
                 relating the area of a regular $2n$-gon to that of a
                 regular $n$-gon / 53 \\
                 \\
                 10. Wallis. Computation of $\pi$ by Successive
                 Interpolations (1655) / How Wallis derived the infinite
                 product for $\pi$ that bears his name / 68 \\
                 \\
                 11. Wallis. Arithmetica Infinitorum (1655) / An excerpt
                 including Prop. 189, 191 and an alternate form of the
                 result that gives Wm. Brounker's continued fraction
                 expression for $4/\pi$ / 78 \\
                 \\
                 12. Huygens. De Circuli Magnitudine Inventa (1724) /
                 Huygens's proof of W. Snell's discovery of improvements
                 in Archimedes' method of estimating the lengths of
                 circular arcs / 81 \\
                 \\
                 13. Gregory. Correspondence with John Collins (1671) /
                 A letter to Collins in which he gives his series for
                 arctangent, carried to the ninth power. / 87 \\
                 \\
                 14. Roy. The Discovery of the Series Formula for $\pi$
                 by Leibniz, Gregory, and Nilakantha (1990) / A
                 discussion of the discovery of the series $\pi/4 = 1 -
                 1/3 + 1/5, \cdots{}$ / 92 \\
                 \\
                 15. Jones. The First Use of $\pi$ for the Circle Ratio
                 (1706) / An excerpt from Jones' book, the Synopsis
                 Palmariorum Matheseos: or, a New Introduction to the
                 Mathematics, London, 1706 / 108 \\
                 \\
                 16. Newton. Of the Method of Fluxions and Infinite
                 Series (1737) / An excerpt giving Newton's calculation
                 of $\pi$ to 16 decimal places / 110 \\
                 \\
                 17. Euler. Chapter 10 of Introduction to Analysis of
                 the Infinite (On the Use of the Discovered Fractions to
                 Sum Infinite Series) (1748) / This includes many of
                 Euler's infinite series for $\pi$ and powers of $\pi$ /
                 112 \\
                 \\
                 18. Lambert. M{\'e}moire Sur Quelques
                 Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s
                 Transcendentes Circulaires et Logarithmiques (1761) /
                 An excerpt from Lambert's original proof of the
                 irrationality of $\pi$ / 129 \\
                 \\
                 19. Lambert. Irrationality of $\pi$ (1969) / A
                 translation and Struik's discussion of Lambert's proof
                 of the irrationality of $\pi$ / 141 \\
                 \\
                 20. Shanks. Contributions to Mathematics Comprising
                 Chiefly of the Rectification of the Circle to 607
                 Places of Decimals (1853) / Pages from Shank's report
                 of his monumental hand calculation of $\pi$ / 147 \\
                 \\
                 21. Hermite. Sur La Fonction Exponentielle (1873) / The
                 first proof of the transcendence of $e$ / 162 \\
                 \\
                 22. Lindemann. Ueber die Zahl $\pi$ (1882) / The first
                 proof of the transcendence of $\pi$ / 194 \\
                 \\
                 23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die
                 Ludolphsche Zahl'' (1885) / Weierstrass' proof of the
                 transcendence of $\pi$ / 207 \\
                 \\
                 24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und
                 $\pi$ (1893) / Hilbert's short and elegant
                 simplification of the transcendence proofs for $e$ and
                 $\pi$ / 226 \\
                 \\
                 25. Goodwin. Quadrature of the Circle (1894) / The
                 dubious origin of the attempted legislation of the
                 value of $\pi$ in Indiana / 230 \\
                 \\
                 26. Edington. House Bill No. 246, Indiana State
                 Legislature, 1897 (1935) / A summary of the action
                 taken by the Indiana State Legislature to fix the value
                 of $\pi$ (including a copy of the actual bill that was
                 proposed) / 231 \\
                 \\
                 27. Singmaster. The Legal Values of Pi (1985) / A
                 history of the attempt by Indiana to legislate the
                 value of $\pi$ / 236 \\
                 \\
                 28. Ramanujan. Squaring the Circle (1913) / A geometric
                 approximation to $\pi$ / 240 \\
                 \\
                 29. Ramanujan. Modular Equations and Approximations to
                 $\pi$ (1914) / Ramanujan's seminal paper on $\pi$ that
                 includes a number of striking series and algebraic
                 approximations / 241 \\
                 \\
                 30. Watson. The Marquis and the Land Agent: A Tale of
                 the Eighteenth Century (1933) / A Presidential address
                 to the Mathematical Association in which the author
                 gives an account of ``some of the elementary work on
                 arcs and ellipses and other curves which led up to the
                 idea of inverting an elliptic integral, and so laying
                 the foundations of elliptic functions and doubly
                 periodic functions generally.'' / 258 \\
                 \\
                 31. Ballantine. The Best (?) Formula for Computing
                 $\pi$ to a Thousand Places (1939) / An early attempt to
                 orchestrate the calculation of $\pi$ more cleverly /
                 271 \\
                 \\
                 32. Birch. An Algorithm for Construction of Arctangent
                 Relations (1946) / The object of this note is to
                 express $\pi / 4 $ as a sum of arctan relations in
                 powers of 10 / 274 \\
                 \\
                 33. Niven. A Simple Proof that $\pi$ Is Irrational
                 (1947) / A very concise proof of the irrationality of
                 $\pi$ / 276 \\
                 \\
                 34. Reitwiesner. An ENIAC Determination of $\pi$ and
                 $e$ to 2000 Decimal Places (1950) / One of the first
                 computer-based computations / 277 \\
                 \\
                 35. Schepler. The Chronology of Pi (1950) / A fairly
                 reliable outline of the history of $\pi$ from 3000 BC
                 to 1949 / 282 \\
                 \\
                 36. Mahler. On the Approximation of $\pi$ (1953) /
                 ``The aim of this paper is to determine an explicit
                 lower bound free of unknown constants for the distance
                 of $\pi$ from a given rational or algebraic number'' /
                 306 \\
                 \\
                 37. Wrench, Jr. The Evolution of Extended Decimal
                 Approximations to $\pi$ (1960) / A history of the
                 calculation of the digits of $\pi$ to 1960 \\
                 \\
                 38. Shanks and Wrench, Jr. Calculation of $\pi$ to
                 100,000 Decimals (1962) / A landmark computation of
                 $\pi$ to more than 100,000 places / 326 \\
                 \\
                 39. Sweeny. On the Computation of Euler's Constant
                 (1963) / The computation of Euler's constant to 3566
                 decimal places / 350 \\
                 \\
                 40. Baker. Approximations to the Logarithms of Certain
                 Rational Numbers (1964) / The main purpose of this deep
                 and fundamental paper is to ``deduce results concerning
                 the accuracy with which the natural logarithms of
                 certain rational numbers may be approximated by
                 rational numbers, or, more generally, by algebraic
                 numbers of bounded degree.'' / 359 \\
                 \\
                 41. Adams. Asymptotic Diophantine Approximations to $E$
                 (1966) / An asymptotic estimate for the rational
                 approximation to $e$ which disproves the conjecture
                 that $e$ behaves like almost all numbers in this
                 respect / 368 \\
                 \\
                 42. Mahler. Applications of Some Formulae by Hermite to
                 the Approximations of Exponentials of Logarithms (1967)
                 / An important extension of Hilbert's approach to the
                 study of transcendence / 372 \\
                 \\
                 43. Eves. In Mathematical Circles; A Selection of
                 Mathematical Stories and Anecdotes (excerpt) (1969) / A
                 collection of mathematical stories and anecdotes about
                 $\pi$ / 400 \\
                 \\
                 44. Eves. Mathematical Circles Revisited; A Second
                 Collection of Mathematical Stories and Anecdotes
                 (excerpt) (1971) / A further collection of mathematical
                 stories and anecdotes about $\pi$ / 402 \\
                 \\
                 45. Todd. The Lemniscate Constants (1975) / A unifying
                 account of some of the methods used for computing the
                 lemniscate constants / 412 \\
                 \\
                 46. Salamin. Computation of r Using
                 Arithmetic-Geometric Mean (1976) / The first
                 quadratically converging algorithm for $\pi$ based on
                 Gauss's AGM and on Legendre's relation for elliptic
                 integrals / 418 \\
                 \\
                 47. Brent. Fast Multiple-Precision Evaluation of
                 Elementary Functions (1976) / ``This paper contains the
                 `Gauss-Legendre' method and some different algorithms
                 for log and exp (using Landen transformations).'' / 424
                 \\
                 \\
                 48. Beukers. A Note on the Irrationality of $\zeta(2)$
                 and $\zetq(3)$ (1979) / A short and elegant recasting
                 of Ap{\'e}ry's proof of the irrationality of $\zeta(3)$
                 (and $\zeta(2)$) / 434 \\
                 \\
                 49. van der Poorten. A Proof that Euler Missed \ldots{}
                 Ap{\'e}ry's Proof of the Irrationality of $\zeta(3)$
                 (1979) / An illuminating account of Ap{\'e}ry's
                 astonishing proof of the irrationality of $\zeta(3)$ /
                 439 \\
                 \\
                 50. Brent and McMillan. Some New Algorithms for
                 High-Precision Computation of Euler's Constant (1980) /
                 Several new algorithms for high precision calculation
                 of Euler's constant, including one which was used to
                 compute 30,100 decimal places / 448 \\
                 \\
                 51. Apostol. A Proof that Euler Missed: Evaluating
                 $\zeta(2)$ the Easy Way (1983) / This note shows that
                 one of the double integrals considered by Beukers ([48]
                 in the table of contents) can be used to establish
                 directly that $\zeta(2) = \pi / 6$ / 456 \\
                 \\
                 52. O'Shaughnessy. Putting God Back in Math (1983) / An
                 article about the Institute of Pi Research, an
                 organization that ``pokes fun at creationists by
                 pointing out that even the Bible makes mistakes.'' /
                 458 \\
                 \\
                 53. Stern. A Remarkable Approximation to $\pi$ (1985) /
                 Justification of the value of $\pi$ in the Bible
                 through numerological interpretations / 460 \\
                 \\
                 54. Newman and Shanks. On a Sequence Arising in Series
                 for $\pi$ (1984) / More connections between $\pi$ and
                 modular equations / 462 \\
                 \\
                 55. Cox. The Arithmetic-Geometric Mean of Gauss (1984)
                 / An extensive study of the complex analytic properties
                 of the AGM / 481 \\
                 \\
                 56. Borwein and Borwein. The Arithmetic-Geometric Mean
                 and Fast Computation of Elementary Functions (1984) /
                 The relationship between the AGM iteration and fast
                 computation of elementary functions (one of the
                 by-products is an algorithm for $\pi$) / 537 \\
                 \\
                 57. Newman. A Simplified Version of the Fast Algorithms
                 of Brent and Salamin (1984) / Elementary algorithms for
                 evaluating $e^x$ and $\pi$ using the Gauss AGM without
                 explicit elliptic function theory / 553 \\
                 \\
                 58. Wagon. Is Pi Normal? (1985) / A discussion of the
                 conjecture that $\pi$ has randomly distributed digits /
                 557 \\
                 \\
                 59. Keith. Circle Digits: A Self-Referential Story
                 (1986) / A mnemonic for the first 402 decimal places of
                 $\pi$ / 560 \\
                 \\
                 60. Bailey. The Computation of $\pi$ to 29,360,000
                 Decimal Digits Using Borweins' Quartically Convergent
                 Algorithm (1988) / The algorithms used, both for $\pi$
                 and for performing the required multiple-precision
                 arithmetic / 562 \\
                 \\
                 61. Kanada. Vectorization of Multiple-Precision
                 Arithmetic Program and 201,326,000 Decimal Digits of 1
                 Calculation (1988) / Details of the computation and
                 statistical tests of the first 200 million digits of
                 $\pi$ / 576 \\
                 \\
                 62. Borwein and Borwein. Ramanujan and Pi (1988) / This
                 article documents Ramanujan's life, his ingenious
                 approach to calculating $\pi$, and how his approach is
                 now incorporated into modern computer algorithms / 588
                 \\
                 \\
                 63. Chudnovsky and Chudnovsky. Approximations and
                 Complex Multiplication According to Ramanujan (1988) /
                 This excerpt describes ``Ramanujan's original quadratic
                 period--quasiperiod relations for elliptic curves with
                 complex multiplication and their applications to
                 representations of fractions of $\pi$ and other
                 logarithms in terms of rapidly convergent nearly
                 integral (hypergeometric) series.'' / 596 \\
                 \\
                 64. Borwein, Borwein and Bailey. Ramanujan, Modular
                 Equations, and Approximations to Pi or How to Compute
                 One Billion Digits of Pi (1989) / An exposition of the
                 computation of $\pi$ using mathematics rooted in
                 Ramanujan's work / 623 \\
                 \\
                 65. Borwein, Borwein and Dilcher. Pi, Euler Numbers,
                 and Asymptotic Expansions (1989) / An explanation as to
                 why the slowly convergent Gregory series for $\pi$,
                 truncated at 500,000 terms, gives $\pi$ to 40 places
                 with only the 6th, 17th, 18th, and 29th places being
                 incorrect / 642 \\
                 \\
                 66. Beukers, B{\'e}zivin, and Robba. An Alternative
                 Proof of the Lindemann--Weierstrass Theorem (1990) /
                 The Lindemann--Weierstrass theorem as a by-product of a
                 criterion for rationality of solutions of differential
                 equations / 649 \\
                 \\
                 67. Webster. The Tail of Pi (1991) / Various anecdotes
                 about $\pi$ from the 14th annual IMO Lecture to the
                 Royal Society / 654 \\
                 \\
                 68. Eco. An excerpt from Foucault's Pendulum (1993) /
                 ``The unnumbered perfection of the circle itself.'' /
                 658 \\
                 \\
                 69. Keith. Pi Mnemonics and the Art of Constrained
                 Writing (1996) / A mnemonic for $\pi$ based on Edgar
                 Allen Poe's poem ``The Raven.'' / 659 \\
                 \\
                 70. Bailey, Borwein, and Plouffe. On the Rapid
                 Computation of Various Polylogarithmic Constants (1996)
                 / A fast method for computing individual digits of
                 $\pi$ in base 2 / 663 \\
                 Appendix I --- On the Early History of Pi / 677 \\
                 \\
                 Appendix II --- A Computational Chronology of Pi / 683
                 \\
                 \\
                 Appendix III --- Selected Formulae for Pi / 686 \\
                 \\
                 Appendix IV --- Translations of Vi{\`e}te and Huygens /
                 690 \\
                 Bibliography / 711 \\
                 \\
                 Credits / 717 \\
                 \\
                 Index / 721",
}

@Proceedings{Cocolicchio:2000:ASF,
  editor =       "Decio Cocolicchio and G. Dattoli and H. M.
                 Srivastava",
  booktitle =    "{Advanced special functions and applications:
                 proceedings of the workshop: Melfi (PZ), Italy, 9--12
                 May 1999}",
  title =        "{Advanced special functions and applications:
                 proceedings of the workshop: Melfi (PZ), Italy, 9--12
                 May 1999}",
  volume =       "1",
  publisher =    "Aracne",
  address =      "Roma, Italy",
  edition =      "1.",
  pages =        "336",
  year =         "2000",
  ISBN =         "88-7999-265-X",
  ISBN-13 =      "978-88-7999-265-7",
  LCCN =         "QA351 .A38 2000",
  bibdate =      "Sat Oct 30 19:16:34 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Proceedings of the Melfi school on advanced topics in
                 mathematics and physics",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Congresses",
}

@Proceedings{Dunkl:2000:PIW,
  editor =       "Charles Dunkl and Mourad Ismail and Roderick Wong",
  booktitle =    "{Proceedings of the international workshop, special
                 functions: Hong Kong, 21--25 June 1999}",
  title =        "{Proceedings of the international workshop, special
                 functions: Hong Kong, 21--25 June 1999}",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "xi + 438",
  year =         "2000",
  ISBN =         "981-02-4393-6",
  ISBN-13 =      "978-981-02-4393-7",
  LCCN =         "QA351 .P76 2000",
  bibdate =      "Fri Jul 09 06:30:25 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Sprague:2000:PAH,
  editor =       "Ralph H. Sprague",
  booktitle =    "{Proceedings of the 33rd Annual Hawaii International
                 Conference on System Sciences: abstracts and CD-ROM of
                 full papers: January 4--7, 2000, Maui, Hawaii}",
  title =        "{Proceedings of the 33rd Annual Hawaii International
                 Conference on System Sciences: abstracts and CD-ROM of
                 full papers: January 4--7, 2000, Maui, Hawaii}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "liv + 259",
  year =         "2000",
  ISBN =         "0-7695-0493-0, 0-7695-0494-9, 0-7695-0495-7",
  ISBN-13 =      "978-0-7695-0493-3, 978-0-7695-0494-0,
                 978-0-7695-0495-7",
  LCCN =         "TA168 .H37 2000; TA168 .H37 2000xeb; TA168",
  bibdate =      "Sun Mar 4 21:23:42 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "Hawaii International Conference on System Sciences
                 (33rd: 2000: Maui, Hawaii)",
  remark =       "IEEE Computer Society Order Number: PR00493",
  subject =      "Systems engineering; Congresses; Information theory;
                 Electronic data processing; System design",
}

@Proceedings{Banerji:2001:SFS,
  editor =       "P. K. Banerji",
  booktitle =    "{Special functions: selected articles: proceedings of
                 the First National Conference of the Society for
                 Special Functions and their Applications, March 3--4,
                 2000, Jodhpur, India}",
  title =        "{Special functions: selected articles: proceedings of
                 the First National Conference of the Society for
                 Special Functions and their Applications, March 3--4,
                 2000, Jodhpur, India}",
  publisher =    "Published by Scientific Publishers (India) for the
                 Society for Special Functions and their Applications",
  address =      "Jodhpur, India",
  pages =        "258",
  year =         "2001",
  ISBN =         "81-7233-267-X",
  ISBN-13 =      "978-81-7233-267-9",
  LCCN =         "QA351 .S665 2001",
  bibdate =      "Sat Oct 30 19:13:10 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Congresses",
}

@Proceedings{Burgess:2001:ISC,
  editor =       "N. Burgess and L. Ciminiera",
  booktitle =    "{15th IEEE Symposium on Computer Arithmetic: ARITH-15
                 2001: proceedings: Vail, Colorado, 11--13 June, 2001}",
  title =        "{15th IEEE Symposium on Computer Arithmetic: ARITH-15
                 2001: proceedings: Vail, Colorado, 11--13 June, 2001}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 285",
  year =         "2001",
  ISBN =         "0-7695-1150-3; 0-7695-1152-X",
  ISBN-13 =      "978-0-7695-1150-4; 978-0-7695-1152-8",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62 S95 2001",
  bibdate =      "Fri May 03 14:20:49 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE order no. PR01150.",
  price =        "US\$145",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
  xxnote =       "Check dates: 11--13 or 11--17??",
  xxtitle =      "Computer Arithmetic: Papers presented at the {15th
                 IEEE Symposium on Computer Arithmetic (Arith-15 2001),
                 11--17 June, 2001, Vail, CO}",
}

@Book{Lide:2001:CEM,
  editor =       "David R. Lide",
  booktitle =    "A Century of Excellence in Measurements, Standards,
                 and Technology",
  title =        "A Century of Excellence in Measurements, Standards,
                 and Technology",
  volume =       "958",
  publisher =    pub-NIST,
  address =      pub-NIST:adr,
  pages =        "ix + 386",
  year =         "2001",
  bibdate =      "Fri Jul 09 06:29:11 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "NIST special publication",
  acknowledgement = ack-nhfb,
}

@Proceedings{Siafarikas:2001:PFI,
  editor =       "Panayiotis D. Siafarikas and Theodore Seio Chihara",
  booktitle =    "{Proceedings of the Fifth International Symposium on
                 Orthogonal Polynomials, Special Functions and their
                 Applications: Patras, Greece, 20--24 September 1999}",
  title =        "{Proceedings of the Fifth International Symposium on
                 Orthogonal Polynomials, Special Functions and their
                 Applications: Patras, Greece, 20--24 September 1999}",
  volume =       "133(1/2)",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "xxvii + 705",
  year =         "2001",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  LCCN =         "QA76 J86 v. 133, no. 1/2",
  bibdate =      "Sat Oct 30 19:08:06 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Journal of computational and applied mathematics",
  acknowledgement = ack-nhfb,
}

@Proceedings{Borrione:2002:TIW,
  editor =       "Dominique Borrione",
  booktitle =    "{Third International Workshop on the ACL2 Theorem
                 Prover and its Applications (ACL2-2002), April 8--9,
                 2002, in Grenoble, France. Presentations, affiliated
                 with ETAPS 2002}",
  title =        "{Third International Workshop on the ACL2 Theorem
                 Prover and its Applications (ACL2-2002), April 8--9,
                 2002, in Grenoble, France. Presentations, affiliated
                 with ETAPS 2002}",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  year =         "2002",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Jun 25 12:28:18 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.utexas.edu/users/moore/acl2/workshop-2002/",
  acknowledgement = ack-nhfb,
}

@Book{Lide:2002:CEM,
  editor =       "David R. Lide",
  booktitle =    "A Century of Excellence in Measurements, Standards,
                 and Technology",
  title =        "A Century of Excellence in Measurements, Standards,
                 and Technology",
  publisher =    pub-CRC,
  address =      pub-CRC:adr,
  pages =        "ix + 386",
  year =         "2002",
  ISBN =         "0-8493-1247-7",
  ISBN-13 =      "978-0-8493-1247-2",
  LCCN =         "QC100.U6 .C46 2002",
  bibdate =      "Fri Jul 09 06:29:11 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Republication of \cite{Lide:2001:CEM}.",
  URL =          "http://www.loc.gov/catdir/toc/fy031/2002283707.html",
  acknowledgement = ack-nhfb,
}

@Proceedings{Anonymous:2003:CRN,
  editor =       "Anonymous",
  booktitle =    "5th Conference on Real Numbers and Computers 2003 ---
                 {RNC5}, Lyon, France, September 2003",
  title =        "5th Conference on Real Numbers and Computers 2003 ---
                 {RNC5}, Lyon, France, September 2003",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  year =         "2003",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Jun 25 14:57:33 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Koelink:2003:OPS,
  editor =       "Erik Koelink and Walter {Van Assche}",
  booktitle =    "Orthogonal polynomials and special functions: {Leuven
                 2002}",
  title =        "Orthogonal polynomials and special functions: {Leuven
                 2002}",
  volume =       "1817",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 249",
  year =         "2003",
  ISBN =         "3-540-40375-2",
  ISBN-13 =      "978-3-540-40375-3",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  LCCN =         "33 33-06 33C 68W",
  bibdate =      "Sat Oct 30 17:00:03 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  series =       "Lecture notes in mathematics",
  acknowledgement = ack-nhfb,
  subject =      "functions, special; orthogonal polynomials",
}

@Book{Berggren:2004:PSB,
  editor =       "Lennart Berggren and Jonathan Borwein and Peter
                 Borwein",
  booktitle =    "Pi: a source book",
  title =        "Pi: a source book",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Third",
  pages =        "xx + 797",
  year =         "2004",
  DOI =          "https://doi.org/10.1007/978-1-4757-4217-6",
  ISBN =         "0-387-20571-3",
  ISBN-13 =      "978-0-387-20571-7",
  MRclass =      "11-00 (01A05 01A75 11-03)",
  MRnumber =     "2065455",
  MRreviewer =   "F. Beukers",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 2003:210.",
  tableofcontents = "Preface to the Third Edition / v \\
                 Preface to the Second Edition / vi \\
                 Preface / vii \\
                 Acknowledgments / x \\
                 Introduction / xvii \\
                 1. The Rhind Mathematical Papyrus --- Problem 50
                 ($\approx$1650 B.C.) / A problem dealing with the area
                 of a round field of given diameter / 1 \\
                 2. Engels / Quadrature of the Circle in Ancient Egypt
                 (1977) / A conjectural explanation of how the
                 mathematicians of ancient Egypt approximated the area
                 of a circle / 3 \\
                 3. Archimedes / Measurement of a Circle --- (-250 B.C.)
                 / The seminal work in which Archimedes presents the
                 first true algorithm for $ \pi $ / 7 \\
                 4. Phillips / Archimedes the Numerical --- Analyst
                 (1981) / A summary of Archimedes' work on the
                 computation of $ \pi $ using modem notation / 15 \\
                 5. Lam and Ang / Circle Measurements in Ancient China
                 (1986) / This paper discusses and contains a
                 translation of Liu Hui's (3rd century) method for
                 evaluating $ \pi $ and also examines values for $ \pi $
                 given by Zu Chongzhi (429--500) / 20 \\
                 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane
                 and Solid Figures (--850) / This extract gives an
                 explicit statement and proof that the ratio of the
                 circumference to the diameter is constant / 36 \\
                 7. M{\=a}dhava / The Power Series for Arctan and Pi
                 (-1400) / These theorems by a fifteenth century Indian
                 mathematician give Gregory's series for arctan with
                 remainder terms and Leibniz's series for $ \pi $ / 45
                 \\
                 8. Hope-Jones / Ludolph (or Ludolff or Lucius) van
                 Ceulen (1938) / Correspondence about van Ceulen's
                 tombstone in reference to it containing some digits of
                 $ \pi $ / 51 \\
                 9. Vi{\`e}te / \booktitle{Variorum de Rebus
                 Mathematicis Reponsorum Liber VII} (1593) / Two
                 excerpts. One containing the first infinite expression
                 of $ \pi $, obtained by relating the area of a regular
                 $2n$-gon to that of a regular $n$-gon / 53 \\
                 10. Wallis. Computation of $ \pi $ by Successive
                 Interpolations (1655) / How Wallis derived the infinite
                 product for $ \pi $ that bears his name / 68 \\
                 11. Wallis / \booktitle{Arithmetica Infinitorum} (1655)
                 / An excerpt including Prop. 189, 191 and an alternate
                 form of the result that gives Wm. Brounker's continued
                 fraction expression for $ 4 / \pi$ / ?? \\
                 12. Huygens / \booktitle{De Circuli Magnitudine
                 Inventa} (1654) / Huygens's demonstration of how to
                 triple the number of correct decimals over those in
                 Archimedes' estimate of $ \pi $ / 81 13. Gregory /
                 Correspondence with John Collins (1671) / A letter to
                 Collins in which he gives his series for arctangent,
                 carried to the ninth power / 87 \\
                 14. Roy / The Discovery of the Series Formula for $ \pi
                 $ by Leibniz, Gregory, and Nilakantha (1990) / A
                 discussion of the discovery of the series $ \pi / 4 = 1
                 - 1/3 + 1/5 - \cdots{} $ / 92 \\
                 15. Jones / The First Use of $ \pi $ for the Circle
                 Ratio (1706) / An excerpt from Jones' book, the
                 \booktitle{Synopsis Palmariorum Matheseos: or, a New
                 Introduction to the Mathematics}, London, 1706 / 108
                 \\
                 16. Newton / Of the Method of Fluxions and Infinite
                 Series (1737) / An excerpt giving Newton's calculation
                 of $ \pi $ to 16 decimal places / 110 \\
                 17. Euler / Chapter 10 of \booktitle{Introduction to
                 Analysis of the Infinite (On the Use of the Discovered
                 Fractions to Sum Infinite Series)} (1748) / This
                 includes many of Euler's infinite series for $ \pi $
                 and powers of $ \pi $ / 112 \\
                 18. Lambert / \booktitle{M{\'e}moire Sur Quelques
                 Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s
                 Transcendentes Circulaires et Logarithmiques} (1761) /
                 An excerpt from Lambert's original proof of the
                 irrationality of $ \pi $ / 129 19. Lambert /
                 Irrationality of $ \pi $ (1969) / A translation and
                 Struik's discussion of Lambert's proof of the
                 irrationality of $ \pi $ / 141 \\
                 20. Shanks / Contributions to Mathematics Comprising
                 Chiefly of the Rectification of the Circle to 607
                 Places of Decimals (1853) / Pages from Shanks's report
                 of his monumental hand calculation of $ \pi $ / 147 \\
                 21. Hermite / \booktitle{Sur La Fonction Exponentielle}
                 (1873) / The first proof of the transcendence of $ e $
                 / 162 \\
                 22. Lindemann / \booktitle{Ueber die Zahl $ \pi $}
                 (1882) / The first proof of the transcendence of $ \pi
                 $ / 194 23. Weierstrass / \booktitle{Zu Lindemann's
                 Abhandlung ``{\"U}ber die Ludolphsche Zahl''} (1885) /
                 Weierstrass' proof of the transcendence of $ \pi $ /
                 207 24. Hilbert / \booktitle{Ueber die Transzendenz der
                 Zahlen $ e $ und $ \pi $} (1893) / Hilbert's short and
                 elegant simplification of the transcendence proofs for
                 $ e $ and $ \pi $ / 226 25. Goodwin / Quadrature of the
                 Circle (1894) / The dubious origin of the attempted
                 legislation of the value of $ \pi $ in Indiana / 230
                 \\
                 26. Edington / House Bill No. 246, Indiana State
                 Legislature, 1897 (1935) / A summary of the action
                 taken by the Indiana State Legislature to fix the value
                 of $ \pi $ (including a copy of the actual bill that
                 was proposed) / 231 \\
                 27. Singmaster / The Legal Values of Pi (1985) / A
                 history of the attempt by Indiana to legislate the
                 value of $ \pi $ / 236 \\
                 28. Ramanujan / Squaring the Circle (1913) / A
                 geometric approximation to $ \pi $ / 240 \\
                 29. Ramanujan / Modular Equations and Approximations to
                 $ \pi $ (1914) / Ramanujan's seminal paper on pi that
                 includes a number of striking series and algebraic
                 approximations / 241 \\
                 30. Watson / The Marquis and the Land Agent: A Tale of
                 the Eighteenth Century (1933) / A Presidential address
                 to the Mathematical Association in which the author
                 gives an account of ``some of the elementary work on
                 arcs and ellipses and other curves which led up to the
                 idea of inverting an elliptic integral, and so laying
                 the foundations of elliptic functions and doubly
                 periodic functions generally.'' / ?? \\
                 31. Ballantine / The Best (?) Formula for Computing $
                 \pi $ to a Thousand Places (1939) / An early attempt to
                 orchestrate the calculation of $ \pi $ more cleverly /
                 271 \\
                 32. Birch / An Algorithm for Construction of Arctangent
                 Relations (1946) / The object of this note is to
                 express $ \pi / 4$ as a sum of arctan relations in
                 powers of 10 / 274 \\
                 33. Niven / A Simple Proof that $ \pi $ is Irrational
                 (1947) / A very concise proof of the irrationality of $
                 \pi $ / 276 \\
                 34. Reitwiesner / An ENIAC Determination of $ \pi $ and
                 $ e $ to 2000 Decimal Places (1950) / One of the first
                 computer-based computations / 277 \\
                 35. Schepler / The Chronology of Pi (1950) / A fairly
                 reliable outline of the history of $ \pi $ from 3000
                 B.C. to 1949 / 282 \\
                 36. Mahler / On the Approximation of $ \pi $ (1953) /
                 ``The aim of this paper is to determine an explicit
                 lower bound free of unknown constants for the distance
                 of $ \pi $ from a given rational or algebraic number.''
                 / 306 \\
                 37. Wrench, Jr. / The Evolution of Extended Decimal
                 Approximations to $ \pi $ (1960) / A history of the
                 calculation of the digits of $ \pi $ to 1960 / 319 \\
                 38. Shanks and Wrench, Jr. / Calculation of $ \pi $ to
                 100,000 Decimals (1962) / A landmark computation of $
                 \pi $ to more than 100,000 places / 326 39. Sweeny / On
                 the Computation of Euler's Constant (1963) / The
                 computation of Euler's constant to 3566 decimal places
                 / 350 40. Baker / Approximations to the Logarithms of
                 Certain Rational Numbers (1964) / The main purpose of
                 this deep and fundamental paper is to ``deduce results
                 concerning the accuracy with which the natural
                 logarithms of certain rational numbers may be
                 approximated by rational numbers, or, more generally,
                 by algebraic numbers of bounded degree.'' / 359 \\
                 41. Adams / Asymptotic Diophantine Approximations to e
                 (1966) / An asymptotic estimate for the rational
                 approximation to $ e $ which disproves the conjecture
                 that $ e $ behaves like almost all numbers in this
                 respect / 368 \\
                 42. Mahler / Applications of Some Formulae by Hermite
                 to the Approximations of Exponentials of Logarithms
                 (1967) / An important extension of Hilbert's approach
                 to the study of transcendence / 372 43. Eves / In
                 Mathematical Circles; A Selection of Mathematical
                 Stories and Anecdotes (excerpt) (1969) / A collection
                 of mathematical stories and anecdotes about $ \pi $ /
                 456 \\
                 44. Eves / Mathematical Circles Revisited; A Second
                 Collection of Mathematical Stories and Anecdotes
                 (excerpt) (1971) / A further collection of mathematical
                 stories and anecdotes about $ \pi $ / 402 45. Todd /
                 The Lemniscate Constants (1975) / A unifying account of
                 some of the methods used for computing the lemniscate
                 constants / 412 \\
                 46. Salamin / Computation of $ \pi $ Using
                 Arithmetic--Geometric Mean (1976) / The first
                 quadratically converging algorithm for $ \pi $ based on
                 Gauss's AGM and on Legendre's relation for elliptic
                 integrals / 418 \\
                 47. Brent / Fast Multiple-Precision Evaluation of
                 Elementary Functions (1976) / ``This paper contains the
                 `Gauss--Legendre' method and some different algorithms
                 for $\log$ and $\exp$ (using Landen transformations).''
                 / 424 \\
                 48. Beukers / A Note on the Irrationality of $ \zeta(2)
                 $ and $ \zeta(3) $ (1979) / A short and elegant
                 recasting of Apery's proof of the irrationality of
                 $\zeta(3)$ (and $\zeta(2)$) / 434 \\
                 49. van der Poorten / A Proof that Euler Missed
                 \ldots{} Apery's Proof of the Irrationality of $\zeta
                 (3)$ (1979) / An illuminating account of Apery's
                 astonishing proof of the irrationality of $\zeta (3)$ /
                 439 \\
                 50. Brent and McMillan / Some New Algorithms for
                 High-Precision Computation of Euler's Constant (1980) /
                 Several new algorithms for high-precision calculation
                 of Euler's constant, including one which was used to
                 compute 30,100 decimal places / 448 \\
                 51. Apostol / A Proof that Euler Missed: Evaluating
                 $\zeta(2)$ the Easy Way (1983) / This note shows that
                 one of the double integrals considered by Beukers ([48]
                 in the table of contents) can be used to establish
                 directly that $\zeta(2) = \pi^2 / 6$ / 456 \\
                 52. O'Shaughnessy / Putting God Back in Math (1983) /
                 An article about the Institute of Pi Research, an
                 organization that ``pokes fun at creationists by
                 pointing out that even the Bible makes mistakes.'' /
                 458 \\
                 53. Stern / A Remarkable Approximation to $ \pi $
                 (1985) / Justification of the value of $ \pi $ in the
                 Bible through numerological interpretations / 460 \\
                 54. Newman and Shanks / On a Sequence Arising in Series
                 for $ \pi $ (1984) / More connections between $ \pi $
                 and modular equations / 462 \\
                 55. Cox / The Arithmetic--Geometric Mean of Gauss
                 (1984) / An extensive study of the complex analytic
                 properties of the AGM / 481 \\
                 56. Borwein and Borwein / The Arithmetic--Geometric
                 Mean and Fast Computation of Elementary Functions
                 (1984) / The relationship between the AGM iteration and
                 fast computation of elementary functions (one of the
                 by-products is an algorithm for $ \pi $) / 537 57.
                 Newman / A Simplified Version of the Fast Algorithms of
                 Brent and Salamin (1984) / Elementary algorithms for
                 evaluating $ e^x $ and $ \pi $ using the Gauss AGM
                 without explicit elliptic function theory / 553 \\
                 58. Wagon / Is Pi Normal? (1985) / A discussion of the
                 conjecture that $ \pi $ has randomly distributed digits
                 / 557 \\
                 59. Keith / Circle Digits: A Self-Referential Story
                 (1986) / A mnemonic for the first 402 decimal places of
                 $ \pi $ / 560 \\
                 60. Bailey / The Computation of $ \pi $ to 29,360,000
                 Decimal Digits Using Borwein's Quartically Convergent
                 Algorithm (1988) / The algorithms used, both for $ \pi
                 $ and for performing the required multiple-precision
                 arithmetic / 562 \\
                 61. Kanada / Vectorization of Multiple-Precision
                 Arithmetic Program and 201,326,000 Decimal Digits of $
                 \pi $ Calculation (1988) / Details of the computation
                 and statistical tests of the first 200 million digits
                 of $ \pi $ / 576 \\
                 62. Borwein and Borwein / Ramanujan and Pi (1988) /
                 This article documents Ramanujan's life, his ingenious
                 approach to calculating $ \pi $, and how his approach
                 is now incorporated into modern computer algorithms /
                 588 \\
                 63. Chudnovsky and Chudnovsky / Approximations and
                 Complex Multiplication According to Ramanujan (1988) /
                 This excerpt describes ``Ramanujan's original quadratic
                 period--quasiperiod relations for elliptic curves with
                 complex multiplication and their applications to
                 representations of fractions of $ \pi $ and other
                 logarithms in terms of rapidly convergent nearly
                 integral (hypergeometric) series.'' / 596 \\
                 64. Borwein, Borwein and Bailey / Ramanujan, Modular
                 Equations, and Approximations to Pi or How to Compute
                 One Billion Digits of Pi (1989) / An exposition of the
                 computation of $ \pi $ using mathematics rooted in
                 Ramanujan's work / 623 \\
                 65. Borwein, Borwein and Dilcher / Pi, Euler Numbers,
                 and Asymptotic Expansions (1989) / An explanation as to
                 why the slowly convergent Gregory series for $ \pi $,
                 truncated at 500,000 terms, gives $ \pi $ to 40 places
                 with only the 6th, 17th, 18th, and 29th places being
                 incorrect / 642 \\
                 66. Beukers, Bezivin, and Robba / An Alternative Proof
                 of the Lindemann--Weierstrass Theorem (1990) / The
                 Lindemann--Weierstrass theorem as a by-product of a
                 criterion for rationality of solutions of differential
                 equations / 649 \\
                 67. Webster / The Tale of Pi (1991) / Various anecdotes
                 about $ \pi $ from the 14th annual IMO Lecture to the
                 Royal Society / 654 \\
                 68. Eco / An excerpt from Foucault's Pendulum (1993) /
                 ``The unnumbered perfection of the circle itself.'' /
                 658 \\
                 69. Keith / Pi Mnemonics and the Art of Constrained
                 Writing (1996) / A mnemonic for $ \pi $ based on Edgar
                 Allen Poe's poem ``The Raven.'' / 659 \\
                 70. Bailey, Borwein, and Plouffe / On the Rapid
                 Computation of Various Polylogarithmic Constants (1997)
                 / A fast method for computing individual digits of $
                 \pi $ in base 2 / 663 \\
                 Appendix I --- On the Early History of Pi / 677 \\
                 Appendix II --- A Computational Chronology of Pi / 683
                 \\
                 Appendix III --- Selected Formulae for Pi / 686 \\
                 Appendix IV --- Translations of Viele and Huygens / 690
                 \\
                 Bibliography / 710 \\
                 Credits / 717 \\
                 A Pamphlet on Pi / 721 \\
                 Contents / 723 \\
                 1. Pi and Its Friends / 725 \\
                 2. Normality of Numbers / 741 \\
                 3. Historia Cyclometrica / 753 \\
                 4. Demotica Cyclometrica / 771 \\
                 References / 779 \\
                 Index / 783",
}

@Proceedings{Frougny:2004:RCR,
  editor =       "Christiane Frougny and Vasco Brattka and Norbert
                 M{\"u}ller",
  booktitle =    "{RNC'6, 6th Conference on Real Numbers and Computers:
                 Nov 15--17, 2004, Dagstuhl, Germany}",
  title =        "{RNC'6, 6th Conference on Real Numbers and Computers:
                 Nov 15--17, 2004, Dagstuhl, Germany}",
  publisher =    "Universita{\"a}t Trier, Fachbereich IV, Mathematik,
                 Informatik",
  address =      "Trier, Germany",
  bookpages =    "216 + i",
  pages =        "216 + i",
  year =         "2004",
  ISSN =         "0944-0488",
  ISSN-L =       "0944-0488",
  bibdate =      "Thu Apr 28 05:55:01 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Forschungsbericht Nr. 04-8.",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004;
                 http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6-complete.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "base conversion; decimal floating-point arithmetic",
  tableofcontents = "Introduction / Christiane Frougny / 1--4 \\
                 Invited Lecture: New ideas and results for solving
                 Differential equations symbolically [abstract only] /
                 Benno Fuchssteiner / 5--5 \\
                 Invited Lecture: A survey of Integer Relations
                 algorithms and rational numbers [abstract only] / Simon
                 Plouffe / 6--6 \\
                 Invited Lecture: Real Numbers and Robustness in
                 Computational Geometry / Stefan Schirra / 7--21 \\
                 Bridging the gap between formal specification and
                 bit-level floating-point arithmetic / Sylvie Boldo /
                 22--36 \\
                 Automata, Borel functions and real numbers in Pisot
                 base / B. Cagnard, P. Simonnet / 37--54 \\
                 Generating formally certified bounds on values and
                 round-off errors / Marc Daumas, Guillaume Melquiond /
                 55--70 \\
                 A proven correctly rounded logarithm in
                 double-precision / Florent de Dinechin, Catherine
                 Loirat, Jean-Michel Muller / 71--85 \\
                 A comparison of polynomial evaluation schemes / L.
                 Fousse, S. Schmitt / 86--102 \\
                 A comparison of real and complex pseudozero sets for
                 polynomials with real coefficients / Stef Graillat,
                 Philippe Langlois / 103--112 \\
                 On Intermediate Precision Required for
                 Correctly-Rounding Decimal-to-Binary Floating-Point
                 Conversion / Michel Hack / 113--134 \\
                 The Generic Multiple-Precision Floating-Point Addition
                 With Exact Rounding (as in the MPFR Library) / Vincent
                 Lef{\`e}vre / 135--145 \\
                 Software Division and Square Root Using Goldschmidt's
                 Algorithms / Peter Markstein / 146--157 \\
                 A Fast Algorithm for Julia Sets of Hyperbolic Rational
                 Functions / R. Rettinger / 158--171 \\
                 An extension of Chaitin's halting probability $\Omega$
                 to measurement operator in infinite dimensional quantum
                 system / Kohtaro Tadaki / 172--191 \\
                 On the Hierarchy of $\Delta_2^0$-Real Numbers / Xizhong
                 Zheng / 192--215 \\
                 Trierer Forschungsberichte Mathematik / Informatik [one
                 page list of reports] / 1--1 (216--216)",
}

@Book{Wahdan:2004:IHE,
  editor =       "Abdel-Moniem Wahdan",
  booktitle =    "{ICEEC'04: 2004 International Conference on
                 Electrical, Electronic and Computer Engineering:
                 proceedings: 5--7 September, 2004, Cairo, Egypt}",
  title =        "{ICEEC'04: 2004 International Conference on
                 Electrical, Electronic and Computer Engineering:
                 proceedings: 5--7 September, 2004, Cairo, Egypt}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xlv + 954",
  year =         "2004",
  bibdate =      "Tue Jul 19 08:01:02 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 melvyl.cdlib.org:210/CDL90",
  note =         "IEEE catalog number 04EX893.",
  acknowledgement = ack-nhfb,
  subject =      "Electric engineering; Congresses; Electronics;
                 Congresses; Computer engineering; Congresses",
}

@Proceedings{IEEE:2005:PIS,
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of the 17th IEEE Symposium on Computer
                 Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod,
                 Massachusetts, USA}",
  title =        "{Proceedings of the 17th IEEE Symposium on Computer
                 Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod,
                 Massachusetts, USA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2005",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Jun 21 19:02:16 2005",
  bibsource =    "http://arith17.polito.it/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  xxnote =       "Not yet published: check editor??",
}

@Book{Ismail:2005:TAS,
  editor =       "Mourad E. H. Ismail and Erik Koelink",
  booktitle =    "Theory and Applications of Special Functions: a Volume
                 Dedicated to {Mizan Rahman}",
  title =        "Theory and Applications of Special Functions: a Volume
                 Dedicated to {Mizan Rahman}",
  volume =       "13",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 491",
  year =         "2005",
  ISBN =         "0-387-24231-7 (hardcover), 0-387-24233-3 (e-book)",
  ISBN-13 =      "978-0-387-24231-6 (hardcover),
                 978-0-387-24233-0(e-book)",
  LCCN =         "QA351 .T44 2005",
  bibdate =      "Sat Oct 30 07:35:31 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Developments in mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0663/2005275626-d.html;
                 http://www.loc.gov/catdir/toc/fy0605/2005275626.html",
  abstract =     "This book, dedicated to Mizan Rahman, is made up of a
                 collection of articles on various aspects of q-series
                 and special functions. It also includes an article by
                 Askey, Ismail, and Koelink on Rahman's mathematical
                 contributions and how they influenced the recent
                 upsurge in the subject. Theory and Applications of
                 Special Functions is intended for researchers and
                 graduate students in special functions, algebraic
                 combinatorics, quantum groups, and integrable
                 systems.",
  acknowledgement = ack-nhfb,
  subject =      "Mathematics; Special Functions; Functions, special;
                 Integral Transforms; Approximations and Expansions;
                 Integral Transforms, Operational Calculus",
  tableofcontents = "Mizan Rahman, his mathematics and literary writings
                 / Richard Askey, Mourad E. H. Ismail and Erik Koelink
                 \\
                 On the completeness of sets of $q$-Bessel function
                 $J\nu^{(3)}(x; q)$ / L. D. Abreu and J. Bustoz \\
                 $\alpha$-Gaussian polynomials and finite
                 Rogers-Ramanujan identities / George E. Andrews \\
                 On a generalized gamma convolution related to the
                 $q$-calculus / Christian Berg \\
                 Ramanujan and cranks / Bruce C. Berndt, Heng Huat Chan,
                 Song Heng Chan and Wen-Chin Liaw \\
                 Saalschutz chain reactions and multiple $q$-series
                 transformations / Chu Wenchang \\
                 Painleve equations and associated polynomials / Peter
                 A. Clarkson \\
                 Zeta functions of Heisenberg graphs over finite rings /
                 Michelle DeDeo, Maria Martinez, Archie Medrano, Marvin
                 Minei, Harold Stark and Audrey Terras \\
                 $q$-Analogues of some multivariable biorthogonal
                 polynomials / George Gasper and Mizan Rahman \\
                 ^?? : Some systems of multivariable orthogonal
                 Askey-Wilson polynomials / George Gasper and Mizan
                 Rahman \\
                 Continuous Hahn functions as Clebsch--Gordan
                 coefficients / Wolter Groenevelt, Erik Koelink and
                 Hjalmar Rosengren \\
                 New proofs of some $q$-series results / Mourad E. H.
                 Ismail and Ruiming Zhang \\
                 Little $q$-Jacobi functions of complex order / Kevin W.
                 J. Kadell \\
                 Second addition formula for continuous
                 $q$-ultraspherical polynomials / Tom H. Koornwinder \\
                 Bilateral series involving basic hypergeometric
                 functions / Hjalmar Rosengren \\
                 Hilbert space asymptotics of a class of orthonormal
                 polynomials on a bounded interval / S. N. M.
                 Ruijsenaars \\
                 Abel--Rothe type generalizations of Jacobi's triple
                 product identity / Michael Schlosser \\
                 Summable sums of hypergeometric series / D. Stanton \\
                 Askey--Wilson functions and quantum groups / Jasper V.
                 Stokman \\
                 Analog of the Cauchy--Hadamard formula for expansions
                 in $q$-polynomials /Remarks on some basic
                 hypergeometric series / Changgui Zhang",
}

@Proceedings{Vassiliadis:2005:IIC,
  editor =       "Stamatis Vassiliadis and Nikitas J. Dimopoulos and
                 Sanjay Vishnu Rajopadhye",
  booktitle =    "{16th IEEE International Conference on
                 Application-Specific Systems, Architectures, and
                 Processors: ASAP 2005: 23--25 July 2005, Samos,
                 Greece}",
  title =        "{16th IEEE International Conference on
                 Application-Specific Systems, Architectures, and
                 Processors: ASAP 2005: 23--25 July 2005, Samos,
                 Greece}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 419",
  year =         "2005",
  ISBN =         "0-7695-2407-9",
  ISBN-13 =      "978-0-7695-2407-8",
  LCCN =         "TK7874.6 .I58 2005",
  bibdate =      "Sun Mar 4 21:53:56 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Application-Specific
                 Systems, Architectures, and Processors (16th: 2005:
                 Samos, Greece)",
  subject =      "Array processors; Congresses; Signal processing;
                 Digital techniques; Application specific integrated
                 circuits",
}

@Proceedings{zuCastell:2005:ILO,
  editor =       "Wolfgang zu Castell and Frank Filbir and Brigitte
                 Forster",
  booktitle =    "{Inzell lectures on orthogonal polynomials}",
  title =        "{Inzell lectures on orthogonal polynomials}",
  publisher =    "Nova Science",
  address =      "Hauppauge, NY, USA",
  pages =        "x + 199",
  year =         "2005",
  ISBN =         "1-59454-108-6",
  ISBN-13 =      "978-1-59454-108-7",
  LCCN =         "QA404.5 .I595 2005",
  bibdate =      "Sat Oct 30 17:16:08 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  note =         "Lectures from the Inzell Summer School on Orthogonal
                 Polynomials, Harmonic Analysis, Approximation, and
                 Applications, held in Inzell, Germany, September
                 17--21, 2001.",
  series =       "Advances in the theory of special functions and
                 orthogonal polynomials",
  acknowledgement = ack-nhfb,
  remark =       "Canonical moments, orthogonal polynomials with
                 applications to statistics / Holger Dette \\
                 Discrete commutative hypergroups / Rupert Lasser \\
                 Orthogonal polynomials and Banach algebras / Ryszard
                 Szwarc \\
                 Lecture notes on orthogonal polynomials of several
                 variables / Yuan Xu",
  subject =      "Orthogonal polynomials",
}

@Proceedings{Anonymous:2006:PCR,
  editor =       "Anonymous",
  booktitle =    "{Proceedings of the 7th Conference on Real Numbers and
                 Computers (RNC 7) LORIA, Nancy, France, July 10--12,
                 2006}",
  title =        "{Proceedings of the 7th Conference on Real Numbers and
                 Computers (RNC 7) LORIA, Nancy, France, July 10--12,
                 2006}",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  year =         "2006",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Jun 27 10:26:43 2006",
  bibsource =    "http://rnc7.loria.fr/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Menezes:2006:PAS,
  editor =       "Ronaldo Menezes",
  booktitle =    "{Proceedings of the 44th annual Southeast Regional
                 Conference 2006: Melbourne, Florida, March 10--12,
                 2006}",
  title =        "{Proceedings of the 44th annual Southeast Regional
                 Conference 2006: Melbourne, Florida, March 10--12,
                 2006}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "823",
  year =         "2006",
  ISBN =         "1-59593-315-8 (print)",
  ISBN-13 =      "978-1-59593-315-7 (print)",
  LCCN =         "QA75.5 A184 2006 E",
  bibdate =      "Sat Oct 9 15:04:24 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  subject =      "Computer-assisted instruction; Congresses; Database
                 management; Electronic data processing",
}

@Proceedings{Brown:2007:PIS,
  editor =       "C. W. Brown",
  booktitle =    "{Proceedings of the 2007 International Symposium on
                 Symbolic and Algebraic Computation, July 29--August 1,
                 2007, University of Waterloo, Waterloo, Ontario,
                 Canada}",
  title =        "{Proceedings of the 2007 International Symposium on
                 Symbolic and Algebraic Computation, July 29--August 1,
                 2007, University of Waterloo, Waterloo, Ontario,
                 Canada}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "????",
  year =         "2007",
  ISBN =         "1-59593-743-9 (print), 1-59593-742-0 (CD-ROM)",
  ISBN-13 =      "978-1-59593-743-8 (print), 978-1-59593-742-1
                 (CD-ROM)",
  LCCN =         "QA76.5 S98 2007",
  bibdate =      "Fri Jun 20 08:53:37 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  note =         "ACM order number 505070.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Holzapfel:2007:AGA,
  editor =       "Rolf-Peter Holzapfel and A. Muhammed Uludag and
                 Masaaki Yoshida",
  booktitle =    "{Arithmetic and geometry around hypergeometric
                 functions: lecture notes of a CIMPA Summer School held
                 at Galatasaray University, Istanbul, Turkey, June
                 13--25, 2005}",
  title =        "{Arithmetic and geometry around hypergeometric
                 functions: lecture notes of a CIMPA Summer School held
                 at Galatasaray University, Istanbul, Turkey, June
                 13--25, 2005}",
  volume =       "235",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "viii + 437",
  year =         "2007",
  ISBN =         "3-7643-8283-X",
  ISBN-13 =      "978-3-7643-8283-4",
  LCCN =         "QA245 .S86 2005",
  bibdate =      "Sat Oct 30 21:12:24 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Progress in mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0913/2006939568-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0913/2006939568-t.html",
  acknowledgement = ack-nhfb,
  subject =      "Algebra; Congresses.; Geometry, Algebraic; Congresses;
                 Number theory",
}

@Proceedings{Iske:2007:AAP,
  editor =       "Armin Iske and Jeremy Levesley",
  booktitle =    "{Algorithms for Approximation: Proceedings of the 5th
                 International Conference, Chester, July 2005}",
  title =        "{Algorithms for Approximation: Proceedings of the 5th
                 International Conference, Chester, July 2005}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "300",
  year =         "2007",
  DOI =          "https://doi.org/10.1007/978-3-540-46551-5",
  ISBN =         "3-540-46551-0, 3-540-33283-9",
  ISBN-13 =      "978-3-540-46551-5, 978-3-540-33283-1",
  LCCN =         "QA221 .A44 2007",
  bibdate =      "Thu Dec 1 09:41:19 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  acknowledgement = ack-nhfb,
  subject =      "Mathematics; Special Functions; Functions, special;
                 Engineering mathematics; Mathematics of Computing;
                 Approximations and Expansions; Computer science;
                 Computational Mathematics and Numerical Analysis; Appl.
                 Mathematics / Computational Methods of Engineering",
}

@Proceedings{Kornerup:2007:PIS,
  editor =       "Peter Kornerup and Jean-Michel Muller",
  booktitle =    "{Proceedings of the 18th IEEE Symposium on Computer
                 Arithmetic, June 25--27, 2007, Montpellier, France}",
  title =        "{Proceedings of the 18th IEEE Symposium on Computer
                 Arithmetic, June 25--27, 2007, Montpellier, France}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 269",
  year =         "2007",
  ISBN =         "0-7695-2854-6",
  ISBN-13 =      "978-0-7695-2854-0",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62",
  bibdate =      "Tue Jun 27 10:26:43 2006",
  bibsource =    "http://www.lirmm.fr/arith18/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 odin2.bib.sdu.dk:210/Horizon",
  URL =          "http://www.lirmm.fr/arith18/",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Proceedings{Dominici:2008:SFO,
  editor =       "Diego Dominici and Robert S. Maier",
  booktitle =    "{Special functions and orthogonal polynomials: AMS
                 Special Session on Special Functions and Orthogonal
                 Polynomials, April 21--22, 2007, Tucson, Arizona}",
  title =        "{Special functions and orthogonal polynomials: AMS
                 Special Session on Special Functions and Orthogonal
                 Polynomials, April 21--22, 2007, Tucson, Arizona}",
  volume =       "471",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "v + 218",
  year =         "2008",
  ISBN =         "0-8218-4650-7",
  ISBN-13 =      "978-0-8218-4650-6",
  LCCN =         "????",
  bibdate =      "Sat Oct 30 17:30:10 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  series =       "Contemporary mathematics",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:2008:ICA,
  editor =       "{IEEE}",
  booktitle =    "{2008 International Conference on Application-Specific
                 Systems, Architectures and Processors: Leuven, Belgium,
                 2--4 July 2008}",
  title =        "{2008 International Conference on Application-Specific
                 Systems, Architectures and Processors: Leuven, Belgium,
                 2--4 July 2008}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiv + 309 + 12",
  year =         "2008",
  ISBN =         "1-4244-1897-6 (paperback), 1-4244-1898-4",
  ISBN-13 =      "978-1-4244-1897-8 (paperback), 978-1-4244-1898-5",
  LCCN =         "????",
  bibdate =      "Mon Feb 10 07:31:38 MST 2020",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  note =         "IEEE catalog number CFP08063-PRT.",
  URL =          "http://ieeexplore.ieee.org/servlet/opac?punumber=4569858;
                 http://www.gbv.de/dms/tib-ub-hannover/631855815.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Kongress auch zitiert als: ASAP 08. Parallel als
                 Online-Ausg. erschienen. ASAP 08.",
  tableofcontents = "ASAP08 Conference proceedings / c1--c1 / doi:
                 10.1109/ASAP.2008.4580199 \\
                 ASAP08 Conference proceedings / c2--c2 / doi:
                 10.1109/ASAP.2008.4580200 \\
                 Frontmatter and table of contents / c1--xiii / doi:
                 10.1109/ASAP.2008.4580202 \\
                 ASAP Organizing and Steering Committees / ix \\
                 ASAP Technical Technical Program Committee / x \\
                 Keynote 1: Security and Opportunities for
                 Application-Specific Processors / Ruby B. Lee / xii \\
                 Keynote 2: Art of of Application-Specific Processor
                 Design: Great Artists use Good Tools / Gert Goossens /
                 xiv \\
                 Session 1: Application-Specific Processor Instruction
                 Sets / 1 \\
                 Copyright notice / i--i / doi:
                 10.1109/ASAP.2008.4580197 \\
                 Copyright notice / ii--ii / doi:
                 10.1109/ASAP.2008.4580198 \\
                 K. Atasu, O. Mencer, W. Luk, C. Ozturan and G. Dundar /
                 Fast custom instruction identification by convex
                 subgraph enumeration / 1--6 / doi:
                 10.1109/ASAP.2008.4580145 \\
                 Y. Hilewitz, C. Lauradoux and R. B. Lee / Bit matrix
                 multiplication in commodity processors / 7--12 / doi:
                 10.1109/ASAP.2008.4580146 \\
                 M. Alle et al. / Synthesis of application accelerators
                 on Runtime Reconfigurable Hardware / 13--18 / doi:
                 10.1109/ASAP.2008.4580147 \\
                 A. Amaricai, M. Vladutiu, M. Udrescu, L. Prodan and O.
                 Boncalo / Floating point multiplication rounding
                 schemes for interval arithmetic / 19--24 / doi:
                 10.1109/ASAP.2008.4580148 \\
                 S. Balasubramanian, H. W. Carter, A. Bogdanov, A. Rupp
                 and Jintai Ding / Fast multivariate signature
                 generation in hardware: The case of rainbow / 25--30 /
                 doi: 10.1109/ASAP.2008.4580149 \\
                 M. Hosseinabady and J. Nunez-Yanez / Fault-tolerant
                 dynamically reconfigurable NoC-based SoC / 31--36 /
                 doi: 10.1109/ASAP.2008.4580150 \\
                 T. Lorunser et al. / Security Processor with Quantum
                 Key Distribution / 37--42 / doi:
                 10.1109/ASAP.2008.4580151 \\
                 P. K. Meher and J. C. Patra / Fully-pipelined efficient
                 architectures for FPGA realization of discrete Hadamard
                 transform / 43--48 / doi: 10.1109/ASAP.2008.4580152 \\
                 R. Rajore, G. Garga, H. S. Jamadagni and S. K. Nandy /
                 Reconfigurable Viterbi decoder on mesh connected
                 multiprocessor architecture / 49--54 / doi:
                 10.1109/ASAP.2008.4580153 \\
                 T. Ramdas, G. K. Egan, D. Abramson and K. K. Baldridge
                 / Run-time thread sorting to expose data-level
                 parallelism / 55--60 / doi: 10.1109/ASAP.2008.4580154
                 \\
                 S. Jovanovic, C. Tanougast and S. Weber / A New
                 High-Performance Scalable Dynamic Interconnection for
                 FPGA-based Reconfigurable Systems / 61--66 / doi:
                 10.1109/ASAP.2008.4580155 \\
                 D. Dickin and L. Shannon / Extending the SIMPPL SoC
                 architectural framework to support application-specific
                 architectures on multi-FPGA platforms / 67--72 / doi:
                 10.1109/ASAP.2008.4580156 \\
                 A. E. Kiasari, S. Hessabi and H. Sarbazi-Azad / PERMAP:
                 A performance-aware mapping for application-specific
                 SoCs / 73--78 / doi: 10.1109/ASAP.2008.4580157 \\
                 A. C. Atici, L. Batina, Junfeng Fan, I. Verbauwhede and
                 S. Berna Ors Yalcin / Low-cost implementations of NTRU
                 for pervasive security / 79--84 / doi:
                 10.1109/ASAP.2008.4580158 \\
                 M. Knezzevic, K. Sakiyama, Y. K. Lee and I. Verbauwhede
                 / On the high-throughput implementation of RIPEMD-160
                 hash algorithm / 85--90 / doi:
                 10.1109/ASAP.2008.4580159 \\
                 Wang Haixin, Bai Guoqiang and Chen Hongyi / Zodiac:
                 System architecture implementation for a
                 high-performance Network Security Processor / 91--96 /
                 doi: 10.1109/ASAP.2008.4580160 \\
                 P. K. Meher / Efficient systolization of cyclic
                 convolution for systolic implementation of sinusoidal
                 transforms / 97--101 / doi: 10.1109/ASAP.2008.4580161
                 \\
                 D. B. Thomas and W. Luk / Resource efficient generators
                 for the floating-point uniform and exponential
                 distributions / 102--107 / doi:
                 10.1109/ASAP.2008.4580162 \\
                 I. L. Dalal, D. Stefan and J. Harwayne-Gidansky / Low
                 discrepancy sequences for Monte Carlo simulations on
                 reconfigurable platforms / 108--113 / doi:
                 10.1109/ASAP.2008.4580163 \\
                 Y. Vanderperren and W. Dehaene / A subsampling pulsed
                 UWB demodulator based on a flexible complex SVD /
                 114--119 / doi: 10.1109/ASAP.2008.4580164 \\
                 J. Divyasree, H. Rajashekar and K. Varghese /
                 Dynamically reconfigurable regular expression matching
                 architecture / 120--125 / doi:
                 10.1109/ASAP.2008.4580165 \\
                 J. Khan, S. Niar, A. Menhaj, Y. Elhillali and J. L.
                 Dekeyser / An MPSoC architecture for the Multiple
                 Target Tracking application in driver assistant system
                 / 126--131 / doi: 10.1109/ASAP.2008.4580166 \\
                 Wangyuan Zhang and Tao Li / Managing multi-core
                 soft-error reliability through utility-driven cross
                 domain optimization / 132--137 / doi:
                 10.1109/ASAP.2008.4580167 \\
                 S. Braganza and M. Leeser / An efficient implementation
                 of a phase unwrapping kernel on reconfigurable hardware
                 / 138--143 / doi: 10.1109/ASAP.2008.4580168 \\
                 H. Flatt, S. Blume, S. Hesselbarth, T. Schunemann and
                 P. Pirsch / A parallel hardware architecture for
                 connected component labeling based on fast label
                 merging / 144--149 / doi: 10.1109/ASAP.2008.4580169 \\
                 Yuki Kobayashi, M. Jayapala, P. Raghavan, F. Catthoor
                 and Masaharu Imai / Operation shuffling over cycle
                 boundaries for low energy L0 clustering / 150--155 /
                 doi: 10.1109/ASAP.2008.4580170 \\
                 V. Kundeti, Yunsi Fei and S. Rajasekaran / An efficient
                 digital circuit for implementing Sequence Alignment
                 algorithm in an extended processor / 156--161 / doi:
                 10.1109/ASAP.2008.4580171 \\
                 B. K. Mohanty and P. K. Meher / Concurrent systolic
                 architecture for high-throughput implementation of
                 3-dimensional discrete wavelet transform / 162--166 /
                 doi: 10.1109/ASAP.2008.4580172 \\
                 S. Mirzaei, A. Irturk, R. Kastner, B. T. Weals and R.
                 E. Cagley / Design space exploration of a cooperative
                 MIMO receiver for reconfigurable architectures /
                 167--172 / doi: 10.1109/ASAP.2008.4580173 \\
                 Mao Nakajima and Minoru Watanabe / Dynamic holographic
                 reconfiguration on a four-context ODRGA / 173--178 /
                 doi: 10.1109/ASAP.2008.4580174 \\
                 F. Pardo, P. Lopez and D. Cabello / FPGA-based hardware
                 accelerator of the heat equation with applications on
                 infrared thermography / 179--184 / doi:
                 10.1109/ASAP.2008.4580175 \\
                 M. Rahmati, M. S. Sadri and M. A. Naeini / FPGA based
                 singular value decomposition for image processing
                 applications / 185--190 / doi:
                 10.1109/ASAP.2008.4580176 \\
                 A. Jacob, J. Buhler and R. D. Chamberlain /
                 Accelerating Nussinov RNA secondary structure
                 prediction with systolic arrays on FPGAs / 191--196 /
                 doi: 10.1109/ASAP.2008.4580177 \\
                 J. Lee, L. Shannon, M. J. Yedlin and G. F. Margrave / A
                 multi-FPGA application-specific architecture for
                 accelerating a floating point Fourier Integral Operator
                 / 197--202 / doi: 10.1109/ASAP.2008.4580178 \\
                 K. F. C. Yiu, Chun Hok Ho, N. Grbric, Yao Lu, Xiaoxiang
                 Shi and W. Luk / Reconfigurable acceleration of
                 microphone array algorithms for speech enhancement /
                 203--208 / doi: 10.1109/ASAP.2008.4580179 \\
                 Yang Sun, Yuming Zhu, M. Goel and J. R. Cavallaro /
                 Configurable and scalable high throughput turbo decoder
                 architecture for multiple 4G wireless standards /
                 209--214 / doi: 10.1109/ASAP.2008.4580180 \\
                 M. B. S. Tavares, S. Kunze, E. Matus and G. P. Fettweis
                 / Architecture and VLSI realization of a high-speed
                 programmable decoder for LDPC convolutional codes /
                 215--220 / doi: 10.1109/ASAP.2008.4580181 \\
                 D. Llorente, K. Karras, T. Wild and A. Herkersdorf /
                 Buffer allocation for advanced packet segmentation in
                 Network Processors / 221--226 / doi:
                 10.1109/ASAP.2008.4580182 \\
                 A. Vazquez and E. Antelo / New insights on Ling adders
                 / 227--232 / doi: 10.1109/ASAP.2008.4580183 \\
                 N. Brisebarre, F. de Dinechin and J. Muller / Integer
                 and floating-point constant multipliers for FPGAs /
                 239--244 / doi: 10.1109/ASAP.2008.4580184 \\
                 N. Brisebarre, S. Chevillard, M. D. Ercegovac, J.
                 Muller and S. Torres / An efficient method for
                 evaluating polynomial and rational function
                 approximations / 233--238 / doi:
                 10.1109/ASAP.2008.4580185 \\
                 A. Garcia, M. Berekovic and T. Vander Aa / Mapping of
                 the AES cryptographic algorithm on a Coarse-Grain
                 reconfigurable array processor / 245--250 / doi:
                 10.1109/ASAP.2008.4580186 \\
                 J. Nimmy et al. / RECONNECT: A NoC for polymorphic
                 ASICs using a low overhead single cycle router /
                 251--256 / doi: 10.1109/ASAP.2008.4580187 \\
                 M. Mbaye, N. Belanger, Y. Savaria and S. Pierre /
                 Loop-oriented metrics for exploring an
                 application-specific architecture design-space /
                 257--262 / doi: 10.1109/ASAP.2008.4580188 \\
                 S. K. Dash and T. Srikanthan / Rapid estimation of
                 instruction cache hit rates using loop profiling /
                 263--268 / doi: 10.1109/ASAP.2008.4580189 \\
                 Xuan Guan and Yunsi Fei / Reducing power consumption of
                 embedded processors through register file partitioning
                 and compiler support / 269--274 / doi:
                 10.1109/ASAP.2008.4580190 \\
                 A. Tumeo, M. Monchiero, G. Palermo, F. Ferrandi and D.
                 Sciuto / Lightweight DMA management mechanisms for
                 multiprocessors on FPGA / 275--280 / doi:
                 10.1109/ASAP.2008.4580191 \\
                 P. de Langen and B. Juurlink / Memory copies in
                 multi-level memory systems / 281--286 / doi:
                 10.1109/ASAP.2008.4580192 \\
                 R. Adrsha, Mythri, S. K. Nandy and R. Narayan /
                 Architecture of a polymorphic ASIC for interoperability
                 across multi-mode H.264 decoders / 287--292 / doi:
                 10.1109/ASAP.2008.4580193 \\
                 R. R. Osorio and J. D. Bruguera / An FPGA architecture
                 for CABAC decoding in manycore systems / 293--298 /
                 doi: 10.1109/ASAP.2008.4580194 \\
                 A. Guntoro and M. Glesner / Novel approach on
                 lifting-based DWT and IDWT processor with multi-context
                 configuration to support different wavelet filters /
                 299--304 / doi: 10.1109/ASAP.2008.4580195 \\
                 B. K. Mohanty and P. K. Meher / Throughput-scalable
                 hybrid-pipeline architecture for multilevel lifting 2-D
                 DWT of JPEG 2000 coder / 305--309 / doi:
                 10.1109/ASAP.2008.4580196 \\
                 Author index / 310--321 / doi:
                 10.1109/ASAP.2008.4580201",
}

@Proceedings{Bruguera:2009:PIS,
  editor =       "Javier D. Bruguera and Marius Cornea and Debjit
                 DasSarma and John Harrison",
  booktitle =    "{Proceedings of the 19th IEEE Symposium on Computer
                 Arithmetic, June 8--10, 2009, Portland, Oregon, USA}",
  title =        "{Proceedings of the 19th IEEE Symposium on Computer
                 Arithmetic, June 8--10, 2009, Portland, Oregon, USA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 235",
  year =         "2009",
  ISBN =         "0-7695-3670-0, 1-4244-4329-6",
  ISBN-13 =      "978-0-7695-3670-5, 978-1-4244-4329-1",
  ISSN =         "1063-6889",
  LCCN =         "QA76.6 .S887 2009",
  bibdate =      "Fri Jun 12 12:24:37 2009",
  bibsource =    "http://www.ac.usc.es/arith19/;
                 https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  URL =          "http://www.ac.usc.es/arith19/",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
  tableofcontents = "Keynote Talk \\
                 Anton: A Specialized Machine for Millisecond-Scale
                 Molecular Dynamics Simulations of Proteins / David E.
                 Shaw / 3 \\
                 Session 1: Algorithms and Number Systems \\
                 Efficient Data Structure and Algorithms for Sparse
                 Integers, Sets and Predicates / Jean E. Vuillemin / 7
                 \\
                 A Dual-Purpose Real/Complex Logarithmic Number System
                 ALU / Mark G. Arnold and Sylvain Collange / 15 \\
                 Selected RNS Bases for Modular Multiplication / J. C.
                 Bajard, M. Kaihara, and T. Plantard / 25 \\
                 Invited Talk \\
                 A Historical Perspective on Computer Arithmetic /
                 Stanley Mazor / 35 \\
                 Session 2: Arithmetic Hardware \\
                 Higher Radix Squaring Operations Employing
                 Left-to-Right Dual Recoding / David W. Matula / 39 \\
                 Advanced Clockgating Schemes for
                 Fused-Multiply-Add-Type Floating-Point Units / Jochen
                 Preiss, Maarten Boersma, and Silvia Melitta Mueller /
                 48 \\
                 Unified Approach to the Design of Modulo-$(2^n \pm 1)$
                 Adders Based on Signed-LSB Representation of Residues /
                 Ghassem Jaberipur and Behrooz Parhami / 57 \\
                 Session 3: Finite Fields and Cryptography \\
                 Subquadratic Space Complexity Multiplier for a Class of
                 Binary Fields Using Toeplitz Matrix Approach / M. A.
                 Hasan and C. Negre / 67 \\
                 Hybrid Binary-Ternary Joint Form and Its Application in
                 Elliptic Curve / Cryptography / Jithra Adikari, Vassil
                 Dimitrov, and Laurent Imbert / 76 \\
                 Polynomial Multiplication over Finite Fields Using
                 Field Extensions and Interpolation / Murat Cenk, Cetin
                 Kaya Koc, and Ferruh Ozbudak / 84 \\
                 Session 4: Mathematical Software \\
                 A New Binary Floating-Point Division Algorithm and Its
                 Software Implementation on the ST231 Processor /
                 Claude-Pierre Jeannerod, Herve Knochel, Christophe
                 Monat, Guillaume Revy, and Gilles Villard / 95 \\
                 Fast and Accurate Bessel Function Computation / John
                 Harrison / 104 \\
                 Implementation Specific Verification of Divide and
                 Square Root Instructions / Elena Guralnik, Ariel J.
                 Birnbaum, Anatoly Koyfinan, and Avi Kaplan / 114 \\
                 Session 5: Decimal Hardware \\
                 A Decimal Floating-Point Adder with Decoded Operands
                 and a Decimal Leading-Zero Anticipator / Liang-Kai Wang
                 and Michael J. Schulte / 125 \\
                 A High-Performance Significand BCD Adder with IEEE
                 754-2008 Decimal Rounding / Alvaro Vazquez and Elisardo
                 Antelo / 135 \\
                 Fully Redundant Decimal Arithmetic / Saeid Gorgin and
                 Ghassem Jaberipur / 145 \\
                 Session 6: Floating-Point Techniques \\
                 On the Computation of Correctly-Rounded Sums / P.
                 Kornerup, V. Lefevre, N. Louvet, and J. M. Muller / 155
                 \\
                 Multi-operand Floating-Point Addition / Alexandre F.
                 Tenca / 161 \\
                 Certified and Fast Computation of Supremum Norms of
                 Approximation Errors / Sylvain Chevillard, Mioara
                 Jolde{\c{s}}, and Christoph Lauter / 169 \\
                 Session 7: Decimal Transcendentals \\
                 Computation of Decimal Transcendental Functions Using
                 the CORDIC Algorithm / {\'A}lvaro V{\'a}zquez, Julio
                 Villalba, and Elisardo Antelo / 179 \\
                 Decimal Transcendentals via Binary / John Harrison /
                 187 \\
                 A 32-bit Decimal Floating-Point Logarithmic Converter /
                 Dongdong Chen, Yu Zhang, Younhee Choi, Moon Ho Lee, and
                 Seok-Bum Ko / 195 \\
                 Special Session on Automated Synthesis of Arithmetic
                 Operations \\
                 Datapath Synthesis for Standard-Cell Design / Reto
                 Zimmermann / 207 \\
                 Design Space Exploration for Power-Efficient
                 Mixed-Radix Ling Adders / Chung-Kuan Cheng / 212 \\
                 Challenges in Automatic Optimization of Arithmetic
                 Circuits / Ajay K. Verma, Philip Brisk, and Paolo Ienne
                 / 213 \\
                 Panel on Decimal Arithmetic in Industry \\
                 Energy and Delay Improvement via Decimal Floating Point
                 Units / Hossam A. H. Fahmy, Ramy Raafat, Amira M.
                 Abdel-Majeed, Rodina Samy, Torek ElDeeb, and Yasmin
                 Farouk / 221 \\
                 IEEE 754-2008 Decimal Floating-Point for Intel
                 Architecture Processors / Marius Cornea / 225 \\
                 Special Session on Interval Arithmetic \\
                 IEEE Interval Standard Working Group --- P1788: Current
                 Status / William Edmonson and Guillaume Melquiond / 231
                 \\
                 Author Index",
}

@Proceedings{Fukuda:2010:MSI,
  editor =       "Komei Fukuda and Joris van der Hoeven and Michael
                 Joswig and Nobuki Takayama",
  booktitle =    "{Mathematical software --- ICMS 2010: third
                 International Congress on Mathematical Software,
                 K{\=o}be, Japan, September 13--17, 2010: proceedings}",
  title =        "{Mathematical software --- ICMS 2010: third
                 International Congress on Mathematical Software,
                 K{\=o}be, Japan, September 13--17, 2010: proceedings}",
  volume =       "6327",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 368",
  year =         "2010",
  DOI =          "https://doi.org/10.1007/978-3-642-15582-6",
  ISBN =         "3-642-15581-2 (paperback), 3-642-15582-0 (e-book)",
  ISBN-13 =      "978-3-642-15581-9 (paperback), 978-3-642-15582-6
                 (e-book)",
  LCCN =         "QA76.95 .I5654 2010",
  bibdate =      "Sat Aug 9 14:06:27 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2010a.bib;
                 https://www.math.utah.edu/pub/tex/bib/magma.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       ser-LNCS,
  URL =          "http://link.springer.com/book/10.1007/978-3-642-15582-6",
  acknowledgement = ack-nhfb,
  subject =      "Mathematics; Data processing; Congresses; Computer
                 software",
  tableofcontents = "Plenary \\
                 Computational Discrete Geometry / Thomas C. Hales /
                 1--3 \\
                 Exploiting Structured Sparsity in Large Scale
                 Semidefinite Programming Problems / Masakazu Kojima /
                 4--9 \\
                 Reliable and Efficient Geometric Computing / Kurt
                 Mehlhorn / 10--11 \\
                 The Sage Project: Unifying Free Mathematical Software
                 to Create a Viable Alternative to Magma, Maple,
                 Mathematica and MATLAB / Bur{\c{c}}in Er{\"o}cal,
                 William Stein / 12--27 \\
                 Computation of Special Functions (Invited) \\
                 Sollya: An Environment for the Development of Numerical
                 Codes / Sylvain Chevillard, Mioara Jolde , Christoph
                 Lauter / 28--31 \\
                 Validated Special Functions Software / Annie Cuyt,
                 Franky Backeljauw, Stefan Becuwe, Joris Van Deun /
                 32--34 \\
                 The Dynamic Dictionary of Mathematical Functions (DDMF)
                 / Alexandre Benoit, Fr{\'e}d{\'e}ric Chyzak, Alexis
                 Darrasse, Stefan Gerhold, Marc Mezzarobba, Bruno Salvy
                 / 35--41 \\
                 Reliable Computing with GNU MPFR / Paul Zimmermann /
                 42--45 \\
                 Computational Group Theory (Invited) \\
                 Simplicial Cohomology of Smooth Orbifolds in GAP /
                 Mohamed Barakat, Simon G{\"o}rtzen / 46--49 \\
                 Computing Polycyclic Quotients of Finitely
                 (L-)Presented Groups via Groebner Bases / Bettina Eick,
                 Max Horn / 50--53 \\
                 Constructive Membership Testing in Black-Box Classical
                 Groups / Sophie Ambrose, Scott H. Murray, Cheryl E.
                 Praeger, Csaba Schneider / 54--57 \\
                 Computational Group Theory (Contributed) \\
                 Towards High-Performance Computational Algebra with GAP
                 / Reimer Behrends, Alexander Konovalov, Steve Linton,
                 Frank L{\"u}beck, Max Neunh{\"o}effer / 58--61 \\
                 An Improvement of a Function Computing Normalizers for
                 Permutation Groups / Izumi Miyamoto / 62--68 \\
                 A GAP Package for Computation with Coherent
                 Configurations / Dmitrii V. Pasechnik, Keshav Kini /
                 69--72 \\
                 Computer Algebra (Invited) \\
                 CoCoALib: A C++ Library for Computations in Commutative
                 Algebra \ldots{} and Beyond / John Abbott, Anna M.
                 Bigatti / 73--76 \\
                 LinBox Founding Scope Allocation, Parallel Building
                 Blocks, and Separate Compilation / Jean-Guillaume
                 Dumas, Thierry Gautier, Cl{\'e}ment Pernet, B. David
                 Saunders / 77--83 \\
                 FGb: A Library for Computing Gr{\"o}bner Bases /
                 Jean-Charles Faug{\`e}re / 84--87 \\
                 Fast Library for Number Theory: An Introduction /
                 William B. Hart / 88--91 \\
                 Exact Numeric Computation for Algebraic and Geometric
                 Computation (Invited) \\
                 Controlled Perturbation for Certified Geometric
                 Computing with Fixed-Precision Arithmetic / Dan
                 Halperin / 92--95 \\
                 Exact Numeric Computation for Algebraic and Geometric
                 Computation (Invited) \\
                 Exact Geometric and Algebraic Computations in CGAL /
                 Menelaos I. Karavelas / 96--99 \\
                 On Solving Systems of Bivariate Polynomials / Fabrice
                 Rouillier / 100--104 \\
                 Accurate and Reliable Computing in Floating-Point
                 Arithmetic / Siegfried M. Rump / 105--108 \\
                 Exact Numeric Computation for Algebraic and Geometric
                 Computation (Contributed) \\
                 Deferring Dag Construction by Storing Sums of Floats
                 Speeds-Up Exact Decision Computations Based on
                 Expression Dags / Marc M{\"o}rig / 109--120 \\
                 The Design of Core 2: A Library for Exact Numeric
                 Computation in Geometry and Algebra / Jihun Yu, Chee
                 Yap, Zilin Du, Sylvain Pion, Herv{\'e} Br{\"o}nnimann /
                 121--141 \\
                 Formal Proof (Invited) \\
                 Introducing HOL Zero / Mark Adams / 142--143 \\
                 Euler s Polyhedron Formula in mizar / Jesse Alama /
                 144--147 \\
                 Building a Library of Mechanized Mathematical Proofs:
                 Why Do It? and What Is It Like to Do? / R. D. Arthan /
                 148--148 \\
                 Linear Programs for the Kepler Conjecture / Thomas C.
                 Hales / 149--151 \\
                 A Formal Proof of Pick s Theorem / John Harrison /
                 152--154 \\
                 Formal Proof (Contributed) \\
                 Evaluation of Automated Theorem Proving on the Mizar
                 Mathematical Library / Josef Urban, Krystof Hoder,
                 Andrei Voronkov / 155--166 \\
                 Geometry and Visualization (Invited) \\
                 On Local Deformations of Planar Quad-Meshes / Tim
                 Hoffmann / 167--169 \\
                 Construction of Harmonic Surfaces with Prescribed
                 Geometry / Matthias Weber / 170--173 \\
                 Geometry and Visualization (Contributed) \\
                 A Library of OpenGL-Based Mathematical Image Filters /
                 Martin von Gagern, Christian Mercat / 174--185 \\
                 MD-jeep: An Implementation of a Branch and Prune
                 Algorithm for Distance Geometry Problems / Antonio
                 Mucherino, Leo Liberti, Carlile Lavor / 186--197 \\
                 TADD: A Computational Framework for Data Analysis Using
                 Discrete Morse Theory / Jan Reininghaus, David
                 G{\"u}nther, Ingrid Hotz, Steffen Prohaska,
                 Hans-Christian Hege / 198--208 \\
                 Groebner Bases and Applications (Invited) \\
                 Introduction to Normaliz 2.5 / Winfried Bruns, Bogdan
                 Ichim, Christof S{\"o}ger / 209--212 \\
                 Computer Algebra Methods in Tropical Geometry / Thomas
                 Markwig / 213--216 \\
                 Groebner Bases and Applications (Contributed) \\
                 A New Desingularization Algorithm for Binomial
                 Varieties in Arbitrary Characteristic / Roc{\'\i}o
                 Blanco / 217--220 \\
                 An Algorithm of Computing Inhomogeneous Differential
                 Equations for Definite Integrals / Hiromasa Nakayama,
                 Kenta Nishiyama / 221--232 \\
                 Groebner Bases and Applications (Contributed) \\
                 New Algorithms for Computing Primary Decomposition of
                 Polynomial Ideals / Masayuki Noro / 233--244 \\
                 An Automated Confluence Proof for an Infinite Rewrite
                 System Parametrized over an Integro-Differential
                 Algebra / Loredana Tec, Georg Regensburger, Markus
                 Rosenkranz, Bruno Buchberger / 245--248 \\
                 Operadic Gr{\"o}bner Bases: An Implementation /
                 Vladimir Dotsenko, Mikael Vejdemo-Johansson / 249--252
                 \\
                 Number Theoretical Software (Invited) \\
                 Magma - A Tool for Number Theory / John Cannon, Steve
                 Donnelly, Claus Fieker, Mark Watkins / 253--255 \\
                 Number Theoretical Software (Contributed) \\
                 Enumerating Galois Representations in Sage / Craig
                 Citro, Alexandru Ghitza / 256--259 \\
                 NZMATH 1.0 / Satoru Tanaka, Naoki Ogura, Ken Nakamula,
                 Tetsushi Matsui, Shigenori Uchiyama / 260--269 \\
                 Software for Optimization and Polyhedral Computation
                 (Invited) \\
                 Removing Redundant Quadratic Constraints / David
                 Adjiashvili, Michel Baes, Philipp Rostalski / 270--281
                 \\
                 Traversing Symmetric Polyhedral Fans / Anders
                 Nedergaard Jensen / 282--294 \\
                 C++ Tools for Exploiting Polyhedral Symmetries / Thomas
                 Rehn, Achill Sch{\"u}rmann / 295--298 \\
                 isl: An Integer Set Library for the Polyhedral Model /
                 Sven Verdoolaege / 299--302 \\
                 Software for Optimization and Polyhedral Computation
                 (Contributed) \\
                 The Reformulation-Optimization Software Engine / Leo
                 Liberti, Sonia Cafieri, David Savourey / 303--314 \\
                 Generating Smooth Lattice Polytopes / Christian Haase,
                 Benjamin Lorenz, Andreas Paffenholz / 315--328 \\
                 Reliable Computation (Invited) \\
                 Mathemagix: Towards Large Scale Programming for
                 Symbolic and Certified Numeric Computations /
                 Gr{\'e}goire Lecerf / 329--332 \\
                 Complex Inclusion Functions in the CoStLy C++ Class
                 Library / Markus Neher / 333--336 \\
                 Standardized Interval Arithmetic and Interval
                 Arithmetic Used in Libraries / Nathalie Revol /
                 337--341 \\
                 Reliable Computation (Contributed) \\
                 Efficient Evaluation of Large Polynomials / Charles E.
                 Leiserson, Liyun Li, Marc Moreno Maza, Yuzhen Xie /
                 342--353 \\
                 Communicating Functional Expressions from Mathematica
                 to C-XSC / Evgenija D. Popova, Walter Kr{\"a}mer /
                 354--365 \\
                 Author Index / 367--368",
}

@Book{Olver:2010:NHM,
  editor =       "Frank W. J. Olver and Daniel W. Lozier and Ronald F.
                 Boisvert and Charles W. Clark",
  key =          "NIST",
  booktitle =    "{NIST} Handbook of Mathematical Functions",
  title =        "{NIST} Handbook of Mathematical Functions",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xv + 951",
  year =         "2010",
  ISBN =         "0-521-19225-0",
  ISBN-13 =      "978-0-521-19225-5",
  LCCN =         "QA331 .N57 2010",
  bibdate =      "Sat May 15 09:08:09 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  price =        "US\$99.00",
  URL =          "http://dlmf.nist.gov/;
                 http://www.cambridge.org/9780521140638",
  acknowledgement = ack-nhfb,
  remark =       "Includes a DVD with a searchable PDF of each
                 chapter.",
  tableofcontents = "1. Algebraic and analytic methods [Ranjan Roy,
                 Frank W. J. Olver, Richard A. Askey and Roderick S. C.
                 Wong] \\
                 2. Asymptotic approximations [Frank W. J. Olver and
                 Roderick S. C. Wong] \\
                 3. Numerical methods [Nico M. Temme] \\
                 4. Elementary functions [Ranjan Roy and Frank W. J.
                 Olver] \\
                 5. Gamma function [Richard A. Askey and Ranjan Roy] \\
                 6. Exponential, logarithmic, sine and cosine integrals
                 [Nico M. Temme] \\
                 7. Error functions, Dawson's and Fresnel integrals
                 [Nico M. Temme] \\
                 8. Incomplete gamma and related functions [Richard B.
                 Paris] \\
                 9. Airy and related functions [Frank W. J. Olver] \\
                 10. Bessel functions [Frank W. J. Olver and Leonard C.
                 Maximon] \\
                 11. Struve and related functions [Richard B. Paris] \\
                 12. Parabolic cylinder functions [Nico M. Temme] \\
                 13. Confluent hypergeometric functions [Adri B. Olde
                 Daalhuis] \\
                 14. Legendre and related functions [T. Mark Dunster]
                 \\
                 15. Hypergeometric function [Adri B. Olde Daalhuis] \\
                 16. Generalized hypergeometric functions and Meijer
                 G-function [Richard A. Askey and Adri B. Olde Daalhuis]
                 \\
                 17. q-Hypergeometric and related functions [George E.
                 Andrews] \\
                 18. Orthogonal polynomials [Tom H. Koornwinder,
                 Roderick S. C. Wong, Roelof Koekoek and Rene F.
                 Swarttouw] \\
                 19. Elliptic integrals [Bille C. Carlson] \\
                 20. Theta functions [William P. Reinhardt and Peter L.
                 Walker] \\
                 21. Multidimensional theta functions [Bernard
                 Deconinck] \\
                 22. Jacobian elliptic functions [William P. Reinhardt
                 and Peter L. Walker] \\
                 23. Weierstrass elliptic and modular functions [William
                 P. Reinhardt and Peter L. Walker] \\
                 24. Bernoulli and Euler polynomials [Karl Dilcher] \\
                 25. Zeta and related functions [Tom M. Apostol] \\
                 26. Combinatorial analysis [David M. Bressoud] \\
                 27. Functions of number theory [Tom M. Apostol] \\
                 28. Mathieu functions and Hill's equation [Gerhard
                 Wolf] \\
                 29. Lam{\'e} functions [Hans Volkmer] \\
                 30. Spheroidal wave functions [Hans Volkmer] \\
                 31. Heun functions [Brian D. Sleeman and Vadim
                 Kuznetsov] \\
                 32. Painlev{\'e} transcendents [Peter A. Clarkson] \\
                 33. Coulomb functions [Ian J. Thompson] \\
                 34. 3j, 6j, 9j symbols [Leonard C. Maximon] \\
                 35. Functions of matrix argument [Donald St. P.
                 Richards] \\
                 36. Integrals with coalescing saddles [Michael V. Berry
                 and Chris Howls]",
}

@Proceedings{Schost:2011:IPI,
  editor =       "{\'E}ric Schost and Ioannis Z. Emiris",
  booktitle =    "{ISSAC 2011: Proceedings of the 2011 International
                 Symposium on Symbolic and Algebraic Computation, June
                 7--11, 2011, San Jose, CA, USA}",
  title =        "{ISSAC 2011: Proceedings of the 2011 International
                 Symposium on Symbolic and Algebraic Computation, June
                 7--11, 2011, San Jose, CA, USA}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "362 (est.)",
  year =         "2011",
  ISBN =         "1-4503-0675-6",
  ISBN-13 =      "978-1-4503-0675-1",
  LCCN =         "QA76.95 .I59 2011",
  bibdate =      "Fri Mar 14 12:24:11 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/issac.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Schwarz:2011:PIS,
  editor =       "Eric Schwarz and Vojin G. Oklobdzija",
  booktitle =    "{Proceedings of the 20th IEEE Symposium on Computer
                 Arithmetic, July 25--27, 2011, T{\"u}bingen, Germany}",
  title =        "{Proceedings of the 20th IEEE Symposium on Computer
                 Arithmetic, July 25--27, 2011, T{\"u}bingen, Germany}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xix + 253",
  year =         "2011",
  ISBN =         "0-7695-4318-9, 1-4244-9457-5",
  ISBN-13 =      "978-0-7695-4318-5, 978-1-4244-9457-6",
  LCCN =         "QA76.6",
  bibdate =      "Sat Aug 20 09:19:17 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
  tableofcontents = "Foreword / ix \\
                 Dedication / x \\
                 Steering Committee / xv \\
                 Symposium Committee / xvi \\
                 Program Committee / xvii \\
                 Additional Reviewers / xviii \\
                 Corporate Sponsors / xix \\
                 Session 1: Keynote Talk: Chair: Eric Schwarz and Vojin
                 G. Oklobdzija \\
                 High Intelligence Computing: The New Era of High
                 Performance Computing / Ralf Fischer / 3 \\
                 Session 2: Multiple-Precision Algorithms: Chair: Marius
                 Cornea \\
                 Short Division of Long Integers / David Harvey and Paul
                 Zimmermann / 7 \\
                 High Degree Toom'n'Half for Balanced and Unbalanced
                 Multiplication / Marco Bodrato / 15 \\
                 Augmented Precision Square Roots and 2-D Norms, and
                 Discussion on Correctly Rounding sqrt($x^2 + y^2$) /
                 Nicolas Brisebarre, Mioara Jolde{\c{s}}, Peter
                 Kornerup, Erik Martin-Dorel, and Jean-Michel Muller /
                 23 \\
                 Session 3: Transcendental Methods: Chair: Naofumi
                 Takagi \\
                 Towards a Quaternion Complex Logarithmic Number System
                 / Mark G. Arnold, John Cowles, Vassilis Paliouras, and
                 Ioannis Kouretas / 33 \\
                 ROM-less LNS / R. Che Ismail and J. N. Coleman / 43 \\
                 Composite Iterative Algorithm and Architecture for q-th
                 Root Calculation / Alvaro Vazquez and Javier D.
                 Bruguera / 52 \\
                 On the Fixed-Point Accuracy Analysis and Optimization
                 of FFT Units with CORDIC Multipliers / Omid Sarbishei
                 and Katarzyna Radecka / 62 \\
                 Session 4: Special Session on Industrial Practices:
                 Chair: Mike Schulte \\
                 Self Checking in Current Floating-Point Units / Daniel
                 Lipetz and Eric Schwarz / 73 \\
                 How to Square Floats Accurately and Efficiently on the
                 ST231 Integer Processor/ Claude-Pierre Jeannerod,
                 Jingyan Jourdan-Lu, Christophe Monat, and Guillaume
                 Revy / 77 \\
                 A 1.5 Ghz VLIW DSP CPU with Integrated Floating Point
                 and Fixed Point Instructions in 40 nm CMOS / Timothy
                 Anderson, Due Bui, Shriram Moharil, Soujanya Narnur,
                 Mujibur Rahman, Anthony Lell, Eric Biscondi, Ashish
                 Shrivastava, Peter Dent, Mingjian Yan, and Hasan
                 Mahmood / 82 \\
                 The POWER7 Binary Floating-Point Unit / Maarten
                 Boersma, Michael Kroner, Christophe Layer, Petra Leber,
                 Silvia M. Muller, and Kerstin Schelm / 87 \\
                 Session 5: Addition: Chair: Alberto Nannarelli \\
                 Accelerating Computations on FPGA Carry Chains by
                 Operand Compaction / Thomas B. Preus{\ss}er, Martin
                 Zabel, and Rainer G. Spallek / 95 \\
                 Fast Ripple-Carry Adders in Standard-Cell CMOS VLSI /
                 Neil Burgess / 103 \\
                 A Family of High Radix Signed Digit Adders / Saeid
                 Gorgin and Ghassem Jaberipur / 112 \\
                 Session 6: Floating-Point Units: Chair: Javier Bruguera
                 \\
                 Fused Multiply-Add Microarchitecture Comprising
                 Separate Early-Normalizing Multiply and Add Pipelines /
                 David R. Lutz / 123 \\
                 Latency Sensitive FMA Design / Sameh Galal and Mark
                 Horowitz / 129 \\
                 The IBM zEnterprise-196 Decimal Floating-Point
                 Accelerator / Steven Carlough, Adam Collura, Silvia
                 Mueller, and Michael Kroener / 139 \\
                 Session 7: Division, Square-Root and Reciprocal
                 Square-Root: Chair: Peter Kornerup \\
                 Radix-8 Digit-by-Rounding: Achieving High-Performance
                 Reciprocals, Square Roots, and Reciprocal Square Roots
                 / J. Adam Butts, Ping Tak Peter Tang, Ron O. Dror, and
                 David E. Shaw / 149 \\
                 Tight Certification Techniques for Digit-by-Rounding
                 Algorithms with Application to a New 1/sqrt(x) Design /
                 Ping Tak Peter Tang, J. Adam Butts, Ron O. Dror, and
                 David E. Shaw / 159 \\
                 Radix-16 Combined Division and Square Root Unit /
                 Alberto Nannarelli / 169 \\
                 A Prescale-Lookup-Postscale Additive Procedure for
                 Obtaining a Single Precision Ulp Accurate Reciprocal /
                 David W. Matula and Mihai T. Panu / 177 \\
                 Session 8: Special Session on High Performance
                 Arithmetic for FPGA's: Chair: Martin Langhammer \\
                 Teraflop FPGA Design / Martin Langhammer / 187 \\
                 The Arithmetic Operators You Will Never See in a
                 Microprocessor / Florent de Dinechin / 189 \\
                 Accelerating Large-Scale HPC Applications Using FPGAs /
                 Rob Dimond, Sebastien Racaniere, and Oliver Pell / 191
                 \\
                 Session 9: Arithmetic Algorithms for Cryptography:
                 Chair: David Matula \\
                 A General Approach for Improving RNS Montgomery
                 Exponentiation Using Pre-processing / Filippo Gandino,
                 Fabrizio Lamberti, Paolo Montuschi, and Jean-Claude
                 Bajard / 195 \\
                 Bit-Sliced Binary Normal Basis Multiplication / Billy
                 Bob Brumley and Dan Page / 205 \\
                 Efficient SIMD Arithmetic Modulo a Mersenne Number /
                 Joppe W. Bos, Thorsten Kleinjung, Arjen K. Lenstra, and
                 Peter L. Montgomery / 213 \\
                 Session 10: Tools for Formal Certified Code: Chair:
                 Martin Schmookler \\
                 Automatic Generation of Code for the Evaluation of
                 Constant Expressions at Any Precision with a Guaranteed
                 Error Bound / Sylvain Chevillard / 225 \\
                 Automatic Generation of Fast and Certified Code for
                 Polynomial Evaluation / Christophe Mouilleron and
                 Guillaume Revy / 233 \\
                 Flocq: A Unified Library for Proving Floating-Point
                 Algorithms in Coq / Sylvie Boldo and Guillaume
                 Melquiond / 243 \\
                 Author Index / 253",
}

@Book{Hwu:2012:GCG,
  editor =       "Wen-mei Hwu",
  booktitle =    "{GPU} computing gems",
  title =        "{GPU} computing gems",
  publisher =    "Morgan Kaufmann",
  address =      "Boston, MA",
  edition =      "Jade",
  pages =        "xvi + 541 + 16",
  year =         "2012",
  ISBN =         "0-12-385963-8 (hardback)",
  ISBN-13 =      "978-0-12-385963-1 (hardback)",
  LCCN =         "T385 .G6875 2012",
  bibdate =      "Sat Feb 8 18:16:05 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Applications of GPU computing series",
  abstract =     "Since the introduction of CUDA in 2007, more than 100
                 million computers with CUDA capable GPUs have been
                 shipped to end users. GPU computing application
                 developers can now expect their application to have a
                 mass market. With the introduction of OpenCL in 2010,
                 researchers can now expect to develop GPU applications
                 that can run on hardware from multiple vendors.",
  acknowledgement = ack-nhfb,
  subject =      "Graphics processing units; Programming; Imaging
                 systems; Computer graphics; Image processing; Digital
                 techniques",
  tableofcontents = "Part 1: Parallel Algorithms and Data Structures ---
                 Paulius Micikevicius, NVIDIA \\
                 1 Large-Scale GPU Search \\
                 2 Edge v. Node Parallelism for Graph Centrality Metrics
                 \\
                 3 Optimizing parallel prefix operations for the Fermi
                 architecture \\
                 4 Building an Efficient Hash Table on the GPU \\
                 5 An Efficient CUDA Algorithm for the Maximum Network
                 Flow Problem \\
                 6 On Improved Memory Access Patterns for Cellular
                 Automata Using CUDA \\
                 7 Fast Minimum Spanning Tree Computation on Large
                 Graphs \\
                 8 Fast in-place sorting with CUDA based on bitonic sort
                 \\
                 Part 2: Numerical Algorithms --- Frank Jargstorff,
                 NVIDIA \\
                 9 Interval Arithmetic in CUDA \\
                 10 Approximating the erfinv Function \\
                 11 A Hybrid Method for Solving Tridiagonal Systems on
                 the GPU \\
                 12 LU Decomposition in CULA \\
                 13 GPU Accelerated Derivative-free Optimization \\
                 Part 3: Engineering Simulation --- Peng Wang, NVIDIA
                 \\
                 14 Large-scale gas turbine simulations on GPU clusters
                 \\
                 15 GPU acceleration of rarefied gas dynamic simulations
                 \\
                 16 Assembly of Finite Element Methods on Graphics
                 Processors \\
                 17 CUDA implementation of Vertex-Centered, Finite
                 Volume CFD methods on Unstructured Grids with Flow
                 Control Applications \\
                 18 Solving Wave Equations on Unstructured Geometries
                 \\
                 19 Fast electromagnetic integral equation solvers on
                 graphics processing units (GPUs) \\
                 Part 4: Interactive Physics for Games and Engineering
                 Simulation --- Richard Tonge, NVIDIA \\
                 20 Solving Large Multi-Body Dynamics Problems on the
                 GPU \\
                 21 Implicit FEM Solver in CUDA \\
                 22 Real-time Adaptive GPU multi-agent path planning \\
                 Part 5: Computational Finance --- Thomas Bradley,
                 NVIDIA \\
                 23 High performance finite difference PDE solvers on
                 GPUs for financial option pricing \\
                 24 Identifying and Mitigating Credit Risk using
                 Large-scale Economic Capital Simulations \\
                 25 Financial Market Value-at-Risk Estimation using the
                 Monte Carlo Method \\
                 Part 6: Programming Tools and Techniques --- Cliff
                 Wooley, NVIDIA \\
                 26 Thrust: A Productivity-Oriented Library for CUDA \\
                 27 GPU Scripting and Code Generation with PyCUDA \\
                 28 Jacket: GPU Powered MATLAB Acceleration \\
                 29 Accelerating Development and Execution Speed with
                 Just In Time GPU Code Generation \\
                 30 GPU Application Development, Debugging, and
                 Performance Tuning with GPU Ocelot \\
                 31 Abstraction for AoS and SoA Layout in C++ \\
                 32 Processing Device Arrays with C++ Metaprogramming
                 \\
                 33 GPU Metaprogramming: A Case Study in
                 Biologically-Inspired Machine Vision \\
                 34 A Hybridization Methodology for High-Performance
                 Linear Algebra Software for GPUs \\
                 35 Dynamic Load Balancing using Work-Stealing \\
                 36 Applying software-managed caching and CPU/GPU task
                 scheduling for accelerating dynamic workloads",
}

@Book{Arfken:2013:MMP,
  author =       "George B. (George Brown) Arfken and Hans-J{\"u}rgen
                 Weber and Frank E. Harris",
  booktitle =    "Mathematical Methods for Physicists: a Comprehensive
                 Guide",
  title =        "Mathematical Methods for Physicists: a Comprehensive
                 Guide",
  publisher =    pub-ELSEVIER-ACADEMIC,
  address =      pub-ELSEVIER-ACADEMIC:adr,
  edition =      "Seventh",
  pages =        "xiii + 1205",
  year =         "2013",
  ISBN =         "0-12-384654-4 (hardcover)",
  ISBN-13 =      "978-0-12-384654-9 (hardcover)",
  LCCN =         "QA37.3 .A74 2013",
  bibdate =      "Thu May 3 08:02:53 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
                 jenson.stanford.edu:2210/unicorn",
  acknowledgement = ack-nhfb,
  subject =      "Mathematical analysis; Mathematical physics",
  tableofcontents = "Preface / xi--xiii \\
                 1: Mathematical Preliminaries / 1--82 \\
                 2: Determinants and Matrices / 83--121 \\
                 3: Vector Analysis / 123--203 \\
                 4: Tensors and Differential Forms / 205--249 \\
                 5: Vector Spaces / 251--297 \\
                 6: Eigenvalue Problems / 299--328 \\
                 7: Ordinary Differential Equations / 329--380 \\
                 8: Sturm--Liouville Theory / 381--399 \\
                 9: Partial Differential Equations / 401--445 \\
                 10: Green's Functions / 447--467 \\
                 11: Complex Variable Theory / 469--550 \\
                 12: Further Topics in Analysis / 551--598 \\
                 13: Gamma Function / 599--641 \\
                 14: Bessel Functions / 643--713 \\
                 15: Legendre Functions / 715--772 \\
                 16: Angular Momentum / 773--814 \\
                 17: Group Theory / 815--870 \\
                 18: More Special Functions / 871--933 \\
                 19: Fourier Series / 935--962 \\
                 20: Integral Transforms / 963--1046 \\
                 21: Integral Equations / 1047--1079 \\
                 22: Calculus of Variations / 1081--1124 \\
                 23: Probability and Statistics / 1125--1179 \\
                 Index / 1181--1205",
}

@Proceedings{IEEE:2013:PIS,
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of the 21st IEEE Symposium on Computer
                 Arithmetic, Austin, Texas, USA, 8--10 April 2013}",
  title =        "{Proceedings of the 21st IEEE Symposium on Computer
                 Arithmetic, Austin, Texas, USA, 8--10 April 2013}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xvi + 229",
  year =         "2013",
  ISBN =         "0-7695-4957-8",
  ISBN-13 =      "978-0-7695-4957-6",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62 S95 2013",
  bibdate =      "Sat Aug 01 08:03:11 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic units; correctness proofs;
                 cryptography; domain specific designs; error analysis;
                 exascale computing; floating point arithmetic;
                 floating-point error analysis; formal verification;
                 function approximation; modular arithmetic; theorem
                 proving; verification",
}

@Article{Dunster:2024:CPC,
  author =       "T. M. Dunster and A. Gil and J. Segura",
  title =        "Computation of parabolic cylinder functions having
                 complex argument",
  journal =      j-APPL-NUM-MATH,
  volume =       "197",
  number =       "??",
  pages =        "230--242",
  month =        mar,
  year =         "2024",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1016/j.apnum.2023.11.017",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Mon Dec 18 15:47:31 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0168927423002969",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
}

@Proceedings{Hong:2014:MSI,
  editor =       "Hoon Hong and Chee Yap",
  booktitle =    "Mathematical Software --- {ICMS 2014: 4th
                 International Conference, Seoul, South Korea, August
                 5--9, 2014, Proceedings}",
  title =        "Mathematical Software --- {ICMS 2014: 4th
                 International Conference, Seoul, South Korea, August
                 5--9, 2014, Proceedings}",
  volume =       "8592",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxxii + 735",
  year =         "2014",
  DOI =          "https://doi.org/10.1007/978-3-662-44199-2",
  ISBN =         "3-662-44198-5 (paperback), 3-662-44199-3 (e-book)",
  ISBN-13 =      "978-3-662-44198-5 (paperback), 978-3-662-44199-2
                 (e-book)",
  LCCN =         "QA76.9.M35",
  bibdate =      "Sat Sep 23 09:59:48 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/magma.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook3.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Front Matter \\
                 Invited Talks \\
                 Experimental Computation and Visual Theorems / Jonathan
                 M. Borwein / 1--8 \\
                 Soft Math Math Soft / Bruno Buchberger / 9--15 \\
                 Mathematical Theory Exploration \\
                 Flyspecking Flyspeck / Mark Adams / 16--20 \\
                 Symbolic Computing Package for Mathematica for
                 Versatile Manipulation of Mathematical Expressions /
                 Youngjoo Chung / 21--25 \\
                 Representing, Archiving, and Searching the Space of
                 Mathematical Knowledge / Mihnea Iancu, Michael
                 Kohlhase, Corneliu Prodescu / 26--30 \\
                 Early Examples of Software in Mathematical Knowledge
                 Management / Patrick Ion / 31--35 \\
                 Discourse-Level Parallel Markup and Meaning Adoption in
                 Flexiformal Theory Graphs / Michael Kohlhase, Mihnea
                 Iancu / 36--40 \\
                 Complexity Analysis of the Bivariate Buchberger
                 Algorithm in Theorema / Alexander Maletzky, Bruno
                 Buchberger / 41--48 \\
                 Theorema 2.0: A System for Mathematical Theory
                 Exploration / Wolfgang Windsteiger / 49--52 \\
                 Computational Group Theory \\
                 New Approaches in Black Box Group Theory / Alexandre
                 Borovik, {\c{S}}{\"u}kr{\"u} Yal{\c{c}}{\i}nkaya /
                 53--58 \\
                 A GAP Package for Computing with Real Semisimple Lie
                 Algebras / Heiko Dietrich, Paolo Faccin, Willem A. de
                 Graaf / 59--66 \\
                 Bacterial Genomics and Computational Group Theory: The
                 BioGAP Package for GAP / Attila Egri-Nagy, Andrew R.
                 Francis, Volker Gebhardt / 67--74 \\
                 SgpDec: Cascade (De)Compositions of Finite
                 Transformation Semigroups and Permutation Groups /
                 Attila Egri-Nagy, James D. Mitchell, Chrystopher L.
                 Nehaniv / 75--82 \\
                 Approximating Generators for Integral Arithmetic Groups
                 / Bettina Eick / 83--86 \\
                 Software for Groups: Theory and Practice / Alexander
                 Hulpke / 87--91 \\
                 Computation of Genus 0 Belyi Functions / Mark van
                 Hoeij, Raimundas Vidunas / 92--98 \\
                 On Computation of the First Baues--Wirsching Cohomology
                 of a Freely-Generated Small Category / Yasuhiro Momose,
                 Yasuhide Numata / 99--105 \\
                 Coding Theory \\
                 Codes over a Non Chain Ring with Some Applications /
                 Aysegul Bayram, Elif Segah Oztas, Irfan Siap / 106--110
                 \\
                 On the Weight Enumerators of the Projections of the
                 2-adic Golay Code of Length 24 to $\mathbb{Z}_{2^e}$ /
                 Sunghyu Han / 111--114 \\
                 Coding Theory \\
                 Computer Based Reconstruction of Binary Extremal
                 Self-dual Codes of Length 32 / Jon-Lark Kim / 115--118
                 \\
                 Magma Implementation of Decoding Algorithms for General
                 Algebraic Geometry Codes / Kwankyu Lee / 119--123 \\
                 Reversible Codes and Applications to DNA / Elif Segah
                 Oztas, Irfan Siap, Bahattin Yildiz / 124--128 \\
                 Computational Topology \\
                 javaPlex: A Research Software Package for Persistent
                 (Co)Homology / Henry Adams, Andrew Tausz, Mikael
                 Vejdemo-Johansson / 129--136 \\
                 PHAT --- Persistent Homology Algorithms Toolbox /
                 Ulrich Bauer, Michael Kerber, Jan Reininghaus, Hubert
                 Wagner / 137--143 \\
                 Computing Persistence Modules on Commutative Ladders of
                 Finite Type / Emerson G. Escolar, Yasuaki Hiraoka /
                 144--151 \\
                 Heuristics for Sphere Recognition / Michael Joswig,
                 Frank H. Lutz, Mimi Tsuruga / 152--159 \\
                 CAPD::RedHom v2 --- Homology Software Based on
                 Reduction Algorithms / Mateusz Juda, Marian Mrozek /
                 160--166 \\
                 The Gudhi Library: Simplicial Complexes and Persistent
                 Homology / Cl{\'e}ment Maria, Jean-Daniel Boissonnat,
                 Marc Glisse, Mariette Yvinec / 167--174 \\
                 Numerical Algebraic Geometry \\
                 Bertini_real: Software for One- and Two-Dimensional
                 Real Algebraic Sets / Daniel A. Brake, Daniel J. Bates,
                 Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese,
                 CharlesW. Wampler / 175--182 \\
                 Hom4PS-3: A Parallel Numerical Solver for Systems of
                 Polynomial Equations Based on Polyhedral Homotopy
                 Continuation Methods / Tianran Chen, Tsung-Lin Lee,
                 Tien-Yien Li / 183--190 \\
                 Geometry \\
                 CGAL --- Reliable Geometric Computing for Academia and
                 Industry / Eric Berberich / 191--197 \\
                 Implementing the $L_\infty$ Segment Voronoi Diagram in
                 CGAL and Applying in VLSI Pattern Analysis / Panagiotis
                 Cheilaris, Sandeep Kumar Dey, Maria Gabrani, Evanthia
                 Papadopoulou / 198--205 \\
                 BULL! --- The Molecular Geometry Engine Based on
                 Voronoi Diagram, Quasi-Triangulation, and Beta-Complex
                 / Deok-Soo Kim, Youngsong Cho, Jae-Kwan Kim, Joonghyun
                 Ryu, Mokwon Lee, Jehyun Cha et al. / 206--213 \\
                 Integrating Circumradius and Area Formulae for Cyclic
                 Pentagons / Shuichi Moritsugu / 214--221 \\
                 Computer Aided Geometry / Douglas Navarro Guevara,
                 Adrian Navarro Alvarez / 222--229 \\
                 The Sustainability of Digital Educational Resources /
                 Yongsheng Rao, Ying Wang, Yu Zou, Jingzhong Zhang /
                 230--234 \\
                 A Touch-Operation-Based Dynamic Geometry System: Design
                 and Implementation / Wei Su, Paul S. Wang, Chuan Cai,
                 Lian Li / 235--239 \\
                 OpenGeo: An Open Geometric Knowledge Base / Dongming
                 Wang, Xiaoyu Chen, Wenya An, Lei Jiang, Dan Song /
                 240--245 \\
                 Curves and Surfaces \\
                 On Computing a Cell Decomposition of a Real Surface
                 Containing Infinitely Many Singularities / Daniel J.
                 Bates, Daniel A. Brake, Jonathan D. Hauenstein, Andrew
                 J. Sommese, Charles W. Wampler / 246--252 \\
                 Robustly and Efficiently Computing Algebraic Curves and
                 Surfaces / Eric Berberich / 253--260 \\
                 Computing the Orthogonal Projection of Rational Curves
                 onto Rational Parameterized Surface by Symbolic Methods
                 / Zhiwang Gan, Meng Zhou / 261--268 \\
                 Isotopic $\epsilon$-Approximation of Algebraic Curves /
                 Kai Jin / 269--276 \\
                 Isotopic Arrangement of Simple Curves: An Exact
                 Numerical Approach Based on Subdivision / Jyh-Ming
                 Lien, Vikram Sharma, Gert Vegter, Chee Yap / 277--282
                 \\
                 Quantified Reasoning \\
                 Real Quantifier Elimination in the RegularChains
                 Library / Changbo Chen, Marc Moreno Maza / 283--290 \\
                 Software for Quantifier Elimination in Propositional
                 Logic / Eugene Goldberg, Panagiotis Manolios / 291--294
                 \\
                 Quantifier Elimination for Linear Modular Constraints /
                 Ajith K. John, Supratik Chakraborty / 295--302 \\
                 Skolemization Modulo Theories / Konstantin Korovin,
                 Margus Veanes / 303--306 \\
                 Incremental QBF Solving by DepQBF / Florian Lonsing,
                 Uwe Egly / 307--314 \\
                 NLCertify: A Tool for Formal Nonlinear Optimization /
                 Victor Magron / 315--320 \\
                 Special Functions and Concrete Mathematics \\
                 Developing Linear Algebra Packages on Risa/Asir for
                 Eigenproblems / Katsuyoshi Ohara, Shinichi Tajima,
                 Akira Terui / 321--324 \\
                 Mathematical Software for Modified Bessel Functions /
                 Juri Rappoport / 325--332 \\
                 BetaSCP2: A Program for the Optimal Prediction of
                 Side-Chains in Proteins / Joonghyun Ryu, Mokwon Lee,
                 Jehyun Cha, Chanyoung Song, Deok-Soo Kim / 333--340 \\
                 Computation of an Improved Lower Bound to Giuga's
                 Primality Conjecture / Matthew Skerritt / 341--345 \\
                 An Extension and Efficient Calculation of the Horner's
                 Rule for Matrices / Shinichi Tajima, Katsuyoshi Ohara,
                 Akira Terui / 346--351 \\
                 Groebner Bases \\
                 What Is New in CoCoA? / John Abbott, Anna Maria Bigatti
                 / 352--358 \\
                 Maximizing Likelihood Function for Parameter Estimation
                 in Point Clouds via Groebner Basis / Joseph Awange,
                 B{\'e}la Pal{\'a}ncz, Robert Lewis / 359--366 \\
                 Groebner Basis in Geodesy and Geoinformatics / Joseph
                 Awange, B{\'e}la Pal{\'a}ncz, Robert Lewis / 367--373
                 \\
                 Groebner Bases in Theorema / Bruno Buchberger,
                 Alexander Maletzky / 374--381 \\
                 Effective Computation of Radical of Ideals and Its
                 Application to Invariant Theory / Amir Hashemi /
                 382--389 \\
                 Generic and Parallel Groebner Bases in JAS / Heinz
                 Kredel / 390--397 \\
                 Application of Groebner Basis Methodology to Nonlinear
                 Mechanics Problems / Y. Jane Liu, John Peddieson /
                 398--405 \\
                 Software for Discussing Parametric Polynomial Systems:
                 The Gr{\"o}bner Cover / Antonio Montes, Michael Wibmer
                 / 406--413 \\
                 An Algorithm for Computing Standard Bases by Change of
                 Ordering via Algebraic Local Cohomology / Katsusuke
                 Nabeshima, Shinichi Tajima / 414--418 \\
                 Verification of Gr{\"o}bner Basis Candidates / Masayuki
                 Noro, Kazuhiro Yokoyama / 419--424 \\
                 Triangular Decompositions of Polynomial Systems \\
                 Cylindrical Algebraic Decomposition in the
                 RegularChains Library / Changbo Chen, Marc Moreno Maza
                 / 425--433 \\
                 Hierarchical Comprehensive Triangular Decomposition /
                 Zhenghong Chen, Xiaoxian Tang, Bican Xia / 434--441 \\
                 A Package for Parametric Matrix Computations / Robert
                 M. Corless, Steven E. Thornton / 442--449 \\
                 Choosing a Variable Ordering for Truth-Table Invariant
                 Cylindrical Algebraic Decomposition by Incremental
                 Triangular Decomposition / Matthew England, Russell
                 Bradford, James H. Davenport, David Wilson / 450--457
                 \\
                 Using the Regular Chains Library to Build Cylindrical
                 Algebraic Decompositions by Projecting and Lifting /
                 Matthew England, David Wilson, Russell Bradford, James
                 H. Davenport / 458--465 \\
                 An Improvement of Rosenfeld--Gr{\"o}bner Algorithm /
                 Amir Hashemi, Zahra Touraji / 466--471 \\
                 Doing Algebraic Geometry with the RegularChains Library
                 / Parisa Alvandi, Changbo Chen, Steffen Marcus, Marc
                 Moreno Maza, {\'E}ric Schost, Paul Vrbik / 472--479 \\
                 On Multivariate Birkhoff Rational Interpolation / Peng
                 Xia, Bao-Xin Shang, Na Lei / 480--483 \\
                 Computing Moore--Penrose Inverses of Ore Polynomial
                 Matrices / Yang Zhang / 484--491 \\
                 Parametric Polynomial Systems \\
                 Software Using the Gr{\"o}bner Cover for Geometrical
                 Loci Computation and Classification / Miguel A.
                 Ab{\'a}nades, Francisco Botana, Antonio Montes,
                 Tom{\'a}s Recio / 492--499 \\
                 Using Maple's RegularChains Library to Automatically
                 Classify Plane Geometric Loci / Francisco Botana,
                 Tom{\'a}s Recio / 500--503 \\
                 Solving Parametric Polynomial Systems by
                 RealComprehensiveTriangularize / Changbo Chen, Marc
                 Moreno Maza / 504--511 \\
                 QE Software Based on Comprehensive Gr{\"o}bner Systems
                 / Ryoya Fukasaku / 512--517 \\
                 SyNRAC: A Toolbox for Solving Real Algebraic
                 Constraints / Hidenao Iwane, Hitoshi Yanami, Hirokazu
                 Anai / 518--522 \\
                 An Algorithm for Computing Tjurina Stratifications of
                 $\mu$-Constant Deformations by Using Local Cohomology
                 Classes with Parameters / Katsusuke Nabeshima, Shinichi
                 Tajima / 523--530 \\
                 An Implementation Method of Boolean Gr{\"o}bner Bases
                 and Comprehensive Boolean Gr{\"o}bner Bases on General
                 Computer Algebra Systems / Akira Nagai, Shutaro Inoue /
                 531--536 \\
                 A Method to Determine if Two Parametric Polynomial
                 Systems Are Equal / Jie Zhou, Dingkang Wang / 537--544
                 \\
                 Mathematical Web/Mobile Interfaces and Visualization
                 \\
                 An Implementation Method of a CAS with a Handwriting
                 Interface on Tablet Devices / Mitsushi Fujimoto /
                 545--548 \\
                 New Way of Explanation of the Stochastic Interpretation
                 of Wave Functions and Its Teaching Materials Using
                 KETpic / Kenji Fukazawa / 549--553 \\
                 {IFSGen4\LaTeX}: Interactive Graphical User Interface
                 for Generation and Visualization of Iterated Function
                 Systems in {\LaTeX} / Akemi G{\'a}lvez, Kiyoshi
                 Kitahara, Masataka Kaneko / 554--561 \\
                 GNU {\TeX}MACS: towards a Scientific Office Suite /
                 Massimiliano Gubinelli, Joris van der Hoeven,
                 Fran{\c{c}}ois Poulain, Denis Raux / 562--569 \\
                 Computer Software Program for Representation and
                 Visualization of Free-Form Curves through Bio-inspired
                 Optimization Techniques / Andr{\'e}s Iglesias, Akemi
                 G{\'a}lvez / 570--577 \\
                 On Some Attempts to Verify the Effect of Using
                 High-Quality Graphics in Mathematics Education /
                 Kiyoshi Kitahara, Tadashi Takahashi, Masataka Kaneko /
                 578--585 \\
                 Math Web Search Interfaces and the Generation Gap of
                 Mathematicians / Andrea Kohlhase / 586--593 \\
                 Practice with Computer Algebra Systems in Mathematics
                 Education and Teacher Training Courses / Hideyo
                 Makishita / 594--600 \\
                 Development of Visual Aid Materials in Teaching the
                 Bivariate Normal Distributions / Toshifumi Nomachi,
                 Toshihiko Koshiba, Shunji Ouchi / 601--606 \\
                 Creating Interactive Graphics for Mathematics Education
                 Utilizing KETpic / Shunji Ouchi, Yoshifumi Maeda,
                 Kiyoshi Kitahara, Naoki Hamaguchi / 607--613 \\
                 A Tablet-Compatible Web-Interface for Mathematical
                 Collaboration / Marco Pollanen, Jeff Hooper, Bruce
                 Cater, Sohee Kang / 614--620 \\
                 Development and Evaluation of a Web-Based Drill System
                 to Master Basic Math Formulae Using a New Interactive
                 Math Input Method / Shizuka Shirai, Tetsuo Fukui /
                 621--628 \\
                 Generating Data of Mathematical Figures for 3D Printers
                 with KETpic and Educational Impact of the Printed
                 Models / Setsuo Takato, Naoki Hamaguchi, Haiduke
                 Sarafian / 629--634 \\
                 A Touch-Based Mathematical Expression Editor / Wei Su,
                 Paul S. Wang, Lian Li / 635--640 \\
                 Establishment of KETpic Programming Styles for Drawing
                 / Satoshi Yamashita, Yoshifumi Maeda, Hisashi Usui,
                 Kiyoshi Kitahara, Hideyo Makishita, Kazushi Ahara /
                 641--646 \\
                 General Session \\
                 Integration of Libnormaliz in CoCoALib and CoCoA 5 /
                 John Abbott, Anna Maria Bigatti, Christof S{\"o}ger /
                 647--653 \\
                 Elements of Design for Containers and Solutions in the
                 LinBox Library / Brice Boyer, Jean-Guillaume Dumas,
                 Pascal Giorgi, Cl{\'e}ment Pernet, B. David Saunders /
                 654--662 \\
                 Recent Developments in Normaliz / Winfried Bruns,
                 Christof S{\"o}ger / 663--668 \\
                 The Basic Polynomial Algebra Subprograms / Changbo
                 Chen, Svyatoslav Covanov, Farnam Mansouri, Marc Moreno
                 Maza, Ning Xie, Yuzhen Xie / 669--676 \\
                 Function Interval Arithmetic / Jan Duracz, Amin
                 Farjudian, Michal Kone{\v{c}}n{\'y}, Walid Taha /
                 677--684 \\
                 Generating Optimized Sparse Matrix Vector Product over
                 Finite Fields / Pascal Giorgi, Bastien Vialla /
                 685--690 \\
                 swMATH --- An Information Service for Mathematical
                 Software / Gert-Martin Greuel, Wolfram Sperber /
                 691--701 \\
                 MathLibre: Modifiable Desktop Environment for
                 Mathematics / Tatsuyoshi Hamada / 702--705 \\
                 Software Packages for Holonomic Gradient Method / Tamio
                 Koyama, Hiromasa Nakayama, Katsuyoshi Ohara, Tomonari
                 Sei, Nobuki Takayama / 706--712 \\
                 Metalibm: A Mathematical Functions Code Generator /
                 Olga Kupriianova, Christoph Lauter / 713--717 \\
                 From Calculus to Algorithms without Errors / Norbert
                 M{\"u}ller, Martin Ziegler / 718--724 \\
                 Dense Arithmetic over Finite Fields with the CUMODP
                 Library / Sardar Anisul Haque, Xin Li, Farnam Mansouri,
                 Marc Moreno Maza, Wei Pan, Ning Xie / 725--732 \\
                 Back Matter / / 733--735",
}

@Book{Higham:2015:PCA,
  editor =       "Nicholas J. Higham and Mark R. Dennis and Paul
                 Glendinning and Paul A. Martin and Fadil Santosa and
                 Jared Tanner",
  booktitle =    "The {Princeton} Companion to Applied Mathematics",
  title =        "The {Princeton} Companion to Applied Mathematics",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "994 (est.)",
  year =         "2015",
  ISBN =         "0-691-15039-7 (hardcover)",
  ISBN-13 =      "978-0-691-15039-0 (hardcover)",
  LCCN =         "QA155 .P75 2015",
  bibdate =      "Wed Sep 9 05:32:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Algebra; Mathematics; Mathematical models",
  tableofcontents = "Preface / ix \\
                 Contributors / xiii \\
                 Part I: Introduction to Applied Mathematics \\
                 I.1 What Is Applied Mathematics? / 1 \\
                 I.2 The Language of Applied Mathematics / 8 \\
                 I.3 Methods of Solution / 27 \\
                 I.4 Algorithms / 40 \\
                 I.5 Goals of Applied Mathematical Research / 48 \\
                 I.6 The History of Applied Mathematics / 55 \\
                 Part II: Concepts \\
                 II.1 Asymptotics / 81 \\
                 II.2 Boundary Layer / 82 \\
                 II.3 Chaos and Ergodicity / 82 \\
                 II.4 Complex Systems / 83 \\
                 II.5 Conformal Mapping / 84 \\
                 II.6 Conservation Laws / 86 \\
                 II.7 Control / 88 \\
                 II.8 Convexity / 89 \\
                 II.9 Dimensional Analysis and Scaling / 90 \\
                 II.10 The Fast Fourier Transform / 94 \\
                 II.11 Finite Differences / 95 \\
                 II.12 The Finite-Element Method / 96 \\
                 II.13 Floating-Point Arithmetic / 96 \\
                 II.14 Functions of Matrices / 97 \\
                 II.15 Function Spaces / 99 \\
                 II.16 Graph Theory / 101 \\
                 II.17 Homogenization / 103 \\
                 II.18 Hybrid Systems / 103 \\
                 II.19 Integral Transforms and Convolution / 104 \\
                 II.20 Interval Analysis / 105 \\
                 II.21 Invariants and Conservation Laws / 106 \\
                 II.22 The Jordan Canonical Form / 112 \\
                 II.23 Krylov Subspaces / 113 \\
                 II.24 The Level Set Method / 114 \\
                 II.25 Markov Chains / 116 \\
                 II.26 Model Reduction / 117 \\
                 II.27 Multiscale Modeling / 119 \\
                 II.28 Nonlinear Equations and Newton's Method / 120 \\
                 II.29 Orthogonal Polynomials / 122 \\
                 II.30 Shocks / 122 \\
                 II.31 Singularities / 124 \\
                 II.32 The Singular Value Decomposition / 126 \\
                 II.33 Tensors and Manifolds / 127 \\
                 II.34 Uncertainty Quantification / 131 \\
                 II.35 Variational Principle / 134 \\
                 II.36 Wave Phenomena / 134 \\
                 Part III: Equations, Laws, and Functions of Applied
                 Mathematics \\
                 III.1 Benford's Law / 135 \\
                 III.2 Bessel Functions / 137 \\
                 III.3 The Black--Scholes Equation / 137 \\
                 III.4 The Burgers Equation / 138 \\
                 III.5 The Cahn--Hilliard Equation / 138 \\
                 III.6 The Cauchy--Riemann Equations / 139 \\
                 III.7 The Delta Function and Generalized Functions /
                 139 \\
                 III.8 The Diffusion Equation / 142 \\
                 III.9 The Dirac Equation / 142 \\
                 III.10 Einstein's Field Equations / 144 \\
                 III.11 The Euler Equations / 146 \\
                 III.12 The Euler--Lagrange Equations / 147 \\
                 III.13 The Gamma Function / 148 \\
                 III.14 The Ginzburg--Landau Equation / 148 \\
                 III.15 Hooke's Law / 149 \\
                 III.16 The Korteweg--de Vries Equation / 150 \\
                 III.17 The Lambert $W$ Function / 151 \\
                 III.18 Laplace's Equation / 155 \\
                 III.19 The Logistic Equation / 156 \\
                 III.20 The Lorenz Equations / 158 \\
                 III.21 Mathieu Functions / 159 \\
                 III.22 Maxwell's Equations / 160 \\
                 III.23 The Navier--Stokes Equations / 162 \\
                 III.24 The Painlev{\'e} Equations / 163 \\
                 III.25 The Riccati Equation / 165 \\
                 III.26 Schr{\"o}dinger's Equation / 167 \\
                 III.27 The Shallow-Water Equations / 167 \\
                 III.28 The Sylvester and Lyapunov Equations / 168 \\
                 III.29 The Thin-Film Equation / 169 \\
                 III.30 The Tricomi Equation / 170 \\
                 III.31 The Wave Equation / 171 \\
                 Part IV: Areas of Applied Mathematics \\
                 IV.1 Complex Analysis / 173 \\
                 IV.2 Ordinary Differential Equations / 181 \\
                 IV.3 Partial Differential Equations / 190 \\
                 IV.4 Integral Equations / 200 \\
                 IV.5 Perturbation Theory and Asymptotics / 208 \\
                 IV.6 Calculus of Variations / 218 \\
                 IV.7 Special Functions / 227 \\
                 IV.8 Spectral Theory / 236 \\
                 IV.9 Approximation Theory / 248 \\
                 IV.10 Numerical Linear Algebra and Matrix Analysis /
                 263 \\
                 IV.11 Continuous Optimization (Nonlinear and Linear
                 Programming) / 281 \\
                 IV.12 Numerical Solution of Ordinary Differential
                 Equations / 293 \\
                 IV.13 Numerical Solution of Partial Differential
                 Equations / 306 \\
                 IV.14 Applications of Stochastic Analysis / 319 \\
                 IV.15 Inverse Problems / 327 \\
                 IV.16 Computational Science / 335 \\
                 IV.17 Data Mining and Analysis / 350 \\
                 IV.18 Network Analysis / 360 \\
                 IV.19 Classical Mechanics / 374 \\
                 IV.20 Dynamical Systems / 383 \\
                 IV.21 Bifurcation Theory / 393 \\
                 IV.22 Symmetry in Applied Mathematics / 402 \\
                 IV.23 Quantum Mechanics / 411 \\
                 IV.24 Random-Matrix Theory / 419 \\
                 IV.25 Kinetic Theory / 428 \\
                 IV.26 Continuum Mechanics / 446 \\
                 IV.27 Pattern Formation / 458 \\
                 IV.28 Fluid Dynamics / 467 \\
                 IV.29 Magnetohydrodynamics / 476 \\
                 IV.30 Earth System Dynamics / 485 \\
                 IV.31 Effective Medium Theories / 500 \\
                 IV.32 Mechanics of Solids / 505 \\
                 IV.33 Soft Matter / 516 \\
                 IV.34 Control Theory / 523 \\
                 IV.35 Signal Processing / 533 \\
                 IV.36 Information Theory / 545 \\
                 IV.37 Applied Combinatorics and Graph Theory / 552 \\
                 IV.38 Combinatorial Optimization / 564 \\
                 IV.39 Algebraic Geometry / 570 \\
                 IV.40 General Relativity and Cosmology / 579 \\
                 Part V: Modeling \\
                 V.1 The Mathematics of Adaptation (Or the Ten Avatars
                 of Vishnu) / 591 \\
                 V.2 Sport / 598 \\
                 V.3 Inerters / 604 \\
                 V.4 Mathematical Biomechanics / 609 \\
                 V.5 Mathematical Physiology / 616 \\
                 V.6 Cardiac Modeling / 623 \\
                 V.7 Chemical Reactions / 627 \\
                 V.8 Divergent Series: Taming the Tails / 634 \\
                 V.9 Financial Mathematics / 640 \\
                 V.10 Portfolio Theory / 648 \\
                 V.11 Bayesian Inference in Applied Mathematics / 658
                 \\
                 V.12 A Symmetric Framework with Many Applications / 661
                 \\
                 V.13 Granular Flows / 665 \\
                 V.14 Modern Optics / 673 \\
                 V.15 Numerical Relativity / 680 \\
                 V.16 The Spread of Infectious Diseases / 687 \\
                 V.17 The Mathematics of Sea Ice / 694 \\
                 V.18 Numerical Weather Prediction / 705 \\
                 V.19 Tsunami Modeling / 712 \\
                 V.20 Shock Waves / 720 \\
                 V.21 Turbulence / 724 \\
                 Part VI: Example Problems \\
                 VI.1 Cloaking / 733 \\
                 VI.2 Bubbles / 735 \\
                 VI.3 Foams / 737 \\
                 VI.4 Inverted Pendulums / 741 \\
                 VI.5 Insect Flight / 743 \\
                 VI.6 The Flight of a Golf Ball / 746 \\
                 VI.7 Automatic Differentiation / 749 \\
                 VI.8 Knotting and Linking of Macromolecules / 752 \\
                 VI.9 Ranking Web Pages / 755 \\
                 VI.10 Searching a Graph / 757 \\
                 VI.11 Evaluating Elementary Functions / 759 \\
                 VI.12 Random Number Generation / 761 \\
                 VI.13 Optimal Sensor Location in the Control of
                 Energy-Efficient Buildings / 763 \\
                 VI.14 Robotics / 767 \\
                 VI.15 Slipping, Sliding, Rattling, and Impact:
                 Nonsmooth Dynamics and Its Applications / 769 \\
                 VI.16 From the $N$-Body Problem to Astronomy and Dark
                 Matter / 771 \\
                 VI.17 The $N$-Body Problem and the Fast Multipole
                 Method / 775 \\
                 VI.18 The Traveling Salesman Problem / 778 \\
                 Part VII: Application Areas \\
                 VII.1 Aircraft Noise / 783 \\
                 VII.2 A Hybrid Symbolic--Numeric Approach to Geometry
                 Processing and Modeling / 787 \\
                 VII.3 Computer-Aided Proofs via Interval Analysis / 790
                 \\
                 VII.4 Applications of Max-Plus Algebra / 795 \\
                 VII.5 Evolving Social Networks, Attitudes, and Beliefs
                 --- and Counterterrorism / 800 \\
                 VII.6 Chip Design / 804 \\
                 VII.7 Color Spaces and Digital Imaging / 808 \\
                 VII.8 Mathematical Image Processing / 813 \\
                 VII.9 Medical Imaging / 816 \\
                 VII.10 Compressed Sensing / 823 \\
                 VII.11 Programming Languages: An Applied Mathematics
                 View / 828 \\
                 VII.12 High-Performance Computing / 839 \\
                 VII.13 Visualization / 843 \\
                 VII.14 Electronic Structure Calculations (Solid State
                 Physics) / 847 \\
                 VII.15 Flame Propagation / 852 \\
                 VII.16 Imaging the Earth Using Green's Theorem / 857
                 \\
                 VII.17 Radar Imaging / 860 \\
                 VII.18 Modeling a Pregnancy Testing Kit / 864 \\
                 VII.19 Airport Baggage Screening with X-Ray Tomography
                 / 866 \\
                 VII.20 Mathematical Economics / 868 \\
                 VII.21 Mathematical Neuroscience / 873 \\
                 VII.22 Systems Biology / 879 \\
                 VII.23 Communication Networks / 883 \\
                 VII.24 Text Mining / 887 \\
                 VII.25 Voting Systems / 891 \\
                 Part VIII: Final Perspectives \\
                 VIII.1 Mathematical Writing / 897 \\
                 VIII.2 How to Read and Understand a Paper / 903 \\
                 VIII.3 How to Write a General Interest Mathematics Book
                 / 906 \\
                 VIII.4 Workflow / 912 \\
                 VIII.5 Reproducible Research in the Mathematical
                 Sciences / 916 \\
                 VIII.6 Experimental Applied Mathematics / 925 \\
                 VIII.7 Teaching Applied Mathematics / 933 \\
                 VIII.8 Mediated Mathematics: Representations of
                 Mathematics in Popular Culture and Why These Matter /
                 943 \\
                 VIII.9 Mathematics and Policy / 953 \\
                 Index / 963",
}

@Proceedings{Muller:2015:ISC,
  editor =       "Jean-Michel Muller and Arnaud Tisserand and Julio
                 Villalba",
  booktitle =    "{2015 IEEE 22nd Symposium on Computer Arithmetic
                 (ARITH 2015) Lyon, France, 22--24 June 2015}",
  title =        "{2015 IEEE 22nd Symposium on Computer Arithmetic
                 (ARITH 2015) Lyon, France, 22--24 June 2015}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 176",
  year =         "2015",
  ISBN =         "1-4799-8665-8, 1-4799-8663-1",
  ISBN-13 =      "978-1-4799-8665-1, 978-1-4799-8663-7",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62 S95 2015",
  bibdate =      "Sat Aug 01 08:03:11 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  URL =          "http://ieeexplore.ieee.org/servlet/opac?punumber=7193754",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic units; correctness proofs;
                 cryptography; domain specific designs; error analysis;
                 exascale computing; floating point arithmetic;
                 floating-point error analysis; formal verification;
                 function approximation; modular arithmetic; theorem
                 proving; verification",
}

@Proceedings{Greuel:2016:MSI,
  editor =       "Gert-Martin Greuel",
  booktitle =    "{Mathematical Software --- ICMS 2016: 5th
                 International Conference, Berlin, Germany, July 11--14,
                 2016: proceedings}",
  title =        "{Mathematical Software --- ICMS 2016: 5th
                 International Conference, Berlin, Germany, July 11--14,
                 2016: proceedings}",
  volume =       "9725",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxiv + 532",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-42432-3",
  ISBN =         "3-319-42431-9 (print), 3-319-42432-7 (electronic)",
  ISBN-13 =      "978-3-319-42431-6 (print), 978-3-319-42432-3
                 (electronic)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  LCCN =         "QA76.9.M35",
  bibdate =      "Mon Feb 5 08:28:37 MST 2018",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
  series =       ser-LNCS # "\slash " # ser-LNAI,
  URL =          "http://zbmath.org/?q=an:1342.68017",
  abstract =     "This book constitutes the proceedings of the 5th
                 International Conference on Mathematical Software, ICMS
                 2015, held in Berlin, Germany, in July 2016. The 68
                 papers included in this volume were carefully reviewed
                 and selected from numerous submissions. The papers are
                 organized in topical sections named: univalent
                 foundations and proof assistants; software for
                 mathematical reasoning and applications; algebraic and
                 toric geometry; algebraic geometry in applications;
                 software of polynomial systems; software for
                 numerically solving polynomial systems; high-precision
                 arithmetic, effective analysis, and special functions;
                 mathematical optimization; interactive operation to
                 scientific artwork and mathematical reasoning;
                 information services for mathematics: software,
                 services, models, and data; semDML: towards a semantic
                 layer of a world digital mathematical library;
                 miscellanea.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Montuschi:2016:ISC,
  editor =       "Paolo Montuschi and Michael Schulte and Javier Hormigo
                 and Stuart Oberman and Nathalie Revol",
  booktitle =    "{2016 IEEE 23nd Symposium on Computer Arithmetic
                 (ARITH 2016), Santa Clara, California, USA, 10--13 July
                 2016}",
  title =        "{2016 IEEE 23nd Symposium on Computer Arithmetic
                 (ARITH 2016), Santa Clara, California, USA, 10--13 July
                 2016}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxi + 182",
  year =         "2016",
  ISBN =         "1-5090-1615-5",
  ISBN-13 =      "978-1-5090-1615-0",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62 S95 2016",
  bibdate =      "Fri Dec 16 15:16:45 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  URL =          "http://ieeexplore.ieee.org/servlet/opac?punumber=7562813",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic units; correctness proofs;
                 cryptography; domain specific designs; error analysis;
                 exascale computing; floating point arithmetic;
                 floating-point error analysis; formal verification;
                 function approximation; modular arithmetic; theorem
                 proving; verification",
}

@Proceedings{Burgess:2017:ISC,
  editor =       "Neil Burgess and Javier Bruguera and Florent de
                 Dinechin",
  booktitle =    "{24th IEEE Symposium on Computer Arithmetic (ARITH
                 24), London, UK, 24--26 July 2017}",
  title =        "{2017 IEEE 24th Symposium on Computer Arithmetic
                 (ARITH 24), London, UK, 24--26 July 2017}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 198",
  year =         "2017",
  ISBN =         "1-5386-1966-0 (print), 1-5386-1965-2, 1-5386-1964-4",
  ISBN-13 =      "978-1-5386-1966-7 (print), 978-1-5386-1965-0,
                 978-1-5386-1964-3",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62 S95 2017",
  bibdate =      "Fri Nov 17 10:14:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib",
  URL =          "http://ieeexplore.ieee.org/servlet/opac?punumber=8019911",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic units; correctness proofs;
                 cryptography; domain specific designs; error analysis;
                 exascale computing; floating point arithmetic;
                 floating-point error analysis; formal verification;
                 function approximation; modular arithmetic; theorem
                 proving; verification",
}

@Proceedings{Tenca:2018:PIS,
  editor =       "Alexandre Tenca and Naofumi Takagi",
  booktitle =    "Proceedings of the {25th International Symposium on
                 Computer Arithmetic, 25--27 June 2018 Amherst, MA,
                 USA}",
  title =        "Proceedings of the {25th International Symposium on
                 Computer Arithmetic, 25--27 June 2018 Amherst, MA,
                 USA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "17 + 152",
  month =        jun,
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464697",
  ISBN =         "1-5386-2612-8 (USB), 1-5386-2665-9",
  ISBN-13 =      "978-1-5386-2612-2 (USB), 978-1-5386-2613-9,
                 978-1-5386-2665-8",
  ISSN =         "2576-2265",
  LCCN =         "QA76.9.C62",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number CFP18121-USB.",
  abstract =     "Presents the title page of the proceedings record.",
  acknowledgement = ack-nhfb,
  subject =      "ARITH-25; Computer arithmetic; Congresses; Computer
                 programming; Floating-point arithmetic; Computer
                 arithmetic and logic units",
}

@Proceedings{Takagi:2019:ISC,
  editor =       "Naofumi Takagi and Sylvie Boldo and Martin
                 Langhammer",
  booktitle =    "{2019 IEEE 26th Symposium on Computer Arithmetic
                 ARITH-26 (2019), Kyoto, Japan, 10--12 June 2019}",
  title =        "{2019 IEEE 26th Symposium on Computer Arithmetic
                 ARITH-26 (2019), Kyoto, Japan, 10--12 June 2019}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "15 + 220",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00001",
  ISBN =         "1-72813-366-1",
  ISBN-13 =      "978-1-72813-366-9",
  ISSN =         "1063-6889",
  ISSN-L =       "1063-6889",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents the title page of the proceedings record.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26",
}

@Proceedings{Bigatti:2020:MSI,
  editor =       "Anna Maria Bigatti and Jacques Carette and James H.
                 Davenport and Michael Joswig and Timo de Wolff",
  booktitle =    "Mathematical Software --- {ICMS 2020: 7th
                 International Conference, Braunschweig, Germany, July
                 13--16, 2020, Proceedings}",
  title =        "Mathematical Software --- {ICMS 2020: 7th
                 International Conference, Braunschweig, Germany, July
                 13--16, 2020, Proceedings}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxiii + 494",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-52200-1",
  bibdate =      "Sat Sep 23 06:50:01 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/julia.bib;
                 https://www.math.utah.edu/pub/tex/bib/macaulay2.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook3.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Front Matter / / i--xxiii \\
                 Gr{\"o}bner Bases in Theory and Practice \\
                 Front Matter / / 1--1 A Design and an Implementation of
                 an Inverse Kinematics Computation in Robotics Using
                 Gr{\"o}bner Bases / Noriyuki Horigome, Akira Terui,
                 Masahiko Mikawa / 3--13 \\
                 Real Algebraic Geometry \\
                 Front Matter / / 15--15 \\
                 Curtains in CAD: Why Are They a Problem and How Do We
                 Fix Them? / Akshar Nair, James Davenport, Gregory
                 Sankaran / 17--26 \\
                 Chordality Preserving Incremental Triangular
                 Decomposition and Its Implementation / Changbo Chen /
                 27--36 \\
                 Algebraic Geometry via Numerical Computation \\
                 Front Matter / / 37--37 \\
                 $\mathbb{Q}(\sqrt{-3})$-Integral Points on a Mordell
                 Curve / Francesca Bianchi / 39--50 \\
                 A Numerical Approach for Computing Euler
                 Characteristics of Affine Varieties / Xiaxin Li, Jose
                 Israel Rodriguez, Botong Wang / 51--60 \\
                 Evaluating and Differentiating a Polynomial Using a
                 Pseudo-witness Set / Jonathan D. Hauenstein, Margaret
                 H. Regan / 61--69 \\
                 Computational Algebraic Analysis \\
                 Front Matter / / 71--71 \\
                 Algorithms for Pfaffian Systems and Cohomology
                 Intersection Numbers of Hypergeometric Integrals /
                 Saiei-Jaeyeong Matsubara-Heo, Nobuki Takayama / 73--84
                 \\
                 Software for Number Theory and Arithmetic Geometry \\
                 Front Matter / / 85--85 \\
                 Computations with Algebraic Surfaces / Andreas-Stephan
                 Elsenhans, J{\"o}rg Jahnel / 87--93 \\
                 Evaluating Fractional Derivatives of the Riemann Zeta
                 Function / Ricky E. Farr, Sebastian Pauli, Filip Saidak
                 / 94--101 \\
                 Groups and Group Actions \\
                 Front Matter / / 103--103 \\
                 Towards Efficient Normalizers of Primitive Groups /
                 Sergio Siccha / 105--114 \\
                 Homomorphic Encryption and Some Black Box Attacks /
                 Alexandre Borovik, {\c{S}}{\"u}kr{\"u}
                 Yal{\c{c}}{\i}nkaya / 115--124 \\
                 Nilpotent Quotients of Associative
                 $\mathbb{Z}$-Algebras and Augmentation Quotients of
                 Baumslag--Solitar Groups / Tobias Moede / 125--130 \\
                 The GAP Package LiePRing / Bettina Eick, Michael
                 Vaughan-Lee / 131--140 \\
                 The Classification Problem in Geometry \\
                 Front Matter / / 141--141 \\
                 Classifying Simplicial Dissections of Convex Polyhedra
                 with Symmetry / Anton Betten, Tarun Mukthineni /
                 143--152 \\
                 Classification Results for Hyperovals of Generalized
                 Quadrangles / Bart De Bruyn / 153--161 \\
                 Isomorphism and Invariants of Parallelisms of
                 Projective Spaces / Svetlana Topalova, Stela Zhelezova
                 / 162--172 \\
                 Classification of Linear Codes by Extending Their
                 Residuals / Stefka Bouyuklieva, Iliya Bouyukliev /
                 173--180 \\
                 The Program Generation in the Software Package
                 QextNewEdition / Iliya Bouyukliev / 181--189 \\
                 Polyhedral Methods in Geometry and Optimization \\
                 Front Matter / / 191--191 \\
                 Algebraic Polytopes in Normaliz / Winfried Bruns /
                 193--201 \\
                 Real Tropical Hyperfaces by Patchworking in polymake /
                 Michael Joswig, Paul Vater / 202--211 \\
                 Practical Volume Estimation of Zonotopes by a New
                 Annealing Schedule for Cooling Convex Bodies /
                 Apostolos Chalkis, Ioannis Z. Emiris, Vissarion
                 Fisikopoulos / 212--221 \\
                 Slack Ideals in Macaulay2 / Antonio Macchia, Amy Wiebe
                 / 222--231 \\
                 Hyperplane Arrangements in polymake / Lars Kastner,
                 Marta Panizzut / 232--240 \\
                 A Convex Programming Approach to Solve Posynomial
                 Systems / Marianne Akian, Xavier Allamigeon, Marin
                 Boyet, St{\'e}phane Gaubert / 241--250 \\
                 Univalent Mathematics: Theory and Implementation \\
                 Front Matter / / 251--251 \\
                 Equality Checking for General Type Theories in
                 Andromeda 2 / Andrej Bauer, Philipp G. Haselwarter,
                 Anja Petkovi / 253--259 \\
                 Artificial Intelligence and Mathematical Software \\
                 Front Matter / / 261--261 \\
                 GeoLogic --- Graphical Interactive Theorem Prover for
                 Euclidean Geometry / Miroslav Ol{\v{s}}{\'a}k /
                 263--271 \\
                 A Formalization of Properties of Continuous Functions
                 on Closed Intervals / Yaoshun Fu, Wensheng Yu /
                 272--280 \\
                 Variable Ordering Selection for Cylindrical Algebraic
                 Decomposition with Artificial Neural Networks / Changbo
                 Chen, Zhangpeng Zhu, Haoyu Chi / 281--291 \\
                 Applying Machine Learning to Heuristics for Real
                 Polynomial Constraint Solving / Christopher W. Brown,
                 Glenn Christopher Daves / 292--301 \\
                 A Machine Learning Based Software Pipeline to Pick the
                 Variable Ordering for Algorithms with Polynomial Inputs
                 / Dorian Florescu, Matthew England / 302--311 \\
                 Databases in Mathematics \\
                 Front Matter / / 313--313 \\
                 FunGrim: A Symbolic Library for Special Functions /
                 Fredrik Johansson / 315--323 \\
                 Accelerating Innovation Speed in Mathematics by Trading
                 Mathematical Research Data \\
                 Front Matter / / 325--325 \\
                 Operational Research Literature as a Use Case for the
                 Open Research Knowledge Graph / Mila Runnwerth, Markus
                 Stocker, S{\"o}ren Auer / 327--334 \\
                 Making Presentation Math Computable: Proposing a
                 Context Sensitive Approach for Translating {\LaTeX} to
                 Computer Algebra Systems / Andr{\'e} Greiner-Petter,
                 Moritz Schubotz, Akiko Aizawa, Bela Gipp / 335--341 \\
                 Employing C++ Templates in the Design of a Computer
                 Algebra Library / Alexander Brandt, Robert H. C. Moir,
                 Marc Moreno Maza / 342--352 \\
                 Mathematical World Knowledge Contained in the
                 Multilingual Wikipedia Project / Dennis Tobias Halbach
                 / 353--361 \\
                 Archiving and Referencing Source Code with Software
                 Heritage / Roberto Di Cosmo / 362--373 \\
                 The Jupyter Environment for Computational Mathematics
                 \\
                 Front Matter / / 375--375 \\
                 Polymake.jl: A New Interface to polymake / Marek
                 Kaluba, Benjamin Lorenz, Sascha Timme / 377--385 \\
                 Web Based Notebooks for Teaching, an Experience at
                 Universidad de Zaragoza / Miguel Angel Marco Buzunariz
                 / 386--392 \\
                 Phase Portraits of Bi-dimensional Zeta Values / Olivier
                 Bouillot / 393--405 \\
                 Prototyping Controlled Mathematical Languages in
                 Jupyter Notebooks / Jan Frederik Schaefer, Kai Amann,
                 Michael Kohlhase / 406--415 \\
                 General Session \\
                 Front Matter / / 417--417 \\
                 Method to Create Multiple Choice Exercises for Computer
                 Algebra System / Tatsuyoshi Hamada, Yoshiyuki Nakagawa,
                 Makoto Tamura / 419--425 \\
                 A Flow-Based Programming Environment for Geometrical
                 Construction / Kento Nakamura, Kazushi Ahara / 426--431
                 \\
                 MORLAB --- A Model Order Reduction Framework in MATLAB
                 and Octave / Peter Benner, Steffen W. R. Werner /
                 432--441 \\
                 FlexRiLoG --- A SageMath Package for Motions of Graphs
                 / Georg Grasegger, Jan Legersk{\'y} / 442--450 \\
                 Markov Transition Matrix Analysis of Mathematical
                 Expression Input Models / Francis Quinby, Seyeon Kim,
                 Sohee Kang, Marco Pollanen, Michael G. Reynolds, Wesley
                 S. Burr / 451--461 \\
                 Certifying Irreducibility in $\mathbb{Z}[ ]$ / John
                 Abbott / 462--472 \\
                 A Content Dictionary for In-Object Comments / Lars
                 Hellstr{\"o}m / 473--481 \\
                 Implementing the Tangent Graeffe Root Finding Method /
                 Joris van der Hoeven, Michael Monagan / 482--492 \\
                 Back Matter / / 493--494",
}

@Proceedings{Cornea:2020:ISC,
  editor =       "Marius Cornea and Weiqiang Liu and Arnaud Tisserand",
  booktitle =    "{2020 27th IEEE Symposium on Computer Arithmetic:
                 ARITH 2020: proceedings: Portland, Oregon, USA, 7--10
                 June 2020}",
  title =        "{2020 27th IEEE Symposium on Computer Arithmetic:
                 ARITH 2020: proceedings: Portland, Oregon, USA, 7--10
                 June 2020}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020",
  ISBN =         "1-72817-120-2, 1-72817-121-0",
  ISBN-13 =      "978-1-72817-120-3, 978-1-72817-121-0",
  LCCN =         "????",
  bibdate =      "Wed Jul 7 06:23:45 MDT 2021",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=9146973",
  acknowledgement = ack-nhfb,
}

@Book{Ismail:2020:ESF,
  editor =       "Mourad H. Ismail and Walter Van Assche",
  booktitle =    "Encyclopedia of Special Functions: the {Askey--Bateman
                 Project}. Volume 1, Univariate Orthogonal Polynomials",
  title =        "Encyclopedia of Special Functions: the {Askey--Bateman
                 Project}. Volume 1, Univariate Orthogonal Polynomials",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xiv + 388",
  year =         "2020",
  DOI =          "https://doi.org/10.1017/9780511979156",
  ISBN =         "0-511-97915-0 (e-book), 0-521-19742-2 (hardcover),
                 1-108-76433-9 (e-book)",
  ISBN-13 =      "978-0-511-97915-6 (e-book), 978-0-521-19742-7
                 (hardcover), 978-1-108-76433-9 (e-book)",
  LCCN =         "QA351 .E63 2020",
  bibdate =      "Fri Nov 10 17:02:40 MST 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This is the first of three volumes that form the
                 Encyclopedia of Special Functions, an extensive update
                 of the Bateman Manuscript Project. Volume 1 contains
                 most of the material on orthogonal polynomials, from
                 the classical orthogonal polynomials of Hermite,
                 Laguerre and Jacobi to the Askey--Wilson polynomials,
                 which are the most general basic hypergeometric
                 orthogonal polynomials. Separate chapters cover
                 orthogonal polynomials on the unit circle, zeros of
                 orthogonal polynomials and matrix orthogonal
                 polynomials, with detailed results about matrix-valued
                 Jacobi polynomials. A chapter on moment problems
                 provides many examples of indeterminate moment
                 problems. A thorough bibliography rounds off what will
                 be an essential reference.",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Encyclopedias; Fonctions
                 sp{\'e}ciales; Encyclop{\'e}dies; Functions,
                 Special",
  tableofcontents = "Frontmatter / i--iv \\
                 Contents / v--viii \\
                 Contributors / ix--x \\
                 Preface / xi--xiv \\
                 1: Preliminaries / Mourad E. H. Ismail / 1--15 \\
                 2: General Orthogonal Polynomials / Mourad E. H. Ismail
                 / 16--50 \\
                 3: Jacobi and Related Polynomials / Mourad E. H. Ismail
                 / 51--99 \\
                 4: Recursively Defined Polynomials / Mourad E. H.
                 Ismail / 100--118 \\
                 5: Wilson and Related Polynomials / Mourad E. H. Ismail
                 / 119--128 \\
                 6: Discrete Orthogonal Polynomials / Mourad E. H.
                 Ismail / 129--156 \\
                 7: Some $q$-Orthogonal Polynomials / Mourad E. H.
                 Ismail / 157--177 \\
                 8: The Askey--Wilson Family of Polynomials / Mourad E.
                 H. Ismail / 178--198 \\
                 9: Orthogonal Polynomials on the Unit Circle / Leonid
                 Golinskii / 199--241 \\
                 10: Zeros of Orthogonal Polynomials / Andrea Laforgia
                 and Martin E. Muldoon / 242--268 \\
                 11: The Moment Problem / Christian Berg and Jacob S.
                 Christiansen / 269--306 \\
                 12: Matrix--Valued Orthogonal Polynomials and
                 Differential Equations / Antonio J. Dur{\'a}n and F.
                 Alberto Gr{\"u}nbaum / 307--333 \\
                 13: Some Families of Matrix--Valued Jacobi Orthogonal
                 Polynomials / F. Alberto Gr{\"u}nbaum, I. Pacharoni and
                 J. A. Tirao / 334--356 \\
                 References / 357--384 \\
                 Index / 385--388",
}

@Book{Koornwinder:2020:ESF,
  editor =       "T. H. Koornwinder and Jasper V. Stokman",
  booktitle =    "Encyclopedia of Special Functions: the {Askey--Bateman
                 Project}. Volume 2. Multivariable Special Functions",
  title =        "Encyclopedia of Special Functions: the {Askey--Bateman
                 Project}. Volume 2. Multivariable Special Functions",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xii + 427",
  year =         "2020",
  DOI =          "https://doi.org/10.1017/9780511777165",
  ISBN =         "0-511-77716-7 (e-book), 1-107-00373-3 (hardcover)",
  ISBN-13 =      "978-0-511-77716-5 (e-book), 978-1-107-00373-6
                 (hardcover)",
  LCCN =         "QA351 .E63 2021",
  bibdate =      "Fri Nov 10 17:39:45 MST 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Frontmatter / i--iv \\
                 Contents / v--viii \\
                 List of Contributors / ix--x \\
                 Preface / xi--xii \\
                 1: General Overview of Multivariable Special Functions
                 / T. H. Koornwinder, J. V. Stokman / 1--18 \\
                 2: Orthogonal Polynomials of Several Variables / Yuan
                 Xu / 19--78 \\
                 3: Appell and Lauricella Hypergeometric Functions / K.
                 Matsumoto / 79--100 \\
                 4: A-Hypergeometric Functions / N. Takayama / 101--121
                 \\
                 5: Hypergeometric and Basic Hypergeometric Series and
                 Integrals Associated with Root Systems / M. J.
                 Schlosser / 122--158 \\
                 6: Elliptic Hypergeometric Functions Associated with
                 Root Systems / H. Rosengren, S. O. Warnaar / 159--186
                 \\
                 7: Dunkl Operators and Related Special Functions / C.
                 F. Dunkl / 187--216 \\
                 8: Jacobi Polynomials and Hypergeometric Functions
                 Associated with Root Systems / G. J. Heckman, E. M.
                 Opdam / 217--257 \\
                 9: Macdonald--Koornwinder Polynomials / J. V. Stokman /
                 258--313 \\
                 10: Combinatorial Aspects of Macdonald and Related
                 Polynomials / J. Haglund / 314--367 \\
                 11: Knizhnik--Zamolodchikov-Type Equations, Selberg
                 Integrals and Related Special Functions / V. Tarasov,
                 A. Varchenko / 368--401 \\
                 12: $9 j$--Coefficients and Higher / J. Van der Jeugt /
                 402--419 \\
                 Index / 420--428",
}

@Proceedings{IEEE:2021:ISC,
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE 28th Symposium on Computer Arithmetic:
                 ARITH 2021: virtual conference, 14--16 June 2021:
                 proceedings}",
  title =        "{2021 IEEE 28th Symposium on Computer Arithmetic:
                 ARITH 2021: virtual conference, 14--16 June 2021:
                 proceedings}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021",
  ISBN =         "1-66542-293-9 (print), 1-66544-648-X (e-book)",
  ISBN-13 =      "978-1-66542-293-2 (print), 978-1-66544-648-8
                 (e-book)",
  LCCN =         "????",
  bibdate =      "Thu Sep 21 10:36:52 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-28",
  meetingname =  "IEEE International Symposium on Computer Arithmetic
                 28. 2021",
  remark =       "The 28th IEEE Symposium on Computer Arithmetic ---
                 ARITH 2021 --- originally scheduled in Turin, Italy, is
                 held in June 2021 as a virtual conference due to the
                 uncertainty of the world health and travel situation.",
}

@Proceedings{IEEE:2022:ISC,
  editor =       "{IEEE}",
  booktitle =    "{2022 IEEE 29th Symposium on Computer Arithmetic:
                 ARITH 2022: virtual conference, 12--14 September 2022:
                 proceedings}",
  title =        "{2022 IEEE 29th Symposium on Computer Arithmetic:
                 ARITH 2022: virtual conference, 12--14 September 2022:
                 proceedings}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022",
  ISBN =         "1-66547-827-6, 1-66547-828-4",
  ISBN-13 =      "978-1-66547-827-4, 978-1-66547-828-1",
  LCCN =         "????",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29",
  meetingname =  "IEEE Symposium on Computer Arithmetic 29. 2022",
}